Quizbank/University Physics Semester 2/T2
University Physics Semester 2/T2 ID153341821922
For more information visit Quizbank/University Physics Semester 2
Exams: A0 A1 A2 B0 B1 B2 C0 C1 C2 D0 D1 D2 E0 E1 E2 F0 F1 F2 G0 G1 G2 H0 H1 H2 I0 I1 I2 J0 J1 J2 K0 K1 K2 L0 L1 L2 M0 M1 M2 N0 N1 N2 O0 O1 O2 P0 P1 P2 Q0 Q1 Q2 R0 R1 R2 S0 S1 S2 T0 T1 T2 U0 U1 U2 V0 V1 V2 W0 W1 W2 X0 X1 X2 Y0 Y1 Y2 Z0 Z1 Z2
Answers: A0 A1 A2 B0 B1 B2 C0 C1 C2 D0 D1 D2 E0 E1 E2 F0 F1 F2 G0 G1 G2 H0 H1 H2 I0 I1 I2 J0 J1 J2 K0 K1 K2 L0 L1 L2 M0 M1 M2 N0 N1 N2 O0 O1 O2 P0 P1 P2 Q0 Q1 Q2 R0 R1 R2 S0 S1 S2 T0 T1 T2 U0 U1 U2 V0 V1 V2 W0 W1 W2 X0 X1 X2 Y0 Y1 Y2 Z0 Z1 Z2
78 Tests = 3 versions x 26 variations: Each of the 26 variations (A, B, ...) represents a different random selection of questions taken from the study guide.The 3 versions (0,1,..) all have the same questions but in different order and with different numerical inputs. Unless all students take version "0" it is best to reserve it for the instructor because the questions are grouped according to the order in which they appear on the study guide.
Links: Quizbank/Instructions Study guide file:QB-University Physics Semester 2-T2.pdf
Contact me at User talk:Guy vandegrift if you need any help.
T2 A0[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
- a) 8.545E+01 V·m
- b) 9.400E+01 V·m
- c) 1.034E+02 V·m
- d) 1.137E+02 V·m
- e) 1.251E+02 V·m
- a) 4.777E+01 N·m2/C
- b) 5.254E+01 N·m2/C
- c) 5.780E+01 N·m2/C
- d) 6.358E+01 N·m2/C
- e) 6.993E+01 N·m2/C
- a) 4.125E+01 N·m2/C
- b) 4.537E+01 N·m2/C
- c) 4.991E+01 N·m2/C
- d) 5.490E+01 N·m2/C
- e) 6.039E+01 N·m2/C
- a) 5.606E+01 N·m2/C
- b) 6.167E+01 N·m2/C
- c) 6.784E+01 N·m2/C
- d) 7.462E+01 N·m2/C
- e) 8.208E+01 N·m2/C
5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 6.69E+03
- b) 8.10E+03
- c) 9.81E+03
- d) 1.19E+04
- e) 1.44E+04
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 4.593E+03
- b) 5.564E+03
- c) 6.741E+03
- d) 8.167E+03
- e) 9.894E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
8) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
10) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
T2 A1[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
2) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
- a) 6.364E+01 N·m2/C
- b) 7.000E+01 N·m2/C
- c) 7.700E+01 N·m2/C
- d) 8.470E+01 N·m2/C
- e) 9.317E+01 N·m2/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 5.40E+02
- b) 6.55E+02
- c) 7.93E+02
- d) 9.61E+02
- e) 1.16E+03
6) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
- a) 2.610E+03 V·m
- b) 2.871E+03 V·m
- c) 3.158E+03 V·m
- d) 3.474E+03 V·m
- e) 3.822E+03 V·m
7) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 4.593E+03
- b) 5.564E+03
- c) 6.741E+03
- d) 8.167E+03
- e) 9.894E+03
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
- a) 5.606E+01 N·m2/C
- b) 6.167E+01 N·m2/C
- c) 6.784E+01 N·m2/C
- d) 7.462E+01 N·m2/C
- e) 8.208E+01 N·m2/C
- a) 5.439E+01 N·m2/C
- b) 5.983E+01 N·m2/C
- c) 6.581E+01 N·m2/C
- d) 7.239E+01 N·m2/C
- e) 7.963E+01 N·m2/C
T2 A2[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
2) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 6.201E+02
- b) 7.513E+02
- c) 9.102E+02
- d) 1.103E+03
- e) 1.336E+03
- a) 3.924E+01 N·m2/C
- b) 4.316E+01 N·m2/C
- c) 4.748E+01 N·m2/C
- d) 5.222E+01 N·m2/C
- e) 5.745E+01 N·m2/C
4) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 4.69E+03
- b) 5.69E+03
- c) 6.89E+03
- d) 8.35E+03
- e) 1.01E+04
5) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
- a) 1.969E+02 V·m
- b) 2.166E+02 V·m
- c) 2.383E+02 V·m
- d) 2.621E+02 V·m
- e) 2.883E+02 V·m
8) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
- a) 2.012E+01 N·m2/C
- b) 2.213E+01 N·m2/C
- c) 2.435E+01 N·m2/C
- d) 2.678E+01 N·m2/C
- e) 2.946E+01 N·m2/C
- a) 6.614E+01 N·m2/C
- b) 7.275E+01 N·m2/C
- c) 8.003E+01 N·m2/C
- d) 8.803E+01 N·m2/C
- e) 9.683E+01 N·m2/C
T2 B0[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=6), and (x=7, y=6), where x and y are measured in meters. The electric field is,
- a) 3.337E+03 V·m
- b) 3.670E+03 V·m
- c) 4.037E+03 V·m
- d) 4.441E+03 V·m
- e) 4.885E+03 V·m
- a) 7.876E+01 N·m2/C
- b) 8.664E+01 N·m2/C
- c) 9.531E+01 N·m2/C
- d) 1.048E+02 N·m2/C
- e) 1.153E+02 N·m2/C
- a) 3.662E+01 N·m2/C
- b) 4.028E+01 N·m2/C
- c) 4.430E+01 N·m2/C
- d) 4.873E+01 N·m2/C
- e) 5.361E+01 N·m2/C
4) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?
- a) 1.383E+02 N/C
- b) 1.522E+02 N/C
- c) 1.674E+02 N/C
- d) 1.841E+02 N/C
- e) 2.025E+02 N/C
5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 9.41E+03
- b) 1.14E+04
- c) 1.38E+04
- d) 1.67E+04
- e) 2.03E+04
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 4.489E+02
- b) 5.438E+02
- c) 6.589E+02
- d) 7.983E+02
- e) 9.671E+02
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
9) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 B1[edit | edit source]
1) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 8.528E+02
- b) 1.033E+03
- c) 1.252E+03
- d) 1.516E+03
- e) 1.837E+03
2) A non-conducting sphere of radius R=2.2 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=3 nC·m-1.6. What is the magnitude of the electric field at a distance of 0.86 m from the center?
- a) 4.874E+01 N/C
- b) 5.362E+01 N/C
- c) 5.898E+01 N/C
- d) 6.488E+01 N/C
- e) 7.137E+01 N/C
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
- a) 6.898E+01 N·m2/C
- b) 7.588E+01 N·m2/C
- c) 8.347E+01 N·m2/C
- d) 9.181E+01 N·m2/C
- e) 1.010E+02 N·m2/C
5) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
- a) 3.429E+03 V·m
- b) 3.771E+03 V·m
- c) 4.149E+03 V·m
- d) 4.564E+03 V·m
- e) 5.020E+03 V·m
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
- a) 8.921E+01 N·m2/C
- b) 9.813E+01 N·m2/C
- c) 1.079E+02 N·m2/C
- d) 1.187E+02 N·m2/C
- e) 1.306E+02 N·m2/C
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
10) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 4.63E+03
- b) 5.61E+03
- c) 6.79E+03
- d) 8.23E+03
- e) 9.97E+03
T2 B2[edit | edit source]
- a) 3.712E+01 N·m2/C
- b) 4.083E+01 N·m2/C
- c) 4.491E+01 N·m2/C
- d) 4.940E+01 N·m2/C
- e) 5.434E+01 N·m2/C
2) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 9.41E+02
- b) 1.14E+03
- c) 1.38E+03
- d) 1.67E+03
- e) 2.03E+03
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
- a) 2.210E+04 V·m
- b) 2.431E+04 V·m
- c) 2.674E+04 V·m
- d) 2.941E+04 V·m
- e) 3.235E+04 V·m
4) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 6.731E+02
- b) 8.154E+02
- c) 9.879E+02
- d) 1.197E+03
- e) 1.450E+03
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
- a) 1.737E+01 N·m2/C
- b) 1.910E+01 N·m2/C
- c) 2.101E+01 N·m2/C
- d) 2.311E+01 N·m2/C
- e) 2.543E+01 N·m2/C
8) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?
- a) 2.039E+01 N/C
- b) 2.243E+01 N/C
- c) 2.467E+01 N/C
- d) 2.714E+01 N/C
- e) 2.985E+01 N/C
9) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 C0[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
- a) 2.067E+03 V·m
- b) 2.274E+03 V·m
- c) 2.501E+03 V·m
- d) 2.752E+03 V·m
- e) 3.027E+03 V·m
- a) 9.823E+00 N·m2/C
- b) 1.080E+01 N·m2/C
- c) 1.189E+01 N·m2/C
- d) 1.307E+01 N·m2/C
- e) 1.438E+01 N·m2/C
- a) 6.614E+01 N·m2/C
- b) 7.275E+01 N·m2/C
- c) 8.003E+01 N·m2/C
- d) 8.803E+01 N·m2/C
- e) 9.683E+01 N·m2/C
4) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?
- a) 3.821E+02 N/C
- b) 4.203E+02 N/C
- c) 4.624E+02 N/C
- d) 5.086E+02 N/C
- e) 5.594E+02 N/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.29E+03
- b) 1.56E+03
- c) 1.89E+03
- d) 2.29E+03
- e) 2.77E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 5.043E+02
- b) 6.109E+02
- c) 7.402E+02
- d) 8.967E+02
- e) 1.086E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
9) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
10) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 C1[edit | edit source]
- a) 3.662E+01 N·m2/C
- b) 4.028E+01 N·m2/C
- c) 4.430E+01 N·m2/C
- d) 4.873E+01 N·m2/C
- e) 5.361E+01 N·m2/C
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
3) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?
- a) 2.274E+02 N/C
- b) 2.501E+02 N/C
- c) 2.751E+02 N/C
- d) 3.026E+02 N/C
- e) 3.329E+02 N/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.59E+03
- b) 1.93E+03
- c) 2.34E+03
- d) 2.83E+03
- e) 3.43E+03
6) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- a) 4.286E+03 V·m
- b) 4.714E+03 V·m
- c) 5.186E+03 V·m
- d) 5.704E+03 V·m
- e) 6.275E+03 V·m
7) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 4.593E+03
- b) 5.564E+03
- c) 6.741E+03
- d) 8.167E+03
- e) 9.894E+03
8) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
- a) 3.074E+01 N·m2/C
- b) 3.382E+01 N·m2/C
- c) 3.720E+01 N·m2/C
- d) 4.092E+01 N·m2/C
- e) 4.501E+01 N·m2/C
10) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
T2 C2[edit | edit source]
- a) 3.662E+01 N·m2/C
- b) 4.028E+01 N·m2/C
- c) 4.430E+01 N·m2/C
- d) 4.873E+01 N·m2/C
- e) 5.361E+01 N·m2/C
2) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
4) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
- a) 5.978E+01 N·m2/C
- b) 6.576E+01 N·m2/C
- c) 7.233E+01 N·m2/C
- d) 7.957E+01 N·m2/C
- e) 8.752E+01 N·m2/C
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.09E+03
- b) 1.32E+03
- c) 1.60E+03
- d) 1.94E+03
- e) 2.35E+03
7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
- a) 8.545E+01 V·m
- b) 9.400E+01 V·m
- c) 1.034E+02 V·m
- d) 1.137E+02 V·m
- e) 1.251E+02 V·m
8) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?
- a) 2.274E+02 N/C
- b) 2.501E+02 N/C
- c) 2.751E+02 N/C
- d) 3.026E+02 N/C
- e) 3.329E+02 N/C
9) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 5.043E+02
- b) 6.109E+02
- c) 7.402E+02
- d) 8.967E+02
- e) 1.086E+03
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 D0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?
- a) 3.251E+01 N/C
- b) 3.577E+01 N/C
- c) 3.934E+01 N/C
- d) 4.328E+01 N/C
- e) 4.760E+01 N/C
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- a) 7.054E+03 V·m
- b) 7.759E+03 V·m
- c) 8.535E+03 V·m
- d) 9.388E+03 V·m
- e) 1.033E+04 V·m
- a) 2.756E+01 N·m2/C
- b) 3.032E+01 N·m2/C
- c) 3.335E+01 N·m2/C
- d) 3.668E+01 N·m2/C
- e) 4.035E+01 N·m2/C
- a) 7.793E+01 N·m2/C
- b) 8.572E+01 N·m2/C
- c) 9.429E+01 N·m2/C
- d) 1.037E+02 N·m2/C
- e) 1.141E+02 N·m2/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 4.489E+02
- b) 5.438E+02
- c) 6.589E+02
- d) 7.983E+02
- e) 9.671E+02
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 9.205E+02
- b) 1.115E+03
- c) 1.351E+03
- d) 1.637E+03
- e) 1.983E+03
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
10) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 D1[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
2) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
3) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 5.610E+02
- b) 6.796E+02
- c) 8.234E+02
- d) 9.975E+02
- e) 1.209E+03
- a) 5.408E+01 N·m2/C
- b) 5.949E+01 N·m2/C
- c) 6.544E+01 N·m2/C
- d) 7.198E+01 N·m2/C
- e) 7.918E+01 N·m2/C
5) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 1.704E+03
- b) 2.064E+03
- c) 2.501E+03
- d) 3.030E+03
- e) 3.671E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
- a) 2.186E+01 N·m2/C
- b) 2.404E+01 N·m2/C
- c) 2.645E+01 N·m2/C
- d) 2.909E+01 N·m2/C
- e) 3.200E+01 N·m2/C
9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?
- a) 2.837E+01 N/C
- b) 3.121E+01 N/C
- c) 3.433E+01 N/C
- d) 3.776E+01 N/C
- e) 4.154E+01 N/C
10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- a) 1.997E+03 V·m
- b) 2.197E+03 V·m
- c) 2.417E+03 V·m
- d) 2.659E+03 V·m
- e) 2.924E+03 V·m
T2 D2[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
2) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
3) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 8.528E+02
- b) 1.033E+03
- c) 1.252E+03
- d) 1.516E+03
- e) 1.837E+03
4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.6 m from the center of the shells?
- a) 9.642E+00 N/C
- b) 1.061E+01 N/C
- c) 1.167E+01 N/C
- d) 1.283E+01 N/C
- e) 1.412E+01 N/C
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 4.021E+02
- b) 4.872E+02
- c) 5.902E+02
- d) 7.151E+02
- e) 8.663E+02
- a) 8.921E+01 N·m2/C
- b) 9.813E+01 N·m2/C
- c) 1.079E+02 N·m2/C
- d) 1.187E+02 N·m2/C
- e) 1.306E+02 N·m2/C
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
- a) 3.924E+01 N·m2/C
- b) 4.316E+01 N·m2/C
- c) 4.748E+01 N·m2/C
- d) 5.222E+01 N·m2/C
- e) 5.745E+01 N·m2/C
10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
- a) 2.694E+03 V·m
- b) 2.963E+03 V·m
- c) 3.259E+03 V·m
- d) 3.585E+03 V·m
- e) 3.944E+03 V·m
T2 E0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.4 m from the center of the shells?
- a) 8.580E+00 N/C
- b) 9.438E+00 N/C
- c) 1.038E+01 N/C
- d) 1.142E+01 N/C
- e) 1.256E+01 N/C
- a) 7.876E+01 N·m2/C
- b) 8.664E+01 N·m2/C
- c) 9.531E+01 N·m2/C
- d) 1.048E+02 N·m2/C
- e) 1.153E+02 N·m2/C
- a) 1.737E+01 N·m2/C
- b) 1.910E+01 N·m2/C
- c) 2.101E+01 N·m2/C
- d) 2.311E+01 N·m2/C
- e) 2.543E+01 N·m2/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
- a) 1.206E+03 V·m
- b) 1.326E+03 V·m
- c) 1.459E+03 V·m
- d) 1.605E+03 V·m
- e) 1.765E+03 V·m
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 2.454E+02
- b) 2.973E+02
- c) 3.601E+02
- d) 4.363E+02
- e) 5.286E+02
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 6.69E+03
- b) 8.10E+03
- c) 9.81E+03
- d) 1.19E+04
- e) 1.44E+04
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
T2 E1[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?
- a) 9.592E+00 N/C
- b) 1.055E+01 N/C
- c) 1.161E+01 N/C
- d) 1.277E+01 N/C
- e) 1.404E+01 N/C
2) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
- a) 1.969E+02 V·m
- b) 2.166E+02 V·m
- c) 2.383E+02 V·m
- d) 2.621E+02 V·m
- e) 2.883E+02 V·m
- a) 1.992E+01 N·m2/C
- b) 2.192E+01 N·m2/C
- c) 2.411E+01 N·m2/C
- d) 2.652E+01 N·m2/C
- e) 2.917E+01 N·m2/C
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.13E+03
- b) 1.37E+03
- c) 1.66E+03
- d) 2.01E+03
- e) 2.44E+03
- a) 9.823E+00 N·m2/C
- b) 1.080E+01 N·m2/C
- c) 1.189E+01 N·m2/C
- d) 1.307E+01 N·m2/C
- e) 1.438E+01 N·m2/C
8) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 5.610E+02
- b) 6.796E+02
- c) 8.234E+02
- d) 9.975E+02
- e) 1.209E+03
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 E2[edit | edit source]
1) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 4.162E+02
- b) 5.042E+02
- c) 6.109E+02
- d) 7.401E+02
- e) 8.967E+02
2) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
- a) 2.610E+03 V·m
- b) 2.871E+03 V·m
- c) 3.158E+03 V·m
- d) 3.474E+03 V·m
- e) 3.822E+03 V·m
- a) 4.988E+01 N·m2/C
- b) 5.487E+01 N·m2/C
- c) 6.035E+01 N·m2/C
- d) 6.639E+01 N·m2/C
- e) 7.303E+01 N·m2/C
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
6) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
7) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.08E+03
- b) 1.30E+03
- c) 1.58E+03
- d) 1.91E+03
- e) 2.32E+03
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.5 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?
- a) 2.601E+01 N/C
- b) 2.861E+01 N/C
- c) 3.147E+01 N/C
- d) 3.462E+01 N/C
- e) 3.808E+01 N/C
- a) 5.385E+01 N·m2/C
- b) 5.923E+01 N·m2/C
- c) 6.516E+01 N·m2/C
- d) 7.167E+01 N·m2/C
- e) 7.884E+01 N·m2/C
T2 F0[edit | edit source]
- a) 6.364E+01 N·m2/C
- b) 7.000E+01 N·m2/C
- c) 7.700E+01 N·m2/C
- d) 8.470E+01 N·m2/C
- e) 9.317E+01 N·m2/C
2) A non-conducting sphere of radius R=1.4 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.6 (r≤R) where a=3 nC·m-1.4. What is the magnitude of the electric field at a distance of 1.3 m from the center?
- a) 1.457E+02 N/C
- b) 1.603E+02 N/C
- c) 1.763E+02 N/C
- d) 1.939E+02 N/C
- e) 2.133E+02 N/C
- a) 2.134E+01 N·m2/C
- b) 2.347E+01 N·m2/C
- c) 2.582E+01 N·m2/C
- d) 2.840E+01 N·m2/C
- e) 3.124E+01 N·m2/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- a) 7.054E+03 V·m
- b) 7.759E+03 V·m
- c) 8.535E+03 V·m
- d) 9.388E+03 V·m
- e) 1.033E+04 V·m
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.09E+03
- b) 1.32E+03
- c) 1.60E+03
- d) 1.94E+03
- e) 2.35E+03
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 5.610E+02
- b) 6.796E+02
- c) 8.234E+02
- d) 9.975E+02
- e) 1.209E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
T2 F1[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
- a) 2.210E+04 V·m
- b) 2.431E+04 V·m
- c) 2.674E+04 V·m
- d) 2.941E+04 V·m
- e) 3.235E+04 V·m
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
- a) 5.978E+01 N·m2/C
- b) 6.576E+01 N·m2/C
- c) 7.233E+01 N·m2/C
- d) 7.957E+01 N·m2/C
- e) 8.752E+01 N·m2/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
- a) 1.737E+01 N·m2/C
- b) 1.910E+01 N·m2/C
- c) 2.101E+01 N·m2/C
- d) 2.311E+01 N·m2/C
- e) 2.543E+01 N·m2/C
6) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?
- a) 3.797E+01 N/C
- b) 4.177E+01 N/C
- c) 4.595E+01 N/C
- d) 5.054E+01 N/C
- e) 5.560E+01 N/C
7) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 9.41E+02
- b) 1.14E+03
- c) 1.38E+03
- d) 1.67E+03
- e) 2.03E+03
8) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 4.027E+02
- b) 4.879E+02
- c) 5.911E+02
- d) 7.162E+02
- e) 8.676E+02
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
T2 F2[edit | edit source]
1) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 3.13E+03
- b) 3.79E+03
- c) 4.59E+03
- d) 5.56E+03
- e) 6.74E+03
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
- a) 3.074E+01 N·m2/C
- b) 3.382E+01 N·m2/C
- c) 3.720E+01 N·m2/C
- d) 4.092E+01 N·m2/C
- e) 4.501E+01 N·m2/C
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
- a) 6.270E+01 N·m2/C
- b) 6.897E+01 N·m2/C
- c) 7.586E+01 N·m2/C
- d) 8.345E+01 N·m2/C
- e) 9.179E+01 N·m2/C
8) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- a) 4.286E+03 V·m
- b) 4.714E+03 V·m
- c) 5.186E+03 V·m
- d) 5.704E+03 V·m
- e) 6.275E+03 V·m
9) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 4.162E+02
- b) 5.042E+02
- c) 6.109E+02
- d) 7.401E+02
- e) 8.967E+02
10) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?
- a) 1.123E+02 N/C
- b) 1.235E+02 N/C
- c) 1.358E+02 N/C
- d) 1.494E+02 N/C
- e) 1.644E+02 N/C
T2 G0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- a) 1.017E+01 N/C
- b) 1.118E+01 N/C
- c) 1.230E+01 N/C
- d) 1.353E+01 N/C
- e) 1.488E+01 N/C
- a) 3.662E+01 N·m2/C
- b) 4.028E+01 N·m2/C
- c) 4.430E+01 N·m2/C
- d) 4.873E+01 N·m2/C
- e) 5.361E+01 N·m2/C
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is,
- a) 8.731E+02 V·m
- b) 9.604E+02 V·m
- c) 1.056E+03 V·m
- d) 1.162E+03 V·m
- e) 1.278E+03 V·m
- a) 1.891E+01 N·m2/C
- b) 2.080E+01 N·m2/C
- c) 2.288E+01 N·m2/C
- d) 2.517E+01 N·m2/C
- e) 2.768E+01 N·m2/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.59E+03
- b) 1.93E+03
- c) 2.34E+03
- d) 2.83E+03
- e) 3.43E+03
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 2.769E+03
- b) 3.354E+03
- c) 4.064E+03
- d) 4.923E+03
- e) 5.965E+03
7) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
T2 G1[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- a) 4.286E+03 V·m
- b) 4.714E+03 V·m
- c) 5.186E+03 V·m
- d) 5.704E+03 V·m
- e) 6.275E+03 V·m
- a) 7.081E+01 N·m2/C
- b) 7.789E+01 N·m2/C
- c) 8.568E+01 N·m2/C
- d) 9.425E+01 N·m2/C
- e) 1.037E+02 N·m2/C
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
- a) 6.270E+01 N·m2/C
- b) 6.897E+01 N·m2/C
- c) 7.586E+01 N·m2/C
- d) 8.345E+01 N·m2/C
- e) 9.179E+01 N·m2/C
5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 6.69E+03
- b) 8.10E+03
- c) 9.81E+03
- d) 1.19E+04
- e) 1.44E+04
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
8) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 3.417E+03
- b) 4.140E+03
- c) 5.016E+03
- d) 6.077E+03
- e) 7.362E+03
9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?
- a) 2.837E+01 N/C
- b) 3.121E+01 N/C
- c) 3.433E+01 N/C
- d) 3.776E+01 N/C
- e) 4.154E+01 N/C
10) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
T2 G2[edit | edit source]
1) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 1.362E+03
- b) 1.650E+03
- c) 2.000E+03
- d) 2.423E+03
- e) 2.935E+03
2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.6 m from the center of the shells?
- a) 6.641E+00 N/C
- b) 7.305E+00 N/C
- c) 8.036E+00 N/C
- d) 8.839E+00 N/C
- e) 9.723E+00 N/C
3) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.13E+03
- b) 1.37E+03
- c) 1.66E+03
- d) 2.01E+03
- e) 2.44E+03
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
- a) 4.820E+03 V·m
- b) 5.302E+03 V·m
- c) 5.832E+03 V·m
- d) 6.415E+03 V·m
- e) 7.057E+03 V·m
- a) 4.953E+01 N·m2/C
- b) 5.449E+01 N·m2/C
- c) 5.993E+01 N·m2/C
- d) 6.593E+01 N·m2/C
- e) 7.252E+01 N·m2/C
- a) 8.921E+01 N·m2/C
- b) 9.813E+01 N·m2/C
- c) 1.079E+02 N·m2/C
- d) 1.187E+02 N·m2/C
- e) 1.306E+02 N·m2/C
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
T2 H0[edit | edit source]
1) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?
- a) 3.797E+01 N/C
- b) 4.177E+01 N/C
- c) 4.595E+01 N/C
- d) 5.054E+01 N/C
- e) 5.560E+01 N/C
- a) 1.388E+01 N·m2/C
- b) 1.526E+01 N·m2/C
- c) 1.679E+01 N·m2/C
- d) 1.847E+01 N·m2/C
- e) 2.032E+01 N·m2/C
- a) 2.186E+01 N·m2/C
- b) 2.404E+01 N·m2/C
- c) 2.645E+01 N·m2/C
- d) 2.909E+01 N·m2/C
- e) 3.200E+01 N·m2/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
- a) 3.429E+03 V·m
- b) 3.771E+03 V·m
- c) 4.149E+03 V·m
- d) 4.564E+03 V·m
- e) 5.020E+03 V·m
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 3.630E+02
- b) 4.398E+02
- c) 5.329E+02
- d) 6.456E+02
- e) 7.821E+02
6) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 7.465E+02
- b) 9.044E+02
- c) 1.096E+03
- d) 1.327E+03
- e) 1.608E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
T2 H1[edit | edit source]
1) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?
- a) 2.039E+01 N/C
- b) 2.243E+01 N/C
- c) 2.467E+01 N/C
- d) 2.714E+01 N/C
- e) 2.985E+01 N/C
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
- a) 1.206E+03 V·m
- b) 1.326E+03 V·m
- c) 1.459E+03 V·m
- d) 1.605E+03 V·m
- e) 1.765E+03 V·m
3) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 9.431E+02
- b) 1.143E+03
- c) 1.384E+03
- d) 1.677E+03
- e) 2.032E+03
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
- a) 1.992E+01 N·m2/C
- b) 2.192E+01 N·m2/C
- c) 2.411E+01 N·m2/C
- d) 2.652E+01 N·m2/C
- e) 2.917E+01 N·m2/C
- a) 7.081E+01 N·m2/C
- b) 7.789E+01 N·m2/C
- c) 8.568E+01 N·m2/C
- d) 9.425E+01 N·m2/C
- e) 1.037E+02 N·m2/C
8) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 4.593E+03
- b) 5.564E+03
- c) 6.741E+03
- d) 8.167E+03
- e) 9.894E+03
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
T2 H2[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
- a) 2.694E+03 V·m
- b) 2.963E+03 V·m
- c) 3.259E+03 V·m
- d) 3.585E+03 V·m
- e) 3.944E+03 V·m
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
3) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
4) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 2.420E+02
- b) 2.931E+02
- c) 3.551E+02
- d) 4.303E+02
- e) 5.213E+02
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 3.630E+02
- b) 4.398E+02
- c) 5.329E+02
- d) 6.456E+02
- e) 7.821E+02
- a) 2.901E+01 N·m2/C
- b) 3.192E+01 N·m2/C
- c) 3.511E+01 N·m2/C
- d) 3.862E+01 N·m2/C
- e) 4.248E+01 N·m2/C
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
9) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?
- a) 3.797E+01 N/C
- b) 4.177E+01 N/C
- c) 4.595E+01 N/C
- d) 5.054E+01 N/C
- e) 5.560E+01 N/C
- a) 4.024E+01 N·m2/C
- b) 4.426E+01 N·m2/C
- c) 4.868E+01 N·m2/C
- d) 5.355E+01 N·m2/C
- e) 5.891E+01 N·m2/C
T2 I0[edit | edit source]
- a) 1.698E+01 N·m2/C
- b) 1.868E+01 N·m2/C
- c) 2.055E+01 N·m2/C
- d) 2.260E+01 N·m2/C
- e) 2.486E+01 N·m2/C
2) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?
- a) 2.039E+01 N/C
- b) 2.243E+01 N/C
- c) 2.467E+01 N/C
- d) 2.714E+01 N/C
- e) 2.985E+01 N/C
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?
- a) 9.592E+00 N/C
- b) 1.055E+01 N/C
- c) 1.161E+01 N/C
- d) 1.277E+01 N/C
- e) 1.404E+01 N/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is,
- a) 8.731E+02 V·m
- b) 9.604E+02 V·m
- c) 1.056E+03 V·m
- d) 1.162E+03 V·m
- e) 1.278E+03 V·m
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 5.610E+02
- b) 6.796E+02
- c) 8.234E+02
- d) 9.975E+02
- e) 1.209E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 3.60E+02
- b) 4.36E+02
- c) 5.29E+02
- d) 6.40E+02
- e) 7.76E+02
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
T2 I1[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
- a) 7.200E+01 V·m
- b) 7.920E+01 V·m
- c) 8.712E+01 V·m
- d) 9.583E+01 V·m
- e) 1.054E+02 V·m
2) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 6.411E+02
- b) 7.767E+02
- c) 9.410E+02
- d) 1.140E+03
- e) 1.381E+03
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.8 m from the center of the shells?
- a) 5.865E+00 N/C
- b) 6.451E+00 N/C
- c) 7.096E+00 N/C
- d) 7.806E+00 N/C
- e) 8.587E+00 N/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
6) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
- a) 5.606E+01 N·m2/C
- b) 6.167E+01 N·m2/C
- c) 6.784E+01 N·m2/C
- d) 7.462E+01 N·m2/C
- e) 8.208E+01 N·m2/C
8) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?
- a) 4.782E+02 N/C
- b) 5.260E+02 N/C
- c) 5.787E+02 N/C
- d) 6.365E+02 N/C
- e) 7.002E+02 N/C
9) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 3.96E+02
- b) 4.79E+02
- c) 5.81E+02
- d) 7.04E+02
- e) 8.53E+02
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 I2[edit | edit source]
1) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 5.91E+02
- b) 7.16E+02
- c) 8.68E+02
- d) 1.05E+03
- e) 1.27E+03
- a) 6.920E+01 N·m2/C
- b) 7.612E+01 N·m2/C
- c) 8.373E+01 N·m2/C
- d) 9.210E+01 N·m2/C
- e) 1.013E+02 N·m2/C
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- a) 1.997E+03 V·m
- b) 2.197E+03 V·m
- c) 2.417E+03 V·m
- d) 2.659E+03 V·m
- e) 2.924E+03 V·m
4) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 4.021E+02
- b) 4.872E+02
- c) 5.902E+02
- d) 7.151E+02
- e) 8.663E+02
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
7) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- a) 1.096E+00 N/C
- b) 1.206E+00 N/C
- c) 1.327E+00 N/C
- d) 1.459E+00 N/C
- e) 1.605E+00 N/C
10) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?
- a) 1.123E+02 N/C
- b) 1.235E+02 N/C
- c) 1.358E+02 N/C
- d) 1.494E+02 N/C
- e) 1.644E+02 N/C
T2 J0[edit | edit source]
1) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?
- a) 3.821E+02 N/C
- b) 4.203E+02 N/C
- c) 4.624E+02 N/C
- d) 5.086E+02 N/C
- e) 5.594E+02 N/C
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
- a) 2.610E+03 V·m
- b) 2.871E+03 V·m
- c) 3.158E+03 V·m
- d) 3.474E+03 V·m
- e) 3.822E+03 V·m
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?
- a) 9.144E+00 N/C
- b) 1.006E+01 N/C
- c) 1.106E+01 N/C
- d) 1.217E+01 N/C
- e) 1.339E+01 N/C
- a) 2.012E+01 N·m2/C
- b) 2.213E+01 N·m2/C
- c) 2.435E+01 N·m2/C
- d) 2.678E+01 N·m2/C
- e) 2.946E+01 N·m2/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 5.311E+02
- b) 6.434E+02
- c) 7.795E+02
- d) 9.444E+02
- e) 1.144E+03
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 3.232E+03
- b) 3.915E+03
- c) 4.743E+03
- d) 5.747E+03
- e) 6.962E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
10) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 J1[edit | edit source]
1) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?
- a) 7.825E+02 N/C
- b) 8.607E+02 N/C
- c) 9.468E+02 N/C
- d) 1.041E+03 N/C
- e) 1.146E+03 N/C
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
5) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 9.205E+02
- b) 1.115E+03
- c) 1.351E+03
- d) 1.637E+03
- e) 1.983E+03
7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
- a) 2.610E+03 V·m
- b) 2.871E+03 V·m
- c) 3.158E+03 V·m
- d) 3.474E+03 V·m
- e) 3.822E+03 V·m
8) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 1.304E+03
- b) 1.579E+03
- c) 1.914E+03
- d) 2.318E+03
- e) 2.809E+03
9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.4 m from the center of the shells?
- a) 8.580E+00 N/C
- b) 9.438E+00 N/C
- c) 1.038E+01 N/C
- d) 1.142E+01 N/C
- e) 1.256E+01 N/C
- a) 4.988E+01 N·m2/C
- b) 5.487E+01 N·m2/C
- c) 6.035E+01 N·m2/C
- d) 6.639E+01 N·m2/C
- e) 7.303E+01 N·m2/C
T2 J2[edit | edit source]
1) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
- a) 1.206E+03 V·m
- b) 1.326E+03 V·m
- c) 1.459E+03 V·m
- d) 1.605E+03 V·m
- e) 1.765E+03 V·m
3) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 6.546E+02
- b) 7.931E+02
- c) 9.609E+02
- d) 1.164E+03
- e) 1.410E+03
4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.4 m from the center of the shells?
- a) 1.491E+01 N/C
- b) 1.640E+01 N/C
- c) 1.804E+01 N/C
- d) 1.984E+01 N/C
- e) 2.182E+01 N/C
- a) 5.439E+01 N·m2/C
- b) 5.983E+01 N·m2/C
- c) 6.581E+01 N·m2/C
- d) 7.239E+01 N·m2/C
- e) 7.963E+01 N·m2/C
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 6.201E+02
- b) 7.513E+02
- c) 9.102E+02
- d) 1.103E+03
- e) 1.336E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
8) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?
- a) 7.825E+02 N/C
- b) 8.607E+02 N/C
- c) 9.468E+02 N/C
- d) 1.041E+03 N/C
- e) 1.146E+03 N/C
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 K0[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
- a) 2.694E+03 V·m
- b) 2.963E+03 V·m
- c) 3.259E+03 V·m
- d) 3.585E+03 V·m
- e) 3.944E+03 V·m
2) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?
- a) 2.285E+01 N/C
- b) 2.514E+01 N/C
- c) 2.765E+01 N/C
- d) 3.042E+01 N/C
- e) 3.346E+01 N/C
- a) 3.662E+01 N·m2/C
- b) 4.028E+01 N·m2/C
- c) 4.430E+01 N·m2/C
- d) 4.873E+01 N·m2/C
- e) 5.361E+01 N·m2/C
- a) 2.186E+01 N·m2/C
- b) 2.404E+01 N·m2/C
- c) 2.645E+01 N·m2/C
- d) 2.909E+01 N·m2/C
- e) 3.200E+01 N·m2/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.59E+03
- b) 1.93E+03
- c) 2.34E+03
- d) 2.83E+03
- e) 3.43E+03
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 3.232E+03
- b) 3.915E+03
- c) 4.743E+03
- d) 5.747E+03
- e) 6.962E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
T2 K1[edit | edit source]
1) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?
- a) 2.285E+01 N/C
- b) 2.514E+01 N/C
- c) 2.765E+01 N/C
- d) 3.042E+01 N/C
- e) 3.346E+01 N/C
2) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
- a) 1.206E+03 V·m
- b) 1.326E+03 V·m
- c) 1.459E+03 V·m
- d) 1.605E+03 V·m
- e) 1.765E+03 V·m
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
- a) 3.695E+01 N·m2/C
- b) 4.065E+01 N·m2/C
- c) 4.472E+01 N·m2/C
- d) 4.919E+01 N·m2/C
- e) 5.411E+01 N·m2/C
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 3.13E+03
- b) 3.79E+03
- c) 4.59E+03
- d) 5.56E+03
- e) 6.74E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
9) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 5.610E+02
- b) 6.796E+02
- c) 8.234E+02
- d) 9.975E+02
- e) 1.209E+03
- a) 2.012E+01 N·m2/C
- b) 2.213E+01 N·m2/C
- c) 2.435E+01 N·m2/C
- d) 2.678E+01 N·m2/C
- e) 2.946E+01 N·m2/C
T2 K2[edit | edit source]
- a) 5.606E+01 N·m2/C
- b) 6.167E+01 N·m2/C
- c) 6.784E+01 N·m2/C
- d) 7.462E+01 N·m2/C
- e) 8.208E+01 N·m2/C
2) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 4.69E+03
- b) 5.69E+03
- c) 6.89E+03
- d) 8.35E+03
- e) 1.01E+04
3) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?
- a) 2.285E+01 N/C
- b) 2.514E+01 N/C
- c) 2.765E+01 N/C
- d) 3.042E+01 N/C
- e) 3.346E+01 N/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
- a) 8.545E+01 V·m
- b) 9.400E+01 V·m
- c) 1.034E+02 V·m
- d) 1.137E+02 V·m
- e) 1.251E+02 V·m
5) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 2.454E+02
- b) 2.973E+02
- c) 3.601E+02
- d) 4.363E+02
- e) 5.286E+02
- a) 3.222E+01 N·m2/C
- b) 3.544E+01 N·m2/C
- c) 3.899E+01 N·m2/C
- d) 4.289E+01 N·m2/C
- e) 4.718E+01 N·m2/C
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
T2 L0[edit | edit source]
- a) 8.314E+01 N·m2/C
- b) 9.146E+01 N·m2/C
- c) 1.006E+02 N·m2/C
- d) 1.107E+02 N·m2/C
- e) 1.217E+02 N·m2/C
- a) 7.081E+01 N·m2/C
- b) 7.789E+01 N·m2/C
- c) 8.568E+01 N·m2/C
- d) 9.425E+01 N·m2/C
- e) 1.037E+02 N·m2/C
3) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.8 (r≤R) where a=2 nC·m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?
- a) 2.079E+02 N/C
- b) 2.287E+02 N/C
- c) 2.516E+02 N/C
- d) 2.767E+02 N/C
- e) 3.044E+02 N/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- a) 7.054E+03 V·m
- b) 7.759E+03 V·m
- c) 8.535E+03 V·m
- d) 9.388E+03 V·m
- e) 1.033E+04 V·m
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 4.63E+02
- b) 5.61E+02
- c) 6.80E+02
- d) 8.23E+02
- e) 9.98E+02
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 3.742E+02
- b) 4.534E+02
- c) 5.493E+02
- d) 6.655E+02
- e) 8.063E+02
7) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
10) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
T2 L1[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
2) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?
- a) 3.821E+02 N/C
- b) 4.203E+02 N/C
- c) 4.624E+02 N/C
- d) 5.086E+02 N/C
- e) 5.594E+02 N/C
3) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
4) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 4.489E+02
- b) 5.438E+02
- c) 6.589E+02
- d) 7.983E+02
- e) 9.671E+02
5) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 3.13E+03
- b) 3.79E+03
- c) 4.59E+03
- d) 5.56E+03
- e) 6.74E+03
- a) 3.249E+01 N·m2/C
- b) 3.574E+01 N·m2/C
- c) 3.931E+01 N·m2/C
- d) 4.324E+01 N·m2/C
- e) 4.757E+01 N·m2/C
- a) 8.314E+01 N·m2/C
- b) 9.146E+01 N·m2/C
- c) 1.006E+02 N·m2/C
- d) 1.107E+02 N·m2/C
- e) 1.217E+02 N·m2/C
9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
- a) 2.210E+04 V·m
- b) 2.431E+04 V·m
- c) 2.674E+04 V·m
- d) 2.941E+04 V·m
- e) 3.235E+04 V·m
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
T2 L2[edit | edit source]
1) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
2) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- a) 7.054E+03 V·m
- b) 7.759E+03 V·m
- c) 8.535E+03 V·m
- d) 9.388E+03 V·m
- e) 1.033E+04 V·m
4) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 1.704E+03
- b) 2.064E+03
- c) 2.501E+03
- d) 3.030E+03
- e) 3.671E+03
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 5.91E+02
- b) 7.16E+02
- c) 8.68E+02
- d) 1.05E+03
- e) 1.27E+03
- a) 5.978E+01 N·m2/C
- b) 6.576E+01 N·m2/C
- c) 7.233E+01 N·m2/C
- d) 7.957E+01 N·m2/C
- e) 8.752E+01 N·m2/C
- a) 3.222E+01 N·m2/C
- b) 3.544E+01 N·m2/C
- c) 3.899E+01 N·m2/C
- d) 4.289E+01 N·m2/C
- e) 4.718E+01 N·m2/C
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?
- a) 6.411E+02 N/C
- b) 7.052E+02 N/C
- c) 7.757E+02 N/C
- d) 8.533E+02 N/C
- e) 9.386E+02 N/C
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
T2 M0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?
- a) 3.251E+01 N/C
- b) 3.577E+01 N/C
- c) 3.934E+01 N/C
- d) 4.328E+01 N/C
- e) 4.760E+01 N/C
2) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.3 m from the center?
- a) 2.777E+02 N/C
- b) 3.055E+02 N/C
- c) 3.361E+02 N/C
- d) 3.697E+02 N/C
- e) 4.066E+02 N/C
- a) 3.712E+01 N·m2/C
- b) 4.083E+01 N·m2/C
- c) 4.491E+01 N·m2/C
- d) 4.940E+01 N·m2/C
- e) 5.434E+01 N·m2/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
- a) 9.027E+03 V·m
- b) 9.930E+03 V·m
- c) 1.092E+04 V·m
- d) 1.202E+04 V·m
- e) 1.322E+04 V·m
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 3.742E+02
- b) 4.534E+02
- c) 5.493E+02
- d) 6.655E+02
- e) 8.063E+02
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 4.027E+02
- b) 4.879E+02
- c) 5.911E+02
- d) 7.162E+02
- e) 8.676E+02
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
10) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
T2 M1[edit | edit source]
1) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 1.692E+03
- b) 2.050E+03
- c) 2.484E+03
- d) 3.009E+03
- e) 3.645E+03
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
- a) 9.952E+03 V·m
- b) 1.095E+04 V·m
- c) 1.204E+04 V·m
- d) 1.325E+04 V·m
- e) 1.457E+04 V·m
5) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
6) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.8 (r≤R) where a=2 nC·m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?
- a) 2.079E+02 N/C
- b) 2.287E+02 N/C
- c) 2.516E+02 N/C
- d) 2.767E+02 N/C
- e) 3.044E+02 N/C
- a) 8.457E+01 N·m2/C
- b) 9.303E+01 N·m2/C
- c) 1.023E+02 N·m2/C
- d) 1.126E+02 N·m2/C
- e) 1.238E+02 N·m2/C
8) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 4.489E+02
- b) 5.438E+02
- c) 6.589E+02
- d) 7.983E+02
- e) 9.671E+02
9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- a) 1.017E+01 N/C
- b) 1.118E+01 N/C
- c) 1.230E+01 N/C
- d) 1.353E+01 N/C
- e) 1.488E+01 N/C
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 M2[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
2) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 2.158E+03
- b) 2.614E+03
- c) 3.167E+03
- d) 3.837E+03
- e) 4.649E+03
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.6 m from the center of the shells?
- a) 6.641E+00 N/C
- b) 7.305E+00 N/C
- c) 8.036E+00 N/C
- d) 8.839E+00 N/C
- e) 9.723E+00 N/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
- a) 2.067E+03 V·m
- b) 2.274E+03 V·m
- c) 2.501E+03 V·m
- d) 2.752E+03 V·m
- e) 3.027E+03 V·m
5) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?
- a) 3.604E+02 N/C
- b) 3.964E+02 N/C
- c) 4.360E+02 N/C
- d) 4.796E+02 N/C
- e) 5.276E+02 N/C
6) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
- a) 8.457E+01 N·m2/C
- b) 9.303E+01 N·m2/C
- c) 1.023E+02 N·m2/C
- d) 1.126E+02 N·m2/C
- e) 1.238E+02 N·m2/C
8) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 3.742E+02
- b) 4.534E+02
- c) 5.493E+02
- d) 6.655E+02
- e) 8.063E+02
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 N0[edit | edit source]
1) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?
- a) 4.782E+02 N/C
- b) 5.260E+02 N/C
- c) 5.787E+02 N/C
- d) 6.365E+02 N/C
- e) 7.002E+02 N/C
- a) 3.249E+01 N·m2/C
- b) 3.574E+01 N·m2/C
- c) 3.931E+01 N·m2/C
- d) 4.324E+01 N·m2/C
- e) 4.757E+01 N·m2/C
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
- a) 7.200E+01 V·m
- b) 7.920E+01 V·m
- c) 8.712E+01 V·m
- d) 9.583E+01 V·m
- e) 1.054E+02 V·m
- a) 7.793E+01 N·m2/C
- b) 8.572E+01 N·m2/C
- c) 9.429E+01 N·m2/C
- d) 1.037E+02 N·m2/C
- e) 1.141E+02 N·m2/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 2.420E+02
- b) 2.931E+02
- c) 3.551E+02
- d) 4.303E+02
- e) 5.213E+02
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 2.597E+03
- b) 3.147E+03
- c) 3.812E+03
- d) 4.619E+03
- e) 5.596E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 N1[edit | edit source]
- a) 5.606E+01 N·m2/C
- b) 6.167E+01 N·m2/C
- c) 6.784E+01 N·m2/C
- d) 7.462E+01 N·m2/C
- e) 8.208E+01 N·m2/C
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
- a) 7.200E+01 V·m
- b) 7.920E+01 V·m
- c) 8.712E+01 V·m
- d) 9.583E+01 V·m
- e) 1.054E+02 V·m
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
4) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 2.597E+03
- b) 3.147E+03
- c) 3.812E+03
- d) 4.619E+03
- e) 5.596E+03
- a) 2.079E+01 N·m2/C
- b) 2.287E+01 N·m2/C
- c) 2.516E+01 N·m2/C
- d) 2.768E+01 N·m2/C
- e) 3.044E+01 N·m2/C
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
7) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 6.546E+02
- b) 7.931E+02
- c) 9.609E+02
- d) 1.164E+03
- e) 1.410E+03
8) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?
- a) 4.782E+02 N/C
- b) 5.260E+02 N/C
- c) 5.787E+02 N/C
- d) 6.365E+02 N/C
- e) 7.002E+02 N/C
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
T2 N2[edit | edit source]
1) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 1.704E+03
- b) 2.064E+03
- c) 2.501E+03
- d) 3.030E+03
- e) 3.671E+03
2) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?
- a) 2.285E+01 N/C
- b) 2.514E+01 N/C
- c) 2.765E+01 N/C
- d) 3.042E+01 N/C
- e) 3.346E+01 N/C
- a) 5.978E+01 N·m2/C
- b) 6.576E+01 N·m2/C
- c) 7.233E+01 N·m2/C
- d) 7.957E+01 N·m2/C
- e) 8.752E+01 N·m2/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
7) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 2.318E+02
- b) 2.808E+02
- c) 3.402E+02
- d) 4.122E+02
- e) 4.994E+02
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- a) 7.054E+03 V·m
- b) 7.759E+03 V·m
- c) 8.535E+03 V·m
- d) 9.388E+03 V·m
- e) 1.033E+04 V·m
- a) 5.606E+01 N·m2/C
- b) 6.167E+01 N·m2/C
- c) 6.784E+01 N·m2/C
- d) 7.462E+01 N·m2/C
- e) 8.208E+01 N·m2/C
T2 O0[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
- a) 2.210E+04 V·m
- b) 2.431E+04 V·m
- c) 2.674E+04 V·m
- d) 2.941E+04 V·m
- e) 3.235E+04 V·m
- a) 3.662E+01 N·m2/C
- b) 4.028E+01 N·m2/C
- c) 4.430E+01 N·m2/C
- d) 4.873E+01 N·m2/C
- e) 5.361E+01 N·m2/C
- a) 1.698E+01 N·m2/C
- b) 1.868E+01 N·m2/C
- c) 2.055E+01 N·m2/C
- d) 2.260E+01 N·m2/C
- e) 2.486E+01 N·m2/C
4) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?
- a) 1.383E+02 N/C
- b) 1.522E+02 N/C
- c) 1.674E+02 N/C
- d) 1.841E+02 N/C
- e) 2.025E+02 N/C
5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 4.593E+03
- b) 5.564E+03
- c) 6.741E+03
- d) 8.167E+03
- e) 9.894E+03
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 9.41E+03
- b) 1.14E+04
- c) 1.38E+04
- d) 1.67E+04
- e) 2.03E+04
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
T2 O1[edit | edit source]
1) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
4) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 6.201E+02
- b) 7.513E+02
- c) 9.102E+02
- d) 1.103E+03
- e) 1.336E+03
6) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?
- a) 1.383E+02 N/C
- b) 1.522E+02 N/C
- c) 1.674E+02 N/C
- d) 1.841E+02 N/C
- e) 2.025E+02 N/C
- a) 2.012E+01 N·m2/C
- b) 2.213E+01 N·m2/C
- c) 2.435E+01 N·m2/C
- d) 2.678E+01 N·m2/C
- e) 2.946E+01 N·m2/C
8) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 3.18E+03
- b) 3.85E+03
- c) 4.66E+03
- d) 5.65E+03
- e) 6.84E+03
9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- a) 1.128E+04 V·m
- b) 1.241E+04 V·m
- c) 1.365E+04 V·m
- d) 1.502E+04 V·m
- e) 1.652E+04 V·m
- a) 4.521E+01 N·m2/C
- b) 4.973E+01 N·m2/C
- c) 5.470E+01 N·m2/C
- d) 6.017E+01 N·m2/C
- e) 6.619E+01 N·m2/C
T2 O2[edit | edit source]
1) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 4.522E+02
- b) 5.478E+02
- c) 6.637E+02
- d) 8.041E+02
- e) 9.742E+02
- a) 4.809E+01 N·m2/C
- b) 5.290E+01 N·m2/C
- c) 5.819E+01 N·m2/C
- d) 6.401E+01 N·m2/C
- e) 7.041E+01 N·m2/C
- a) 8.314E+01 N·m2/C
- b) 9.146E+01 N·m2/C
- c) 1.006E+02 N·m2/C
- d) 1.107E+02 N·m2/C
- e) 1.217E+02 N·m2/C
4) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?
- a) 4.782E+02 N/C
- b) 5.260E+02 N/C
- c) 5.787E+02 N/C
- d) 6.365E+02 N/C
- e) 7.002E+02 N/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 5.91E+02
- b) 7.16E+02
- c) 8.68E+02
- d) 1.05E+03
- e) 1.27E+03
6) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- a) 7.054E+03 V·m
- b) 7.759E+03 V·m
- c) 8.535E+03 V·m
- d) 9.388E+03 V·m
- e) 1.033E+04 V·m
T2 P0[edit | edit source]
- a) 5.989E+01 N·m2/C
- b) 6.588E+01 N·m2/C
- c) 7.247E+01 N·m2/C
- d) 7.971E+01 N·m2/C
- e) 8.769E+01 N·m2/C
2) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?
- a) 3.821E+02 N/C
- b) 4.203E+02 N/C
- c) 4.624E+02 N/C
- d) 5.086E+02 N/C
- e) 5.594E+02 N/C
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
- a) 3.429E+03 V·m
- b) 3.771E+03 V·m
- c) 4.149E+03 V·m
- d) 4.564E+03 V·m
- e) 5.020E+03 V·m
- a) 7.793E+01 N·m2/C
- b) 8.572E+01 N·m2/C
- c) 9.429E+01 N·m2/C
- d) 1.037E+02 N·m2/C
- e) 1.141E+02 N·m2/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 3.356E+02
- b) 4.066E+02
- c) 4.926E+02
- d) 5.968E+02
- e) 7.230E+02
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 3.742E+02
- b) 4.534E+02
- c) 5.493E+02
- d) 6.655E+02
- e) 8.063E+02
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 P1[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
- a) 3.695E+01 N·m2/C
- b) 4.065E+01 N·m2/C
- c) 4.472E+01 N·m2/C
- d) 4.919E+01 N·m2/C
- e) 5.411E+01 N·m2/C
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
4) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?
- a) 4.782E+02 N/C
- b) 5.260E+02 N/C
- c) 5.787E+02 N/C
- d) 6.365E+02 N/C
- e) 7.002E+02 N/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 5.043E+02
- b) 6.109E+02
- c) 7.402E+02
- d) 8.967E+02
- e) 1.086E+03
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
- a) 3.959E+01 N·m2/C
- b) 4.354E+01 N·m2/C
- c) 4.790E+01 N·m2/C
- d) 5.269E+01 N·m2/C
- e) 5.796E+01 N·m2/C
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
9) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 2.454E+02
- b) 2.973E+02
- c) 3.601E+02
- d) 4.363E+02
- e) 5.286E+02
10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
- a) 8.545E+01 V·m
- b) 9.400E+01 V·m
- c) 1.034E+02 V·m
- d) 1.137E+02 V·m
- e) 1.251E+02 V·m
T2 P2[edit | edit source]
- a) 3.222E+01 N·m2/C
- b) 3.544E+01 N·m2/C
- c) 3.899E+01 N·m2/C
- d) 4.289E+01 N·m2/C
- e) 4.718E+01 N·m2/C
2) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 1.304E+03
- b) 1.579E+03
- c) 1.914E+03
- d) 2.318E+03
- e) 2.809E+03
- a) 3.695E+01 N·m2/C
- b) 4.065E+01 N·m2/C
- c) 4.472E+01 N·m2/C
- d) 4.919E+01 N·m2/C
- e) 5.411E+01 N·m2/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
6) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
- a) 2.210E+04 V·m
- b) 2.431E+04 V·m
- c) 2.674E+04 V·m
- d) 2.941E+04 V·m
- e) 3.235E+04 V·m
7) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.3 m from the center?
- a) 2.777E+02 N/C
- b) 3.055E+02 N/C
- c) 3.361E+02 N/C
- d) 3.697E+02 N/C
- e) 4.066E+02 N/C
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
9) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 4.162E+02
- b) 5.042E+02
- c) 6.109E+02
- d) 7.401E+02
- e) 8.967E+02
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
T2 Q0[edit | edit source]
1) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?
- a) 7.825E+02 N/C
- b) 8.607E+02 N/C
- c) 9.468E+02 N/C
- d) 1.041E+03 N/C
- e) 1.146E+03 N/C
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
- a) 7.200E+01 V·m
- b) 7.920E+01 V·m
- c) 8.712E+01 V·m
- d) 9.583E+01 V·m
- e) 1.054E+02 V·m
- a) 8.457E+01 N·m2/C
- b) 9.303E+01 N·m2/C
- c) 1.023E+02 N·m2/C
- d) 1.126E+02 N·m2/C
- e) 1.238E+02 N·m2/C
- a) 5.978E+01 N·m2/C
- b) 6.576E+01 N·m2/C
- c) 7.233E+01 N·m2/C
- d) 7.957E+01 N·m2/C
- e) 8.752E+01 N·m2/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 3.742E+02
- b) 4.534E+02
- c) 5.493E+02
- d) 6.655E+02
- e) 8.063E+02
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 2.93E+02
- b) 3.55E+02
- c) 4.30E+02
- d) 5.21E+02
- e) 6.32E+02
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
8) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
T2 Q1[edit | edit source]
- a) 2.901E+01 N·m2/C
- b) 3.192E+01 N·m2/C
- c) 3.511E+01 N·m2/C
- d) 3.862E+01 N·m2/C
- e) 4.248E+01 N·m2/C
2) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?
- a) 7.825E+02 N/C
- b) 8.607E+02 N/C
- c) 9.468E+02 N/C
- d) 1.041E+03 N/C
- e) 1.146E+03 N/C
3) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 3.417E+03
- b) 4.140E+03
- c) 5.016E+03
- d) 6.077E+03
- e) 7.362E+03
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.59E+03
- b) 1.93E+03
- c) 2.34E+03
- d) 2.83E+03
- e) 3.43E+03
6) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
- a) 4.521E+01 N·m2/C
- b) 4.973E+01 N·m2/C
- c) 5.470E+01 N·m2/C
- d) 6.017E+01 N·m2/C
- e) 6.619E+01 N·m2/C
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
- a) 3.429E+03 V·m
- b) 3.771E+03 V·m
- c) 4.149E+03 V·m
- d) 4.564E+03 V·m
- e) 5.020E+03 V·m
T2 Q2[edit | edit source]
1) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 9.41E+03
- b) 1.14E+04
- c) 1.38E+04
- d) 1.67E+04
- e) 2.03E+04
- a) 7.876E+01 N·m2/C
- b) 8.664E+01 N·m2/C
- c) 9.531E+01 N·m2/C
- d) 1.048E+02 N·m2/C
- e) 1.153E+02 N·m2/C
3) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
4) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
- a) 5.978E+01 N·m2/C
- b) 6.576E+01 N·m2/C
- c) 7.233E+01 N·m2/C
- d) 7.957E+01 N·m2/C
- e) 8.752E+01 N·m2/C
8) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 1.248E+03
- b) 1.512E+03
- c) 1.832E+03
- d) 2.220E+03
- e) 2.689E+03
9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
- a) 2.694E+03 V·m
- b) 2.963E+03 V·m
- c) 3.259E+03 V·m
- d) 3.585E+03 V·m
- e) 3.944E+03 V·m
10) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?
- a) 2.274E+02 N/C
- b) 2.501E+02 N/C
- c) 2.751E+02 N/C
- d) 3.026E+02 N/C
- e) 3.329E+02 N/C
T2 R0[edit | edit source]
- a) 6.920E+01 N·m2/C
- b) 7.612E+01 N·m2/C
- c) 8.373E+01 N·m2/C
- d) 9.210E+01 N·m2/C
- e) 1.013E+02 N·m2/C
2) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.7 m from the center?
- a) 2.579E+02 N/C
- b) 2.837E+02 N/C
- c) 3.121E+02 N/C
- d) 3.433E+02 N/C
- e) 3.776E+02 N/C
- a) 5.978E+01 N·m2/C
- b) 6.576E+01 N·m2/C
- c) 7.233E+01 N·m2/C
- d) 7.957E+01 N·m2/C
- e) 8.752E+01 N·m2/C
- a) 8.921E+01 N·m2/C
- b) 9.813E+01 N·m2/C
- c) 1.079E+02 N·m2/C
- d) 1.187E+02 N·m2/C
- e) 1.306E+02 N·m2/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 3.96E+02
- b) 4.79E+02
- c) 5.81E+02
- d) 7.04E+02
- e) 8.53E+02
6) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 8.528E+02
- b) 1.033E+03
- c) 1.252E+03
- d) 1.516E+03
- e) 1.837E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
T2 R1[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
2) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 3.041E+02
- b) 3.684E+02
- c) 4.464E+02
- d) 5.408E+02
- e) 6.552E+02
- a) 2.756E+01 N·m2/C
- b) 3.032E+01 N·m2/C
- c) 3.335E+01 N·m2/C
- d) 3.668E+01 N·m2/C
- e) 4.035E+01 N·m2/C
- a) 4.024E+01 N·m2/C
- b) 4.426E+01 N·m2/C
- c) 4.868E+01 N·m2/C
- d) 5.355E+01 N·m2/C
- e) 5.891E+01 N·m2/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 4.63E+02
- b) 5.61E+02
- c) 6.80E+02
- d) 8.23E+02
- e) 9.98E+02
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
- a) 1.388E+01 N·m2/C
- b) 1.526E+01 N·m2/C
- c) 1.679E+01 N·m2/C
- d) 1.847E+01 N·m2/C
- e) 2.032E+01 N·m2/C
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
10) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?
- a) 3.604E+02 N/C
- b) 3.964E+02 N/C
- c) 4.360E+02 N/C
- d) 4.796E+02 N/C
- e) 5.276E+02 N/C
T2 R2[edit | edit source]
1) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 5.311E+02
- b) 6.434E+02
- c) 7.795E+02
- d) 9.444E+02
- e) 1.144E+03
2) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.59E+03
- b) 1.93E+03
- c) 2.34E+03
- d) 2.83E+03
- e) 3.43E+03
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
4) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
- a) 7.793E+01 N·m2/C
- b) 8.572E+01 N·m2/C
- c) 9.429E+01 N·m2/C
- d) 1.037E+02 N·m2/C
- e) 1.141E+02 N·m2/C
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
- a) 4.953E+01 N·m2/C
- b) 5.449E+01 N·m2/C
- c) 5.993E+01 N·m2/C
- d) 6.593E+01 N·m2/C
- e) 7.252E+01 N·m2/C
9) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?
- a) 7.825E+02 N/C
- b) 8.607E+02 N/C
- c) 9.468E+02 N/C
- d) 1.041E+03 N/C
- e) 1.146E+03 N/C
- a) 3.959E+01 N·m2/C
- b) 4.354E+01 N·m2/C
- c) 4.790E+01 N·m2/C
- d) 5.269E+01 N·m2/C
- e) 5.796E+01 N·m2/C
T2 S0[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
- a) 2.610E+03 V·m
- b) 2.871E+03 V·m
- c) 3.158E+03 V·m
- d) 3.474E+03 V·m
- e) 3.822E+03 V·m
- a) 6.270E+01 N·m2/C
- b) 6.897E+01 N·m2/C
- c) 7.586E+01 N·m2/C
- d) 8.345E+01 N·m2/C
- e) 9.179E+01 N·m2/C
- a) 7.081E+01 N·m2/C
- b) 7.789E+01 N·m2/C
- c) 8.568E+01 N·m2/C
- d) 9.425E+01 N·m2/C
- e) 1.037E+02 N·m2/C
- a) 2.214E+01 N·m2/C
- b) 2.436E+01 N·m2/C
- c) 2.679E+01 N·m2/C
- d) 2.947E+01 N·m2/C
- e) 3.242E+01 N·m2/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 3.799E+02
- b) 4.603E+02
- c) 5.576E+02
- d) 6.756E+02
- e) 8.185E+02
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 9.41E+03
- b) 1.14E+04
- c) 1.38E+04
- d) 1.67E+04
- e) 2.03E+04
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
T2 S1[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
- a) 4.521E+01 N·m2/C
- b) 4.973E+01 N·m2/C
- c) 5.470E+01 N·m2/C
- d) 6.017E+01 N·m2/C
- e) 6.619E+01 N·m2/C
4) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 3.60E+02
- b) 4.36E+02
- c) 5.29E+02
- d) 6.40E+02
- e) 7.76E+02
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
- a) 8.921E+01 N·m2/C
- b) 9.813E+01 N·m2/C
- c) 1.079E+02 N·m2/C
- d) 1.187E+02 N·m2/C
- e) 1.306E+02 N·m2/C
- a) 1.388E+01 N·m2/C
- b) 1.526E+01 N·m2/C
- c) 1.679E+01 N·m2/C
- d) 1.847E+01 N·m2/C
- e) 2.032E+01 N·m2/C
9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
- a) 7.200E+01 V·m
- b) 7.920E+01 V·m
- c) 8.712E+01 V·m
- d) 9.583E+01 V·m
- e) 1.054E+02 V·m
10) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 7.465E+02
- b) 9.044E+02
- c) 1.096E+03
- d) 1.327E+03
- e) 1.608E+03
T2 S2[edit | edit source]
1) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 5.40E+02
- b) 6.55E+02
- c) 7.93E+02
- d) 9.61E+02
- e) 1.16E+03
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
- a) 9.952E+03 V·m
- b) 1.095E+04 V·m
- c) 1.204E+04 V·m
- d) 1.325E+04 V·m
- e) 1.457E+04 V·m
- a) 6.614E+01 N·m2/C
- b) 7.275E+01 N·m2/C
- c) 8.003E+01 N·m2/C
- d) 8.803E+01 N·m2/C
- e) 9.683E+01 N·m2/C
4) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
- a) 2.214E+01 N·m2/C
- b) 2.436E+01 N·m2/C
- c) 2.679E+01 N·m2/C
- d) 2.947E+01 N·m2/C
- e) 3.242E+01 N·m2/C
- a) 9.823E+00 N·m2/C
- b) 1.080E+01 N·m2/C
- c) 1.189E+01 N·m2/C
- d) 1.307E+01 N·m2/C
- e) 1.438E+01 N·m2/C
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
8) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 2.454E+02
- b) 2.973E+02
- c) 3.601E+02
- d) 4.363E+02
- e) 5.286E+02
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
T2 T0[edit | edit source]
- a) 3.750E+01 N·m2/C
- b) 4.125E+01 N·m2/C
- c) 4.537E+01 N·m2/C
- d) 4.991E+01 N·m2/C
- e) 5.490E+01 N·m2/C
2) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.7 m from the center?
- a) 2.579E+02 N/C
- b) 2.837E+02 N/C
- c) 3.121E+02 N/C
- d) 3.433E+02 N/C
- e) 3.776E+02 N/C
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?
- a) 2.964E+00 N/C
- b) 3.260E+00 N/C
- c) 3.586E+00 N/C
- d) 3.944E+00 N/C
- e) 4.339E+00 N/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
- a) 2.067E+03 V·m
- b) 2.274E+03 V·m
- c) 2.501E+03 V·m
- d) 2.752E+03 V·m
- e) 3.027E+03 V·m
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 5.311E+02
- b) 6.434E+02
- c) 7.795E+02
- d) 9.444E+02
- e) 1.144E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 4.162E+02
- b) 5.042E+02
- c) 6.109E+02
- d) 7.401E+02
- e) 8.967E+02
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
8) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 T1[edit | edit source]
1) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 4.489E+02
- b) 5.438E+02
- c) 6.589E+02
- d) 7.983E+02
- e) 9.671E+02
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
- a) 3.750E+01 N·m2/C
- b) 4.125E+01 N·m2/C
- c) 4.537E+01 N·m2/C
- d) 4.991E+01 N·m2/C
- e) 5.490E+01 N·m2/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
5) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.4 m from the center of the shells?
- a) 8.580E+00 N/C
- b) 9.438E+00 N/C
- c) 1.038E+01 N/C
- d) 1.142E+01 N/C
- e) 1.256E+01 N/C
6) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?
- a) 7.825E+02 N/C
- b) 8.607E+02 N/C
- c) 9.468E+02 N/C
- d) 1.041E+03 N/C
- e) 1.146E+03 N/C
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
8) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 4.162E+02
- b) 5.042E+02
- c) 6.109E+02
- d) 7.401E+02
- e) 8.967E+02
9) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- a) 7.054E+03 V·m
- b) 7.759E+03 V·m
- c) 8.535E+03 V·m
- d) 9.388E+03 V·m
- e) 1.033E+04 V·m
T2 T2[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
2) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 3.417E+03
- b) 4.140E+03
- c) 5.016E+03
- d) 6.077E+03
- e) 7.362E+03
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
4) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
5) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.3 m from the center?
- a) 2.777E+02 N/C
- b) 3.055E+02 N/C
- c) 3.361E+02 N/C
- d) 3.697E+02 N/C
- e) 4.066E+02 N/C
6) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?
- a) 2.964E+00 N/C
- b) 3.260E+00 N/C
- c) 3.586E+00 N/C
- d) 3.944E+00 N/C
- e) 4.339E+00 N/C
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a) none of these are correct
- b)
- c)
- d)
- e)
8) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 3.799E+02
- b) 4.603E+02
- c) 5.576E+02
- d) 6.756E+02
- e) 8.185E+02
9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- a) 1.997E+03 V·m
- b) 2.197E+03 V·m
- c) 2.417E+03 V·m
- d) 2.659E+03 V·m
- e) 2.924E+03 V·m
- a) 2.012E+01 N·m2/C
- b) 2.213E+01 N·m2/C
- c) 2.435E+01 N·m2/C
- d) 2.678E+01 N·m2/C
- e) 2.946E+01 N·m2/C
T2 U0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?
- a) 2.988E+00 N/C
- b) 3.287E+00 N/C
- c) 3.616E+00 N/C
- d) 3.977E+00 N/C
- e) 4.375E+00 N/C
- a) 2.012E+01 N·m2/C
- b) 2.213E+01 N·m2/C
- c) 2.435E+01 N·m2/C
- d) 2.678E+01 N·m2/C
- e) 2.946E+01 N·m2/C
3) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?
- a) 6.411E+02 N/C
- b) 7.052E+02 N/C
- c) 7.757E+02 N/C
- d) 8.533E+02 N/C
- e) 9.386E+02 N/C
- a) 7.793E+01 N·m2/C
- b) 8.572E+01 N·m2/C
- c) 9.429E+01 N·m2/C
- d) 1.037E+02 N·m2/C
- e) 1.141E+02 N·m2/C
5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 9.41E+03
- b) 1.14E+04
- c) 1.38E+04
- d) 1.67E+04
- e) 2.03E+04
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 1.248E+03
- b) 1.512E+03
- c) 1.832E+03
- d) 2.220E+03
- e) 2.689E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
8) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
T2 U1[edit | edit source]
1) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 4.593E+03
- b) 5.564E+03
- c) 6.741E+03
- d) 8.167E+03
- e) 9.894E+03
2) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?
- a) 7.825E+02 N/C
- b) 8.607E+02 N/C
- c) 9.468E+02 N/C
- d) 1.041E+03 N/C
- e) 1.146E+03 N/C
- a) 2.012E+01 N·m2/C
- b) 2.213E+01 N·m2/C
- c) 2.435E+01 N·m2/C
- d) 2.678E+01 N·m2/C
- e) 2.946E+01 N·m2/C
4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- a) 1.096E+00 N/C
- b) 1.206E+00 N/C
- c) 1.327E+00 N/C
- d) 1.459E+00 N/C
- e) 1.605E+00 N/C
5) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
- a) 5.385E+01 N·m2/C
- b) 5.923E+01 N·m2/C
- c) 6.516E+01 N·m2/C
- d) 7.167E+01 N·m2/C
- e) 7.884E+01 N·m2/C
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
9) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 3.18E+03
- b) 3.85E+03
- c) 4.66E+03
- d) 5.65E+03
- e) 6.84E+03
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
T2 U2[edit | edit source]
- a) 3.750E+01 N·m2/C
- b) 4.125E+01 N·m2/C
- c) 4.537E+01 N·m2/C
- d) 4.991E+01 N·m2/C
- e) 5.490E+01 N·m2/C
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- a) 1.096E+00 N/C
- b) 1.206E+00 N/C
- c) 1.327E+00 N/C
- d) 1.459E+00 N/C
- e) 1.605E+00 N/C
4) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 4.63E+02
- b) 5.61E+02
- c) 6.80E+02
- d) 8.23E+02
- e) 9.98E+02
5) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 8.528E+02
- b) 1.033E+03
- c) 1.252E+03
- d) 1.516E+03
- e) 1.837E+03
6) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?
- a) 2.285E+01 N/C
- b) 2.514E+01 N/C
- c) 2.765E+01 N/C
- d) 3.042E+01 N/C
- e) 3.346E+01 N/C
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
- a) 3.712E+01 N·m2/C
- b) 4.083E+01 N·m2/C
- c) 4.491E+01 N·m2/C
- d) 4.940E+01 N·m2/C
- e) 5.434E+01 N·m2/C
10) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
T2 V0[edit | edit source]
- a) 2.079E+01 N·m2/C
- b) 2.287E+01 N·m2/C
- c) 2.516E+01 N·m2/C
- d) 2.768E+01 N·m2/C
- e) 3.044E+01 N·m2/C
- a) 5.989E+01 N·m2/C
- b) 6.588E+01 N·m2/C
- c) 7.247E+01 N·m2/C
- d) 7.971E+01 N·m2/C
- e) 8.769E+01 N·m2/C
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
- a) 2.067E+03 V·m
- b) 2.274E+03 V·m
- c) 2.501E+03 V·m
- d) 2.752E+03 V·m
- e) 3.027E+03 V·m
4) A non-conducting sphere of radius R=1.2 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.6 (r≤R) where a=2 nC·m-1.4. What is the magnitude of the electric field at a distance of 0.76 m from the center?
- a) 2.406E+01 N/C
- b) 2.646E+01 N/C
- c) 2.911E+01 N/C
- d) 3.202E+01 N/C
- e) 3.522E+01 N/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 6.546E+02
- b) 7.931E+02
- c) 9.609E+02
- d) 1.164E+03
- e) 1.410E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 7.933E+02
- b) 9.611E+02
- c) 1.164E+03
- d) 1.411E+03
- e) 1.709E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
10) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
T2 V1[edit | edit source]
1) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 8.528E+02
- b) 1.033E+03
- c) 1.252E+03
- d) 1.516E+03
- e) 1.837E+03
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
- a) 9.952E+03 V·m
- b) 1.095E+04 V·m
- c) 1.204E+04 V·m
- d) 1.325E+04 V·m
- e) 1.457E+04 V·m
3) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
4) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 4.021E+02
- b) 4.872E+02
- c) 5.902E+02
- d) 7.151E+02
- e) 8.663E+02
- a) 6.529E+01 N·m2/C
- b) 7.181E+01 N·m2/C
- c) 7.900E+01 N·m2/C
- d) 8.690E+01 N·m2/C
- e) 9.559E+01 N·m2/C
6) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?
- a) 3.604E+02 N/C
- b) 3.964E+02 N/C
- c) 4.360E+02 N/C
- d) 4.796E+02 N/C
- e) 5.276E+02 N/C
- a) 9.823E+00 N·m2/C
- b) 1.080E+01 N·m2/C
- c) 1.189E+01 N·m2/C
- d) 1.307E+01 N·m2/C
- e) 1.438E+01 N·m2/C
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
T2 V2[edit | edit source]
- a) 3.222E+01 N·m2/C
- b) 3.544E+01 N·m2/C
- c) 3.899E+01 N·m2/C
- d) 4.289E+01 N·m2/C
- e) 4.718E+01 N·m2/C
2) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 6.546E+02
- b) 7.931E+02
- c) 9.609E+02
- d) 1.164E+03
- e) 1.410E+03
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
- a) 7.200E+01 V·m
- b) 7.920E+01 V·m
- c) 8.712E+01 V·m
- d) 9.583E+01 V·m
- e) 1.054E+02 V·m
4) A non-conducting sphere of radius R=2.2 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=3 nC·m-1.6. What is the magnitude of the electric field at a distance of 0.86 m from the center?
- a) 4.874E+01 N/C
- b) 5.362E+01 N/C
- c) 5.898E+01 N/C
- d) 6.488E+01 N/C
- e) 7.137E+01 N/C
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
8) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 5.043E+02
- b) 6.109E+02
- c) 7.402E+02
- d) 8.967E+02
- e) 1.086E+03
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
- a) 5.978E+01 N·m2/C
- b) 6.576E+01 N·m2/C
- c) 7.233E+01 N·m2/C
- d) 7.957E+01 N·m2/C
- e) 8.752E+01 N·m2/C
T2 W0[edit | edit source]
- a) 5.385E+01 N·m2/C
- b) 5.923E+01 N·m2/C
- c) 6.516E+01 N·m2/C
- d) 7.167E+01 N·m2/C
- e) 7.884E+01 N·m2/C
- a) 4.730E+01 N·m2/C
- b) 5.203E+01 N·m2/C
- c) 5.723E+01 N·m2/C
- d) 6.295E+01 N·m2/C
- e) 6.925E+01 N·m2/C
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?
- a) 2.988E+00 N/C
- b) 3.287E+00 N/C
- c) 3.616E+00 N/C
- d) 3.977E+00 N/C
- e) 4.375E+00 N/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
- a) 4.820E+03 V·m
- b) 5.302E+03 V·m
- c) 5.832E+03 V·m
- d) 6.415E+03 V·m
- e) 7.057E+03 V·m
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 5.043E+02
- b) 6.109E+02
- c) 7.402E+02
- d) 8.967E+02
- e) 1.086E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.59E+03
- b) 1.93E+03
- c) 2.34E+03
- d) 2.83E+03
- e) 3.43E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
10) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
T2 W1[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
2) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- a) 1.096E+00 N/C
- b) 1.206E+00 N/C
- c) 1.327E+00 N/C
- d) 1.459E+00 N/C
- e) 1.605E+00 N/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 2.769E+03
- b) 3.354E+03
- c) 4.064E+03
- d) 4.923E+03
- e) 5.965E+03
- a) 3.328E+01 N·m2/C
- b) 3.660E+01 N·m2/C
- c) 4.026E+01 N·m2/C
- d) 4.429E+01 N·m2/C
- e) 4.872E+01 N·m2/C
7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
- a) 2.210E+04 V·m
- b) 2.431E+04 V·m
- c) 2.674E+04 V·m
- d) 2.941E+04 V·m
- e) 3.235E+04 V·m
- a) 3.924E+01 N·m2/C
- b) 4.316E+01 N·m2/C
- c) 4.748E+01 N·m2/C
- d) 5.222E+01 N·m2/C
- e) 5.745E+01 N·m2/C
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
10) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.13E+03
- b) 1.37E+03
- c) 1.66E+03
- d) 2.01E+03
- e) 2.44E+03
T2 W2[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?
- a) 2.837E+01 N/C
- b) 3.121E+01 N/C
- c) 3.433E+01 N/C
- d) 3.776E+01 N/C
- e) 4.154E+01 N/C
2) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.09E+03
- b) 1.32E+03
- c) 1.60E+03
- d) 1.94E+03
- e) 2.35E+03
- a) 8.457E+01 N·m2/C
- b) 9.303E+01 N·m2/C
- c) 1.023E+02 N·m2/C
- d) 1.126E+02 N·m2/C
- e) 1.238E+02 N·m2/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 7.933E+02
- b) 9.611E+02
- c) 1.164E+03
- d) 1.411E+03
- e) 1.709E+03
- a) 2.901E+01 N·m2/C
- b) 3.192E+01 N·m2/C
- c) 3.511E+01 N·m2/C
- d) 3.862E+01 N·m2/C
- e) 4.248E+01 N·m2/C
8) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- a) 1.128E+04 V·m
- b) 1.241E+04 V·m
- c) 1.365E+04 V·m
- d) 1.502E+04 V·m
- e) 1.652E+04 V·m
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
T2 X0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?
- a) 5.058E+00 N/C
- b) 5.564E+00 N/C
- c) 6.120E+00 N/C
- d) 6.732E+00 N/C
- e) 7.405E+00 N/C
- a) 8.921E+01 N·m2/C
- b) 9.813E+01 N·m2/C
- c) 1.079E+02 N·m2/C
- d) 1.187E+02 N·m2/C
- e) 1.306E+02 N·m2/C
3) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?
- a) 3.821E+02 N/C
- b) 4.203E+02 N/C
- c) 4.624E+02 N/C
- d) 5.086E+02 N/C
- e) 5.594E+02 N/C
- a) 1.992E+01 N·m2/C
- b) 2.192E+01 N·m2/C
- c) 2.411E+01 N·m2/C
- d) 2.652E+01 N·m2/C
- e) 2.917E+01 N·m2/C
5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 1.08E+03
- b) 1.30E+03
- c) 1.58E+03
- d) 1.91E+03
- e) 2.32E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 3.742E+02
- b) 4.534E+02
- c) 5.493E+02
- d) 6.655E+02
- e) 8.063E+02
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
T2 X1[edit | edit source]
1) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
- a) 3.695E+01 N·m2/C
- b) 4.065E+01 N·m2/C
- c) 4.472E+01 N·m2/C
- d) 4.919E+01 N·m2/C
- e) 5.411E+01 N·m2/C
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
4) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?
- a) 3.797E+01 N/C
- b) 4.177E+01 N/C
- c) 4.595E+01 N/C
- d) 5.054E+01 N/C
- e) 5.560E+01 N/C
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b)
- c)
- d)
- e) none of these are correct
7) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- a) 1.017E+01 N/C
- b) 1.118E+01 N/C
- c) 1.230E+01 N/C
- d) 1.353E+01 N/C
- e) 1.488E+01 N/C
8) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 5.91E+02
- b) 7.16E+02
- c) 8.68E+02
- d) 1.05E+03
- e) 1.27E+03
- a) 2.134E+01 N·m2/C
- b) 2.347E+01 N·m2/C
- c) 2.582E+01 N·m2/C
- d) 2.840E+01 N·m2/C
- e) 3.124E+01 N·m2/C
10) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 5.043E+02
- b) 6.109E+02
- c) 7.402E+02
- d) 8.967E+02
- e) 1.086E+03
T2 X2[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.6 m from the center of the shells?
- a) 1.114E+01 N/C
- b) 1.225E+01 N/C
- c) 1.347E+01 N/C
- d) 1.482E+01 N/C
- e) 1.630E+01 N/C
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c) none of these are correct
- d)
- e)
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
5) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
- a) 4.420E+01 N·m2/C
- b) 4.862E+01 N·m2/C
- c) 5.348E+01 N·m2/C
- d) 5.882E+01 N·m2/C
- e) 6.471E+01 N·m2/C
7) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 2.597E+03
- b) 3.147E+03
- c) 3.812E+03
- d) 4.619E+03
- e) 5.596E+03
8) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?
- a) 6.411E+02 N/C
- b) 7.052E+02 N/C
- c) 7.757E+02 N/C
- d) 8.533E+02 N/C
- e) 9.386E+02 N/C
- a) 3.959E+01 N·m2/C
- b) 4.354E+01 N·m2/C
- c) 4.790E+01 N·m2/C
- d) 5.269E+01 N·m2/C
- e) 5.796E+01 N·m2/C
10) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- a) 5.91E+02
- b) 7.16E+02
- c) 8.68E+02
- d) 1.05E+03
- e) 1.27E+03
T2 Y0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?
- a) 3.251E+01 N/C
- b) 3.577E+01 N/C
- c) 3.934E+01 N/C
- d) 4.328E+01 N/C
- e) 4.760E+01 N/C
- a) 4.125E+01 N·m2/C
- b) 4.537E+01 N·m2/C
- c) 4.991E+01 N·m2/C
- d) 5.490E+01 N·m2/C
- e) 6.039E+01 N·m2/C
- a) 4.809E+01 N·m2/C
- b) 5.290E+01 N·m2/C
- c) 5.819E+01 N·m2/C
- d) 6.401E+01 N·m2/C
- e) 7.041E+01 N·m2/C
4) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?
- a) 4.782E+02 N/C
- b) 5.260E+02 N/C
- c) 5.787E+02 N/C
- d) 6.365E+02 N/C
- e) 7.002E+02 N/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 1.704E+03
- b) 2.064E+03
- c) 2.501E+03
- d) 3.030E+03
- e) 3.671E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 2.454E+02
- b) 2.973E+02
- c) 3.601E+02
- d) 4.363E+02
- e) 5.286E+02
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
T2 Y1[edit | edit source]
- a) 7.876E+01 N·m2/C
- b) 8.664E+01 N·m2/C
- c) 9.531E+01 N·m2/C
- d) 1.048E+02 N·m2/C
- e) 1.153E+02 N·m2/C
2) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 5.664E+03
- b) 6.863E+03
- c) 8.314E+03
- d) 1.007E+04
- e) 1.220E+04
- a) 2.079E+01 N·m2/C
- b) 2.287E+01 N·m2/C
- c) 2.516E+01 N·m2/C
- d) 2.768E+01 N·m2/C
- e) 3.044E+01 N·m2/C
4) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
5) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?
- a) 3.251E+01 N/C
- b) 3.577E+01 N/C
- c) 3.934E+01 N/C
- d) 4.328E+01 N/C
- e) 4.760E+01 N/C
6) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
7) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 3.799E+02
- b) 4.603E+02
- c) 5.576E+02
- d) 6.756E+02
- e) 8.185E+02
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c) none of these are correct
- d)
- e)
9) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?
- a) 2.039E+01 N/C
- b) 2.243E+01 N/C
- c) 2.467E+01 N/C
- d) 2.714E+01 N/C
- e) 2.985E+01 N/C
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
T2 Y2[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- a)
- b)
- c) none of these are correct
- d)
- e)
- a) 4.420E+01 N·m2/C
- b) 4.862E+01 N·m2/C
- c) 5.348E+01 N·m2/C
- d) 5.882E+01 N·m2/C
- e) 6.471E+01 N·m2/C
3) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 6.546E+02
- b) 7.931E+02
- c) 9.609E+02
- d) 1.164E+03
- e) 1.410E+03
4) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 4.522E+02
- b) 5.478E+02
- c) 6.637E+02
- d) 8.041E+02
- e) 9.742E+02
- a) 5.978E+01 N·m2/C
- b) 6.576E+01 N·m2/C
- c) 7.233E+01 N·m2/C
- d) 7.957E+01 N·m2/C
- e) 8.752E+01 N·m2/C
6) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?
- a) 6.411E+02 N/C
- b) 7.052E+02 N/C
- c) 7.757E+02 N/C
- d) 8.533E+02 N/C
- e) 9.386E+02 N/C
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d)
- e) none of these are correct
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
10) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.9 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.1 m from the center of the shells?
- a) 5.297E+00 N/C
- b) 5.827E+00 N/C
- c) 6.409E+00 N/C
- d) 7.050E+00 N/C
- e) 7.755E+00 N/C
T2 Z0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- a) 1.017E+01 N/C
- b) 1.118E+01 N/C
- c) 1.230E+01 N/C
- d) 1.353E+01 N/C
- e) 1.488E+01 N/C
- a) 3.249E+01 N·m2/C
- b) 3.574E+01 N·m2/C
- c) 3.931E+01 N·m2/C
- d) 4.324E+01 N·m2/C
- e) 4.757E+01 N·m2/C
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
- a) 7.200E+01 V·m
- b) 7.920E+01 V·m
- c) 8.712E+01 V·m
- d) 9.583E+01 V·m
- e) 1.054E+02 V·m
- a) 8.314E+01 N·m2/C
- b) 9.146E+01 N·m2/C
- c) 1.006E+02 N·m2/C
- d) 1.107E+02 N·m2/C
- e) 1.217E+02 N·m2/C
5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 3.232E+03
- b) 3.915E+03
- c) 4.743E+03
- d) 5.747E+03
- e) 6.962E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 5.043E+02
- b) 6.109E+02
- c) 7.402E+02
- d) 8.967E+02
- e) 1.086E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b)
- c)
- d) none of these are correct
- e)
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b)
- c)
- d) none of these are correct
- e)
10) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
T2 Z1[edit | edit source]
1) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b)
- c)
- d)
- e) none of these are correct
2) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 5.610E+02
- b) 6.796E+02
- c) 8.234E+02
- d) 9.975E+02
- e) 1.209E+03
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
- a) 9.952E+03 V·m
- b) 1.095E+04 V·m
- c) 1.204E+04 V·m
- d) 1.325E+04 V·m
- e) 1.457E+04 V·m
4) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 5.311E+02
- b) 6.434E+02
- c) 7.795E+02
- d) 9.444E+02
- e) 1.144E+03
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a)
- b) none of these are correct
- c)
- d)
- e)
- a) 5.989E+01 N·m2/C
- b) 6.588E+01 N·m2/C
- c) 7.247E+01 N·m2/C
- d) 7.971E+01 N·m2/C
- e) 8.769E+01 N·m2/C
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b) none of these are correct
- c)
- d)
- e)
8) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?
- a) 9.144E+00 N/C
- b) 1.006E+01 N/C
- c) 1.106E+01 N/C
- d) 1.217E+01 N/C
- e) 1.339E+01 N/C
- a) 5.000E+01 N·m2/C
- b) 5.500E+01 N·m2/C
- c) 6.050E+01 N·m2/C
- d) 6.656E+01 N·m2/C
- e) 7.321E+01 N·m2/C
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a) none of these are correct
- b)
- c)
- d)
- e)
T2 Z2[edit | edit source]
1) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- a)
- b)
- c)
- d) none of these are correct
- e)
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
3) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- a)
- b) none of these are correct
- c)
- d)
- e)
- a) 8.314E+01 N·m2/C
- b) 9.146E+01 N·m2/C
- c) 1.006E+02 N·m2/C
- d) 1.107E+02 N·m2/C
- e) 1.217E+02 N·m2/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- a) 6.546E+02
- b) 7.931E+02
- c) 9.609E+02
- d) 1.164E+03
- e) 1.410E+03
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- a) none of these are correct
- b)
- c)
- d)
- e)
7) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- a) 5.311E+02
- b) 6.434E+02
- c) 7.795E+02
- d) 9.444E+02
- e) 1.144E+03
8) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- a) 7.054E+03 V·m
- b) 7.759E+03 V·m
- c) 8.535E+03 V·m
- d) 9.388E+03 V·m
- e) 1.033E+04 V·m
9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?
- a) 9.144E+00 N/C
- b) 1.006E+01 N/C
- c) 1.106E+01 N/C
- d) 1.217E+01 N/C
- e) 1.339E+01 N/C
- a) 1.891E+01 N·m2/C
- b) 2.080E+01 N·m2/C
- c) 2.288E+01 N·m2/C
- d) 2.517E+01 N·m2/C
- e) 2.768E+01 N·m2/C
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- blank page
- of 10 blank lines to separate exams from keys
- of 10 blank lines to separate exams from keys
- of 10 blank lines to separate exams from keys
- of 10 blank lines to separate exams from keys
- of 10 blank lines to separate exams from keys
- of 10 blank lines to separate exams from keys
- of 10 blank lines to separate exams from keys
- of 10 blank lines to separate exams from keys
- of 10 blank lines to separate exams from keys
- of 10 blank lines to separate exams from keys
Key: A0[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
- -a) 8.545E+01 V·m
- -b) 9.400E+01 V·m
- -c) 1.034E+02 V·m
- -d) 1.137E+02 V·m
- +e) 1.251E+02 V·m
- -a) 4.777E+01 N·m2/C
- -b) 5.254E+01 N·m2/C
- -c) 5.780E+01 N·m2/C
- +d) 6.358E+01 N·m2/C
- -e) 6.993E+01 N·m2/C
- -a) 4.125E+01 N·m2/C
- -b) 4.537E+01 N·m2/C
- -c) 4.991E+01 N·m2/C
- +d) 5.490E+01 N·m2/C
- -e) 6.039E+01 N·m2/C
- -a) 5.606E+01 N·m2/C
- -b) 6.167E+01 N·m2/C
- -c) 6.784E+01 N·m2/C
- +d) 7.462E+01 N·m2/C
- -e) 8.208E+01 N·m2/C
5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 6.69E+03
- -b) 8.10E+03
- -c) 9.81E+03
- -d) 1.19E+04
- +e) 1.44E+04
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 4.593E+03
- -b) 5.564E+03
- +c) 6.741E+03
- -d) 8.167E+03
- -e) 9.894E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
8) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
10) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
Key: A1[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
2) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
- -a) 6.364E+01 N·m2/C
- -b) 7.000E+01 N·m2/C
- +c) 7.700E+01 N·m2/C
- -d) 8.470E+01 N·m2/C
- -e) 9.317E+01 N·m2/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 5.40E+02
- -b) 6.55E+02
- -c) 7.93E+02
- -d) 9.61E+02
- +e) 1.16E+03
6) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
- -a) 2.610E+03 V·m
- -b) 2.871E+03 V·m
- +c) 3.158E+03 V·m
- -d) 3.474E+03 V·m
- -e) 3.822E+03 V·m
7) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 4.593E+03
- -b) 5.564E+03
- +c) 6.741E+03
- -d) 8.167E+03
- -e) 9.894E+03
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
- -a) 5.606E+01 N·m2/C
- -b) 6.167E+01 N·m2/C
- -c) 6.784E+01 N·m2/C
- +d) 7.462E+01 N·m2/C
- -e) 8.208E+01 N·m2/C
- -a) 5.439E+01 N·m2/C
- -b) 5.983E+01 N·m2/C
- -c) 6.581E+01 N·m2/C
- +d) 7.239E+01 N·m2/C
- -e) 7.963E+01 N·m2/C
Key: A2[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
2) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 6.201E+02
- -b) 7.513E+02
- -c) 9.102E+02
- +d) 1.103E+03
- -e) 1.336E+03
- -a) 3.924E+01 N·m2/C
- -b) 4.316E+01 N·m2/C
- -c) 4.748E+01 N·m2/C
- +d) 5.222E+01 N·m2/C
- -e) 5.745E+01 N·m2/C
4) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 4.69E+03
- -b) 5.69E+03
- +c) 6.89E+03
- -d) 8.35E+03
- -e) 1.01E+04
5) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- -c)
- -d) none of these are correct
- +e)
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a) none of these are correct
- +b)
- -c)
- -d)
- -e)
7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
- -a) 1.969E+02 V·m
- -b) 2.166E+02 V·m
- -c) 2.383E+02 V·m
- -d) 2.621E+02 V·m
- +e) 2.883E+02 V·m
8) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b)
- -c)
- -d) none of these are correct
- +e)
- -a) 2.012E+01 N·m2/C
- -b) 2.213E+01 N·m2/C
- -c) 2.435E+01 N·m2/C
- -d) 2.678E+01 N·m2/C
- +e) 2.946E+01 N·m2/C
- -a) 6.614E+01 N·m2/C
- +b) 7.275E+01 N·m2/C
- -c) 8.003E+01 N·m2/C
- -d) 8.803E+01 N·m2/C
- -e) 9.683E+01 N·m2/C
Key: B0[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=6), and (x=7, y=6), where x and y are measured in meters. The electric field is,
- +a) 3.337E+03 V·m
- -b) 3.670E+03 V·m
- -c) 4.037E+03 V·m
- -d) 4.441E+03 V·m
- -e) 4.885E+03 V·m
- +a) 7.876E+01 N·m2/C
- -b) 8.664E+01 N·m2/C
- -c) 9.531E+01 N·m2/C
- -d) 1.048E+02 N·m2/C
- -e) 1.153E+02 N·m2/C
- -a) 3.662E+01 N·m2/C
- +b) 4.028E+01 N·m2/C
- -c) 4.430E+01 N·m2/C
- -d) 4.873E+01 N·m2/C
- -e) 5.361E+01 N·m2/C
4) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?
- +a) 1.383E+02 N/C
- -b) 1.522E+02 N/C
- -c) 1.674E+02 N/C
- -d) 1.841E+02 N/C
- -e) 2.025E+02 N/C
5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 9.41E+03
- -b) 1.14E+04
- +c) 1.38E+04
- -d) 1.67E+04
- -e) 2.03E+04
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 4.489E+02
- -b) 5.438E+02
- -c) 6.589E+02
- -d) 7.983E+02
- +e) 9.671E+02
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
9) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
Key: B1[edit | edit source]
1) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- +a) 8.528E+02
- -b) 1.033E+03
- -c) 1.252E+03
- -d) 1.516E+03
- -e) 1.837E+03
2) A non-conducting sphere of radius R=2.2 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=3 nC·m-1.6. What is the magnitude of the electric field at a distance of 0.86 m from the center?
- -a) 4.874E+01 N/C
- +b) 5.362E+01 N/C
- -c) 5.898E+01 N/C
- -d) 6.488E+01 N/C
- -e) 7.137E+01 N/C
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
- -a) 6.898E+01 N·m2/C
- +b) 7.588E+01 N·m2/C
- -c) 8.347E+01 N·m2/C
- -d) 9.181E+01 N·m2/C
- -e) 1.010E+02 N·m2/C
5) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
- +a) 3.429E+03 V·m
- -b) 3.771E+03 V·m
- -c) 4.149E+03 V·m
- -d) 4.564E+03 V·m
- -e) 5.020E+03 V·m
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- +a)
- -b)
- -c)
- -d) none of these are correct
- -e)
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
- +a) 8.921E+01 N·m2/C
- -b) 9.813E+01 N·m2/C
- -c) 1.079E+02 N·m2/C
- -d) 1.187E+02 N·m2/C
- -e) 1.306E+02 N·m2/C
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
10) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 4.63E+03
- +b) 5.61E+03
- -c) 6.79E+03
- -d) 8.23E+03
- -e) 9.97E+03
Key: B2[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.7 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 5.6m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 40° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- -a) 3.712E+01 N·m2/C
- -b) 4.083E+01 N·m2/C
- +c) 4.491E+01 N·m2/C
- -d) 4.940E+01 N·m2/C
- -e) 5.434E+01 N·m2/C
2) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 9.41E+02
- +b) 1.14E+03
- -c) 1.38E+03
- -d) 1.67E+03
- -e) 2.03E+03
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
- -a) 2.210E+04 V·m
- +b) 2.431E+04 V·m
- -c) 2.674E+04 V·m
- -d) 2.941E+04 V·m
- -e) 3.235E+04 V·m
4) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 6.731E+02
- +b) 8.154E+02
- -c) 9.879E+02
- -d) 1.197E+03
- -e) 1.450E+03
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- +a)
- -b) none of these are correct
- -c)
- -d)
- -e)
- -a) 1.737E+01 N·m2/C
- -b) 1.910E+01 N·m2/C
- -c) 2.101E+01 N·m2/C
- -d) 2.311E+01 N·m2/C
- +e) 2.543E+01 N·m2/C
8) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?
- -a) 2.039E+01 N/C
- -b) 2.243E+01 N/C
- +c) 2.467E+01 N/C
- -d) 2.714E+01 N/C
- -e) 2.985E+01 N/C
9) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a) none of these are correct
- -b)
- -c)
- +d)
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
Key: C0[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
- -a) 2.067E+03 V·m
- -b) 2.274E+03 V·m
- +c) 2.501E+03 V·m
- -d) 2.752E+03 V·m
- -e) 3.027E+03 V·m
- -a) 9.823E+00 N·m2/C
- +b) 1.080E+01 N·m2/C
- -c) 1.189E+01 N·m2/C
- -d) 1.307E+01 N·m2/C
- -e) 1.438E+01 N·m2/C
- -a) 6.614E+01 N·m2/C
- +b) 7.275E+01 N·m2/C
- -c) 8.003E+01 N·m2/C
- -d) 8.803E+01 N·m2/C
- -e) 9.683E+01 N·m2/C
4) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?
- -a) 3.821E+02 N/C
- -b) 4.203E+02 N/C
- -c) 4.624E+02 N/C
- +d) 5.086E+02 N/C
- -e) 5.594E+02 N/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.29E+03
- -b) 1.56E+03
- -c) 1.89E+03
- +d) 2.29E+03
- -e) 2.77E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 5.043E+02
- -b) 6.109E+02
- -c) 7.402E+02
- +d) 8.967E+02
- -e) 1.086E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- -c) none of these are correct
- -d)
- +e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
9) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
10) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
Key: C1[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- -a) 3.662E+01 N·m2/C
- +b) 4.028E+01 N·m2/C
- -c) 4.430E+01 N·m2/C
- -d) 4.873E+01 N·m2/C
- -e) 5.361E+01 N·m2/C
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
3) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?
- -a) 2.274E+02 N/C
- -b) 2.501E+02 N/C
- +c) 2.751E+02 N/C
- -d) 3.026E+02 N/C
- -e) 3.329E+02 N/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- -c)
- -d) none of these are correct
- +e)
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.59E+03
- -b) 1.93E+03
- +c) 2.34E+03
- -d) 2.83E+03
- -e) 3.43E+03
6) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- -a) 4.286E+03 V·m
- -b) 4.714E+03 V·m
- +c) 5.186E+03 V·m
- -d) 5.704E+03 V·m
- -e) 6.275E+03 V·m
7) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 4.593E+03
- -b) 5.564E+03
- +c) 6.741E+03
- -d) 8.167E+03
- -e) 9.894E+03
8) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
- +a) 3.074E+01 N·m2/C
- -b) 3.382E+01 N·m2/C
- -c) 3.720E+01 N·m2/C
- -d) 4.092E+01 N·m2/C
- -e) 4.501E+01 N·m2/C
10) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
Key: C2[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- -a) 3.662E+01 N·m2/C
- +b) 4.028E+01 N·m2/C
- -c) 4.430E+01 N·m2/C
- -d) 4.873E+01 N·m2/C
- -e) 5.361E+01 N·m2/C
2) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
4) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
- +a) 5.978E+01 N·m2/C
- -b) 6.576E+01 N·m2/C
- -c) 7.233E+01 N·m2/C
- -d) 7.957E+01 N·m2/C
- -e) 8.752E+01 N·m2/C
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.09E+03
- -b) 1.32E+03
- -c) 1.60E+03
- -d) 1.94E+03
- +e) 2.35E+03
7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
- -a) 8.545E+01 V·m
- -b) 9.400E+01 V·m
- -c) 1.034E+02 V·m
- -d) 1.137E+02 V·m
- +e) 1.251E+02 V·m
8) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?
- -a) 2.274E+02 N/C
- -b) 2.501E+02 N/C
- +c) 2.751E+02 N/C
- -d) 3.026E+02 N/C
- -e) 3.329E+02 N/C
9) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 5.043E+02
- -b) 6.109E+02
- -c) 7.402E+02
- +d) 8.967E+02
- -e) 1.086E+03
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
Key: D0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?
- -a) 3.251E+01 N/C
- -b) 3.577E+01 N/C
- -c) 3.934E+01 N/C
- -d) 4.328E+01 N/C
- +e) 4.760E+01 N/C
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- -a) 7.054E+03 V·m
- -b) 7.759E+03 V·m
- -c) 8.535E+03 V·m
- -d) 9.388E+03 V·m
- +e) 1.033E+04 V·m
- -a) 2.756E+01 N·m2/C
- -b) 3.032E+01 N·m2/C
- -c) 3.335E+01 N·m2/C
- -d) 3.668E+01 N·m2/C
- +e) 4.035E+01 N·m2/C
- +a) 7.793E+01 N·m2/C
- -b) 8.572E+01 N·m2/C
- -c) 9.429E+01 N·m2/C
- -d) 1.037E+02 N·m2/C
- -e) 1.141E+02 N·m2/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 4.489E+02
- -b) 5.438E+02
- -c) 6.589E+02
- -d) 7.983E+02
- +e) 9.671E+02
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 9.205E+02
- -b) 1.115E+03
- +c) 1.351E+03
- -d) 1.637E+03
- -e) 1.983E+03
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b)
- -c)
- +d)
- -e) none of these are correct
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
10) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
Key: D1[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
2) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- +a)
- -b) none of these are correct
- -c)
- -d)
- -e)
3) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 5.610E+02
- -b) 6.796E+02
- -c) 8.234E+02
- -d) 9.975E+02
- -e) 1.209E+03
- -a) 5.408E+01 N·m2/C
- +b) 5.949E+01 N·m2/C
- -c) 6.544E+01 N·m2/C
- -d) 7.198E+01 N·m2/C
- -e) 7.918E+01 N·m2/C
5) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 1.704E+03
- -b) 2.064E+03
- -c) 2.501E+03
- +d) 3.030E+03
- -e) 3.671E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a) none of these are correct
- -b)
- -c)
- +d)
- -e)
- -a) 2.186E+01 N·m2/C
- -b) 2.404E+01 N·m2/C
- +c) 2.645E+01 N·m2/C
- -d) 2.909E+01 N·m2/C
- -e) 3.200E+01 N·m2/C
9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?
- -a) 2.837E+01 N/C
- -b) 3.121E+01 N/C
- -c) 3.433E+01 N/C
- -d) 3.776E+01 N/C
- +e) 4.154E+01 N/C
10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- -a) 1.997E+03 V·m
- +b) 2.197E+03 V·m
- -c) 2.417E+03 V·m
- -d) 2.659E+03 V·m
- -e) 2.924E+03 V·m
Key: D2[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
2) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a) none of these are correct
- +b)
- -c)
- -d)
- -e)
3) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- +a) 8.528E+02
- -b) 1.033E+03
- -c) 1.252E+03
- -d) 1.516E+03
- -e) 1.837E+03
4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.6 m from the center of the shells?
- -a) 9.642E+00 N/C
- -b) 1.061E+01 N/C
- +c) 1.167E+01 N/C
- -d) 1.283E+01 N/C
- -e) 1.412E+01 N/C
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 4.021E+02
- -b) 4.872E+02
- -c) 5.902E+02
- -d) 7.151E+02
- -e) 8.663E+02
- +a) 8.921E+01 N·m2/C
- -b) 9.813E+01 N·m2/C
- -c) 1.079E+02 N·m2/C
- -d) 1.187E+02 N·m2/C
- -e) 1.306E+02 N·m2/C
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b) none of these are correct
- -c)
- +d)
- -e)
- -a) 3.924E+01 N·m2/C
- -b) 4.316E+01 N·m2/C
- -c) 4.748E+01 N·m2/C
- +d) 5.222E+01 N·m2/C
- -e) 5.745E+01 N·m2/C
10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
- -a) 2.694E+03 V·m
- -b) 2.963E+03 V·m
- -c) 3.259E+03 V·m
- +d) 3.585E+03 V·m
- -e) 3.944E+03 V·m
Key: E0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.4 m from the center of the shells?
- -a) 8.580E+00 N/C
- -b) 9.438E+00 N/C
- -c) 1.038E+01 N/C
- +d) 1.142E+01 N/C
- -e) 1.256E+01 N/C
- +a) 7.876E+01 N·m2/C
- -b) 8.664E+01 N·m2/C
- -c) 9.531E+01 N·m2/C
- -d) 1.048E+02 N·m2/C
- -e) 1.153E+02 N·m2/C
- -a) 1.737E+01 N·m2/C
- -b) 1.910E+01 N·m2/C
- -c) 2.101E+01 N·m2/C
- -d) 2.311E+01 N·m2/C
- +e) 2.543E+01 N·m2/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
- -a) 1.206E+03 V·m
- +b) 1.326E+03 V·m
- -c) 1.459E+03 V·m
- -d) 1.605E+03 V·m
- -e) 1.765E+03 V·m
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 2.454E+02
- -b) 2.973E+02
- -c) 3.601E+02
- +d) 4.363E+02
- -e) 5.286E+02
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 6.69E+03
- -b) 8.10E+03
- -c) 9.81E+03
- -d) 1.19E+04
- +e) 1.44E+04
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a) none of these are correct
- +b)
- -c)
- -d)
- -e)
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
Key: E1[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?
- +a) 9.592E+00 N/C
- -b) 1.055E+01 N/C
- -c) 1.161E+01 N/C
- -d) 1.277E+01 N/C
- -e) 1.404E+01 N/C
2) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- +a)
- -b) none of these are correct
- -c)
- -d)
- -e)
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b) none of these are correct
- -c)
- -d)
- -e)
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
- -a) 1.969E+02 V·m
- -b) 2.166E+02 V·m
- -c) 2.383E+02 V·m
- -d) 2.621E+02 V·m
- +e) 2.883E+02 V·m
- -a) 1.992E+01 N·m2/C
- -b) 2.192E+01 N·m2/C
- +c) 2.411E+01 N·m2/C
- -d) 2.652E+01 N·m2/C
- -e) 2.917E+01 N·m2/C
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.13E+03
- -b) 1.37E+03
- -c) 1.66E+03
- +d) 2.01E+03
- -e) 2.44E+03
- -a) 9.823E+00 N·m2/C
- +b) 1.080E+01 N·m2/C
- -c) 1.189E+01 N·m2/C
- -d) 1.307E+01 N·m2/C
- -e) 1.438E+01 N·m2/C
8) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 5.610E+02
- -b) 6.796E+02
- -c) 8.234E+02
- -d) 9.975E+02
- -e) 1.209E+03
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b) none of these are correct
- -c)
- +d)
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- -c)
- +d)
- -e) none of these are correct
Key: E2[edit | edit source]
1) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 4.162E+02
- -b) 5.042E+02
- -c) 6.109E+02
- -d) 7.401E+02
- -e) 8.967E+02
2) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b) none of these are correct
- -c)
- +d)
- -e)
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
- -a) 2.610E+03 V·m
- -b) 2.871E+03 V·m
- +c) 3.158E+03 V·m
- -d) 3.474E+03 V·m
- -e) 3.822E+03 V·m
- -a) 4.988E+01 N·m2/C
- -b) 5.487E+01 N·m2/C
- -c) 6.035E+01 N·m2/C
- -d) 6.639E+01 N·m2/C
- +e) 7.303E+01 N·m2/C
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
6) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
7) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.08E+03
- -b) 1.30E+03
- -c) 1.58E+03
- +d) 1.91E+03
- -e) 2.32E+03
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.5 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?
- -a) 2.601E+01 N/C
- -b) 2.861E+01 N/C
- -c) 3.147E+01 N/C
- +d) 3.462E+01 N/C
- -e) 3.808E+01 N/C
- +a) 5.385E+01 N·m2/C
- -b) 5.923E+01 N·m2/C
- -c) 6.516E+01 N·m2/C
- -d) 7.167E+01 N·m2/C
- -e) 7.884E+01 N·m2/C
Key: F0[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.3 m, z=z0=1.8 m, and z=z1=4.9 m. The surfaces in the yz plane each have area 8.1m2. Those in the xy plane have area 7.0m2 ,and those in the zx plane have area 8.4m2. An electric field has the xyz components (0, 9.2, 7.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- -a) 6.364E+01 N·m2/C
- -b) 7.000E+01 N·m2/C
- +c) 7.700E+01 N·m2/C
- -d) 8.470E+01 N·m2/C
- -e) 9.317E+01 N·m2/C
2) A non-conducting sphere of radius R=1.4 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.6 (r≤R) where a=3 nC·m-1.4. What is the magnitude of the electric field at a distance of 1.3 m from the center?
- +a) 1.457E+02 N/C
- -b) 1.603E+02 N/C
- -c) 1.763E+02 N/C
- -d) 1.939E+02 N/C
- -e) 2.133E+02 N/C
- -a) 2.134E+01 N·m2/C
- -b) 2.347E+01 N·m2/C
- +c) 2.582E+01 N·m2/C
- -d) 2.840E+01 N·m2/C
- -e) 3.124E+01 N·m2/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- -a) 7.054E+03 V·m
- -b) 7.759E+03 V·m
- -c) 8.535E+03 V·m
- -d) 9.388E+03 V·m
- +e) 1.033E+04 V·m
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.09E+03
- -b) 1.32E+03
- -c) 1.60E+03
- -d) 1.94E+03
- +e) 2.35E+03
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 5.610E+02
- -b) 6.796E+02
- -c) 8.234E+02
- -d) 9.975E+02
- -e) 1.209E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
Key: F1[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
- -a) 2.210E+04 V·m
- +b) 2.431E+04 V·m
- -c) 2.674E+04 V·m
- -d) 2.941E+04 V·m
- -e) 3.235E+04 V·m
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- -c)
- +d)
- -e) none of these are correct
- +a) 5.978E+01 N·m2/C
- -b) 6.576E+01 N·m2/C
- -c) 7.233E+01 N·m2/C
- -d) 7.957E+01 N·m2/C
- -e) 8.752E+01 N·m2/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b) none of these are correct
- -c)
- +d)
- -e)
- -a) 1.737E+01 N·m2/C
- -b) 1.910E+01 N·m2/C
- -c) 2.101E+01 N·m2/C
- -d) 2.311E+01 N·m2/C
- +e) 2.543E+01 N·m2/C
6) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?
- +a) 3.797E+01 N/C
- -b) 4.177E+01 N/C
- -c) 4.595E+01 N/C
- -d) 5.054E+01 N/C
- -e) 5.560E+01 N/C
7) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 9.41E+02
- +b) 1.14E+03
- -c) 1.38E+03
- -d) 1.67E+03
- -e) 2.03E+03
8) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 4.027E+02
- -b) 4.879E+02
- +c) 5.911E+02
- -d) 7.162E+02
- -e) 8.676E+02
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b) none of these are correct
- -c)
- -d)
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
Key: F2[edit | edit source]
1) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 3.13E+03
- -b) 3.79E+03
- -c) 4.59E+03
- -d) 5.56E+03
- +e) 6.74E+03
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- +a)
- -b) none of these are correct
- -c)
- -d)
- -e)
- +a) 3.074E+01 N·m2/C
- -b) 3.382E+01 N·m2/C
- -c) 3.720E+01 N·m2/C
- -d) 4.092E+01 N·m2/C
- -e) 4.501E+01 N·m2/C
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- -c)
- -d) none of these are correct
- +e)
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
- -a) 6.270E+01 N·m2/C
- -b) 6.897E+01 N·m2/C
- -c) 7.586E+01 N·m2/C
- -d) 8.345E+01 N·m2/C
- +e) 9.179E+01 N·m2/C
8) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- -a) 4.286E+03 V·m
- -b) 4.714E+03 V·m
- +c) 5.186E+03 V·m
- -d) 5.704E+03 V·m
- -e) 6.275E+03 V·m
9) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 4.162E+02
- -b) 5.042E+02
- -c) 6.109E+02
- -d) 7.401E+02
- -e) 8.967E+02
10) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?
- -a) 1.123E+02 N/C
- -b) 1.235E+02 N/C
- +c) 1.358E+02 N/C
- -d) 1.494E+02 N/C
- -e) 1.644E+02 N/C
Key: G0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- +a) 1.017E+01 N/C
- -b) 1.118E+01 N/C
- -c) 1.230E+01 N/C
- -d) 1.353E+01 N/C
- -e) 1.488E+01 N/C
- -a) 3.662E+01 N·m2/C
- +b) 4.028E+01 N·m2/C
- -c) 4.430E+01 N·m2/C
- -d) 4.873E+01 N·m2/C
- -e) 5.361E+01 N·m2/C
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is,
- -a) 8.731E+02 V·m
- -b) 9.604E+02 V·m
- -c) 1.056E+03 V·m
- +d) 1.162E+03 V·m
- -e) 1.278E+03 V·m
- -a) 1.891E+01 N·m2/C
- -b) 2.080E+01 N·m2/C
- +c) 2.288E+01 N·m2/C
- -d) 2.517E+01 N·m2/C
- -e) 2.768E+01 N·m2/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.59E+03
- -b) 1.93E+03
- +c) 2.34E+03
- -d) 2.83E+03
- -e) 3.43E+03
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- +a) 2.769E+03
- -b) 3.354E+03
- -c) 4.064E+03
- -d) 4.923E+03
- -e) 5.965E+03
7) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
Key: G1[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- -a) 4.286E+03 V·m
- -b) 4.714E+03 V·m
- +c) 5.186E+03 V·m
- -d) 5.704E+03 V·m
- -e) 6.275E+03 V·m
- -a) 7.081E+01 N·m2/C
- -b) 7.789E+01 N·m2/C
- +c) 8.568E+01 N·m2/C
- -d) 9.425E+01 N·m2/C
- -e) 1.037E+02 N·m2/C
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
- -a) 6.270E+01 N·m2/C
- -b) 6.897E+01 N·m2/C
- -c) 7.586E+01 N·m2/C
- -d) 8.345E+01 N·m2/C
- +e) 9.179E+01 N·m2/C
5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 6.69E+03
- -b) 8.10E+03
- -c) 9.81E+03
- -d) 1.19E+04
- +e) 1.44E+04
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- -c)
- +d)
- -e) none of these are correct
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
8) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 3.417E+03
- -b) 4.140E+03
- -c) 5.016E+03
- +d) 6.077E+03
- -e) 7.362E+03
9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?
- -a) 2.837E+01 N/C
- -b) 3.121E+01 N/C
- -c) 3.433E+01 N/C
- -d) 3.776E+01 N/C
- +e) 4.154E+01 N/C
10) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- -c) none of these are correct
- -d)
- +e)
Key: G2[edit | edit source]
1) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 1.362E+03
- -b) 1.650E+03
- +c) 2.000E+03
- -d) 2.423E+03
- -e) 2.935E+03
2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.6 m from the center of the shells?
- -a) 6.641E+00 N/C
- -b) 7.305E+00 N/C
- +c) 8.036E+00 N/C
- -d) 8.839E+00 N/C
- -e) 9.723E+00 N/C
3) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.13E+03
- -b) 1.37E+03
- -c) 1.66E+03
- +d) 2.01E+03
- -e) 2.44E+03
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
- -a) 4.820E+03 V·m
- -b) 5.302E+03 V·m
- +c) 5.832E+03 V·m
- -d) 6.415E+03 V·m
- -e) 7.057E+03 V·m
- -a) 4.953E+01 N·m2/C
- -b) 5.449E+01 N·m2/C
- -c) 5.993E+01 N·m2/C
- -d) 6.593E+01 N·m2/C
- +e) 7.252E+01 N·m2/C
- +a) 8.921E+01 N·m2/C
- -b) 9.813E+01 N·m2/C
- -c) 1.079E+02 N·m2/C
- -d) 1.187E+02 N·m2/C
- -e) 1.306E+02 N·m2/C
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- +a)
- -b) none of these are correct
- -c)
- -d)
- -e)
Key: H0[edit | edit source]
1) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?
- +a) 3.797E+01 N/C
- -b) 4.177E+01 N/C
- -c) 4.595E+01 N/C
- -d) 5.054E+01 N/C
- -e) 5.560E+01 N/C
- -a) 1.388E+01 N·m2/C
- +b) 1.526E+01 N·m2/C
- -c) 1.679E+01 N·m2/C
- -d) 1.847E+01 N·m2/C
- -e) 2.032E+01 N·m2/C
- -a) 2.186E+01 N·m2/C
- -b) 2.404E+01 N·m2/C
- +c) 2.645E+01 N·m2/C
- -d) 2.909E+01 N·m2/C
- -e) 3.200E+01 N·m2/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
- +a) 3.429E+03 V·m
- -b) 3.771E+03 V·m
- -c) 4.149E+03 V·m
- -d) 4.564E+03 V·m
- -e) 5.020E+03 V·m
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 3.630E+02
- +b) 4.398E+02
- -c) 5.329E+02
- -d) 6.456E+02
- -e) 7.821E+02
6) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 7.465E+02
- -b) 9.044E+02
- -c) 1.096E+03
- -d) 1.327E+03
- +e) 1.608E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a) none of these are correct
- -b)
- -c)
- +d)
- -e)
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- -c)
- -d) none of these are correct
- +e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
Key: H1[edit | edit source]
1) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?
- -a) 2.039E+01 N/C
- -b) 2.243E+01 N/C
- +c) 2.467E+01 N/C
- -d) 2.714E+01 N/C
- -e) 2.985E+01 N/C
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
- -a) 1.206E+03 V·m
- +b) 1.326E+03 V·m
- -c) 1.459E+03 V·m
- -d) 1.605E+03 V·m
- -e) 1.765E+03 V·m
3) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 9.431E+02
- -b) 1.143E+03
- +c) 1.384E+03
- -d) 1.677E+03
- -e) 2.032E+03
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- -c) none of these are correct
- -d)
- +e)
- -a) 1.992E+01 N·m2/C
- -b) 2.192E+01 N·m2/C
- +c) 2.411E+01 N·m2/C
- -d) 2.652E+01 N·m2/C
- -e) 2.917E+01 N·m2/C
- -a) 7.081E+01 N·m2/C
- -b) 7.789E+01 N·m2/C
- +c) 8.568E+01 N·m2/C
- -d) 9.425E+01 N·m2/C
- -e) 1.037E+02 N·m2/C
8) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 4.593E+03
- -b) 5.564E+03
- +c) 6.741E+03
- -d) 8.167E+03
- -e) 9.894E+03
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
Key: H2[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
- -a) 2.694E+03 V·m
- -b) 2.963E+03 V·m
- -c) 3.259E+03 V·m
- +d) 3.585E+03 V·m
- -e) 3.944E+03 V·m
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
3) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
4) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 2.420E+02
- -b) 2.931E+02
- -c) 3.551E+02
- +d) 4.303E+02
- -e) 5.213E+02
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 3.630E+02
- +b) 4.398E+02
- -c) 5.329E+02
- -d) 6.456E+02
- -e) 7.821E+02
- -a) 2.901E+01 N·m2/C
- -b) 3.192E+01 N·m2/C
- -c) 3.511E+01 N·m2/C
- -d) 3.862E+01 N·m2/C
- +e) 4.248E+01 N·m2/C
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
9) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?
- +a) 3.797E+01 N/C
- -b) 4.177E+01 N/C
- -c) 4.595E+01 N/C
- -d) 5.054E+01 N/C
- -e) 5.560E+01 N/C
- -a) 4.024E+01 N·m2/C
- +b) 4.426E+01 N·m2/C
- -c) 4.868E+01 N·m2/C
- -d) 5.355E+01 N·m2/C
- -e) 5.891E+01 N·m2/C
Key: I0[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- -a) 1.698E+01 N·m2/C
- -b) 1.868E+01 N·m2/C
- -c) 2.055E+01 N·m2/C
- -d) 2.260E+01 N·m2/C
- +e) 2.486E+01 N·m2/C
2) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?
- -a) 2.039E+01 N/C
- -b) 2.243E+01 N/C
- +c) 2.467E+01 N/C
- -d) 2.714E+01 N/C
- -e) 2.985E+01 N/C
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?
- +a) 9.592E+00 N/C
- -b) 1.055E+01 N/C
- -c) 1.161E+01 N/C
- -d) 1.277E+01 N/C
- -e) 1.404E+01 N/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is,
- -a) 8.731E+02 V·m
- -b) 9.604E+02 V·m
- -c) 1.056E+03 V·m
- +d) 1.162E+03 V·m
- -e) 1.278E+03 V·m
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 5.610E+02
- -b) 6.796E+02
- -c) 8.234E+02
- -d) 9.975E+02
- -e) 1.209E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 3.60E+02
- +b) 4.36E+02
- -c) 5.29E+02
- -d) 6.40E+02
- -e) 7.76E+02
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- -c) none of these are correct
- -d)
- +e)
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- +a)
- -b) none of these are correct
- -c)
- -d)
- -e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b) none of these are correct
- -c)
- -d)
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
Key: I1[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
- +a) 7.200E+01 V·m
- -b) 7.920E+01 V·m
- -c) 8.712E+01 V·m
- -d) 9.583E+01 V·m
- -e) 1.054E+02 V·m
2) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 6.411E+02
- -b) 7.767E+02
- -c) 9.410E+02
- +d) 1.140E+03
- -e) 1.381E+03
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.8 m from the center of the shells?
- -a) 5.865E+00 N/C
- -b) 6.451E+00 N/C
- -c) 7.096E+00 N/C
- +d) 7.806E+00 N/C
- -e) 8.587E+00 N/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
6) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
- -a) 5.606E+01 N·m2/C
- -b) 6.167E+01 N·m2/C
- -c) 6.784E+01 N·m2/C
- +d) 7.462E+01 N·m2/C
- -e) 8.208E+01 N·m2/C
8) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?
- +a) 4.782E+02 N/C
- -b) 5.260E+02 N/C
- -c) 5.787E+02 N/C
- -d) 6.365E+02 N/C
- -e) 7.002E+02 N/C
9) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 3.96E+02
- -b) 4.79E+02
- -c) 5.81E+02
- -d) 7.04E+02
- +e) 8.53E+02
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
Key: I2[edit | edit source]
1) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- +a) 5.91E+02
- -b) 7.16E+02
- -c) 8.68E+02
- -d) 1.05E+03
- -e) 1.27E+03
- -a) 6.920E+01 N·m2/C
- -b) 7.612E+01 N·m2/C
- -c) 8.373E+01 N·m2/C
- +d) 9.210E+01 N·m2/C
- -e) 1.013E+02 N·m2/C
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- -a) 1.997E+03 V·m
- +b) 2.197E+03 V·m
- -c) 2.417E+03 V·m
- -d) 2.659E+03 V·m
- -e) 2.924E+03 V·m
4) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 4.021E+02
- -b) 4.872E+02
- -c) 5.902E+02
- -d) 7.151E+02
- -e) 8.663E+02
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- +a)
- -b)
- -c)
- -d) none of these are correct
- -e)
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
7) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- -a) 1.096E+00 N/C
- -b) 1.206E+00 N/C
- -c) 1.327E+00 N/C
- -d) 1.459E+00 N/C
- +e) 1.605E+00 N/C
10) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?
- -a) 1.123E+02 N/C
- -b) 1.235E+02 N/C
- +c) 1.358E+02 N/C
- -d) 1.494E+02 N/C
- -e) 1.644E+02 N/C
Key: J0[edit | edit source]
1) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?
- -a) 3.821E+02 N/C
- -b) 4.203E+02 N/C
- -c) 4.624E+02 N/C
- +d) 5.086E+02 N/C
- -e) 5.594E+02 N/C
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
- -a) 2.610E+03 V·m
- -b) 2.871E+03 V·m
- +c) 3.158E+03 V·m
- -d) 3.474E+03 V·m
- -e) 3.822E+03 V·m
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?
- -a) 9.144E+00 N/C
- -b) 1.006E+01 N/C
- -c) 1.106E+01 N/C
- -d) 1.217E+01 N/C
- +e) 1.339E+01 N/C
- -a) 2.012E+01 N·m2/C
- -b) 2.213E+01 N·m2/C
- -c) 2.435E+01 N·m2/C
- -d) 2.678E+01 N·m2/C
- +e) 2.946E+01 N·m2/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 5.311E+02
- -b) 6.434E+02
- -c) 7.795E+02
- +d) 9.444E+02
- -e) 1.144E+03
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 3.232E+03
- -b) 3.915E+03
- -c) 4.743E+03
- -d) 5.747E+03
- +e) 6.962E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- -c)
- -d) none of these are correct
- +e)
10) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
Key: J1[edit | edit source]
1) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?
- +a) 7.825E+02 N/C
- -b) 8.607E+02 N/C
- -c) 9.468E+02 N/C
- -d) 1.041E+03 N/C
- -e) 1.146E+03 N/C
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- -c) none of these are correct
- -d)
- +e)
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
5) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 9.205E+02
- -b) 1.115E+03
- +c) 1.351E+03
- -d) 1.637E+03
- -e) 1.983E+03
7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
- -a) 2.610E+03 V·m
- -b) 2.871E+03 V·m
- +c) 3.158E+03 V·m
- -d) 3.474E+03 V·m
- -e) 3.822E+03 V·m
8) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 1.304E+03
- -b) 1.579E+03
- +c) 1.914E+03
- -d) 2.318E+03
- -e) 2.809E+03
9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.4 m from the center of the shells?
- -a) 8.580E+00 N/C
- -b) 9.438E+00 N/C
- -c) 1.038E+01 N/C
- +d) 1.142E+01 N/C
- -e) 1.256E+01 N/C
- -a) 4.988E+01 N·m2/C
- -b) 5.487E+01 N·m2/C
- -c) 6.035E+01 N·m2/C
- -d) 6.639E+01 N·m2/C
- +e) 7.303E+01 N·m2/C
Key: J2[edit | edit source]
1) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
- -a) 1.206E+03 V·m
- +b) 1.326E+03 V·m
- -c) 1.459E+03 V·m
- -d) 1.605E+03 V·m
- -e) 1.765E+03 V·m
3) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 6.546E+02
- -b) 7.931E+02
- -c) 9.609E+02
- +d) 1.164E+03
- -e) 1.410E+03
4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.4 m from the center of the shells?
- -a) 1.491E+01 N/C
- -b) 1.640E+01 N/C
- +c) 1.804E+01 N/C
- -d) 1.984E+01 N/C
- -e) 2.182E+01 N/C
- -a) 5.439E+01 N·m2/C
- -b) 5.983E+01 N·m2/C
- -c) 6.581E+01 N·m2/C
- +d) 7.239E+01 N·m2/C
- -e) 7.963E+01 N·m2/C
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 6.201E+02
- -b) 7.513E+02
- -c) 9.102E+02
- +d) 1.103E+03
- -e) 1.336E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a) none of these are correct
- +b)
- -c)
- -d)
- -e)
8) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?
- +a) 7.825E+02 N/C
- -b) 8.607E+02 N/C
- -c) 9.468E+02 N/C
- -d) 1.041E+03 N/C
- -e) 1.146E+03 N/C
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
Key: K0[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
- -a) 2.694E+03 V·m
- -b) 2.963E+03 V·m
- -c) 3.259E+03 V·m
- +d) 3.585E+03 V·m
- -e) 3.944E+03 V·m
2) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?
- +a) 2.285E+01 N/C
- -b) 2.514E+01 N/C
- -c) 2.765E+01 N/C
- -d) 3.042E+01 N/C
- -e) 3.346E+01 N/C
- -a) 3.662E+01 N·m2/C
- +b) 4.028E+01 N·m2/C
- -c) 4.430E+01 N·m2/C
- -d) 4.873E+01 N·m2/C
- -e) 5.361E+01 N·m2/C
- -a) 2.186E+01 N·m2/C
- -b) 2.404E+01 N·m2/C
- +c) 2.645E+01 N·m2/C
- -d) 2.909E+01 N·m2/C
- -e) 3.200E+01 N·m2/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.59E+03
- -b) 1.93E+03
- +c) 2.34E+03
- -d) 2.83E+03
- -e) 3.43E+03
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 3.232E+03
- -b) 3.915E+03
- -c) 4.743E+03
- -d) 5.747E+03
- +e) 6.962E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a) none of these are correct
- +b)
- -c)
- -d)
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
Key: K1[edit | edit source]
1) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?
- +a) 2.285E+01 N/C
- -b) 2.514E+01 N/C
- -c) 2.765E+01 N/C
- -d) 3.042E+01 N/C
- -e) 3.346E+01 N/C
2) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- +a)
- -b)
- -c)
- -d) none of these are correct
- -e)
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
- -a) 1.206E+03 V·m
- +b) 1.326E+03 V·m
- -c) 1.459E+03 V·m
- -d) 1.605E+03 V·m
- -e) 1.765E+03 V·m
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b)
- -c)
- -d) none of these are correct
- -e)
- -a) 3.695E+01 N·m2/C
- -b) 4.065E+01 N·m2/C
- -c) 4.472E+01 N·m2/C
- -d) 4.919E+01 N·m2/C
- +e) 5.411E+01 N·m2/C
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 3.13E+03
- -b) 3.79E+03
- -c) 4.59E+03
- -d) 5.56E+03
- +e) 6.74E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- -c)
- -d) none of these are correct
- +e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a) none of these are correct
- -b)
- -c)
- +d)
- -e)
9) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 5.610E+02
- -b) 6.796E+02
- -c) 8.234E+02
- -d) 9.975E+02
- -e) 1.209E+03
- -a) 2.012E+01 N·m2/C
- -b) 2.213E+01 N·m2/C
- -c) 2.435E+01 N·m2/C
- -d) 2.678E+01 N·m2/C
- +e) 2.946E+01 N·m2/C
Key: K2[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.1 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- -a) 5.606E+01 N·m2/C
- -b) 6.167E+01 N·m2/C
- -c) 6.784E+01 N·m2/C
- +d) 7.462E+01 N·m2/C
- -e) 8.208E+01 N·m2/C
2) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 4.69E+03
- -b) 5.69E+03
- +c) 6.89E+03
- -d) 8.35E+03
- -e) 1.01E+04
3) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?
- +a) 2.285E+01 N/C
- -b) 2.514E+01 N/C
- -c) 2.765E+01 N/C
- -d) 3.042E+01 N/C
- -e) 3.346E+01 N/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
- -a) 8.545E+01 V·m
- -b) 9.400E+01 V·m
- -c) 1.034E+02 V·m
- -d) 1.137E+02 V·m
- +e) 1.251E+02 V·m
5) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 2.454E+02
- -b) 2.973E+02
- -c) 3.601E+02
- +d) 4.363E+02
- -e) 5.286E+02
- +a) 3.222E+01 N·m2/C
- -b) 3.544E+01 N·m2/C
- -c) 3.899E+01 N·m2/C
- -d) 4.289E+01 N·m2/C
- -e) 4.718E+01 N·m2/C
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b) none of these are correct
- -c)
- +d)
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
Key: L0[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.8 m, z=z0=1.7 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.2m2. An electric field of magnitude 14 N/C has components in the y and z directions and is directed at 55° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- +a) 8.314E+01 N·m2/C
- -b) 9.146E+01 N·m2/C
- -c) 1.006E+02 N·m2/C
- -d) 1.107E+02 N·m2/C
- -e) 1.217E+02 N·m2/C
- -a) 7.081E+01 N·m2/C
- -b) 7.789E+01 N·m2/C
- +c) 8.568E+01 N·m2/C
- -d) 9.425E+01 N·m2/C
- -e) 1.037E+02 N·m2/C
3) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.8 (r≤R) where a=2 nC·m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?
- +a) 2.079E+02 N/C
- -b) 2.287E+02 N/C
- -c) 2.516E+02 N/C
- -d) 2.767E+02 N/C
- -e) 3.044E+02 N/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- -a) 7.054E+03 V·m
- -b) 7.759E+03 V·m
- -c) 8.535E+03 V·m
- -d) 9.388E+03 V·m
- +e) 1.033E+04 V·m
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 4.63E+02
- +b) 5.61E+02
- -c) 6.80E+02
- -d) 8.23E+02
- -e) 9.98E+02
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 3.742E+02
- -b) 4.534E+02
- -c) 5.493E+02
- -d) 6.655E+02
- +e) 8.063E+02
7) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- -c) none of these are correct
- -d)
- +e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
10) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
Key: L1[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
2) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?
- -a) 3.821E+02 N/C
- -b) 4.203E+02 N/C
- -c) 4.624E+02 N/C
- +d) 5.086E+02 N/C
- -e) 5.594E+02 N/C
3) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
4) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 4.489E+02
- -b) 5.438E+02
- -c) 6.589E+02
- -d) 7.983E+02
- +e) 9.671E+02
5) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 3.13E+03
- -b) 3.79E+03
- -c) 4.59E+03
- -d) 5.56E+03
- +e) 6.74E+03
- +a) 3.249E+01 N·m2/C
- -b) 3.574E+01 N·m2/C
- -c) 3.931E+01 N·m2/C
- -d) 4.324E+01 N·m2/C
- -e) 4.757E+01 N·m2/C
- +a) 8.314E+01 N·m2/C
- -b) 9.146E+01 N·m2/C
- -c) 1.006E+02 N·m2/C
- -d) 1.107E+02 N·m2/C
- -e) 1.217E+02 N·m2/C
9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
- -a) 2.210E+04 V·m
- +b) 2.431E+04 V·m
- -c) 2.674E+04 V·m
- -d) 2.941E+04 V·m
- -e) 3.235E+04 V·m
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a) none of these are correct
- +b)
- -c)
- -d)
- -e)
Key: L2[edit | edit source]
1) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b)
- -c)
- -d) none of these are correct
- +e)
2) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- -a) 7.054E+03 V·m
- -b) 7.759E+03 V·m
- -c) 8.535E+03 V·m
- -d) 9.388E+03 V·m
- +e) 1.033E+04 V·m
4) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 1.704E+03
- -b) 2.064E+03
- -c) 2.501E+03
- +d) 3.030E+03
- -e) 3.671E+03
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- +a) 5.91E+02
- -b) 7.16E+02
- -c) 8.68E+02
- -d) 1.05E+03
- -e) 1.27E+03
- +a) 5.978E+01 N·m2/C
- -b) 6.576E+01 N·m2/C
- -c) 7.233E+01 N·m2/C
- -d) 7.957E+01 N·m2/C
- -e) 8.752E+01 N·m2/C
- +a) 3.222E+01 N·m2/C
- -b) 3.544E+01 N·m2/C
- -c) 3.899E+01 N·m2/C
- -d) 4.289E+01 N·m2/C
- -e) 4.718E+01 N·m2/C
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
9) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?
- -a) 6.411E+02 N/C
- -b) 7.052E+02 N/C
- +c) 7.757E+02 N/C
- -d) 8.533E+02 N/C
- -e) 9.386E+02 N/C
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
Key: M0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?
- -a) 3.251E+01 N/C
- -b) 3.577E+01 N/C
- -c) 3.934E+01 N/C
- -d) 4.328E+01 N/C
- +e) 4.760E+01 N/C
2) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.3 m from the center?
- -a) 2.777E+02 N/C
- -b) 3.055E+02 N/C
- +c) 3.361E+02 N/C
- -d) 3.697E+02 N/C
- -e) 4.066E+02 N/C
- -a) 3.712E+01 N·m2/C
- -b) 4.083E+01 N·m2/C
- +c) 4.491E+01 N·m2/C
- -d) 4.940E+01 N·m2/C
- -e) 5.434E+01 N·m2/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
- -a) 9.027E+03 V·m
- +b) 9.930E+03 V·m
- -c) 1.092E+04 V·m
- -d) 1.202E+04 V·m
- -e) 1.322E+04 V·m
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 3.742E+02
- -b) 4.534E+02
- -c) 5.493E+02
- -d) 6.655E+02
- +e) 8.063E+02
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 4.027E+02
- -b) 4.879E+02
- +c) 5.911E+02
- -d) 7.162E+02
- -e) 8.676E+02
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- +a)
- -b)
- -c)
- -d) none of these are correct
- -e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
10) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
Key: M1[edit | edit source]
1) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 1.692E+03
- -b) 2.050E+03
- +c) 2.484E+03
- -d) 3.009E+03
- -e) 3.645E+03
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a) none of these are correct
- -b)
- -c)
- +d)
- -e)
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
- -a) 9.952E+03 V·m
- -b) 1.095E+04 V·m
- -c) 1.204E+04 V·m
- +d) 1.325E+04 V·m
- -e) 1.457E+04 V·m
5) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- +a)
- -b) none of these are correct
- -c)
- -d)
- -e)
6) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.8 (r≤R) where a=2 nC·m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?
- +a) 2.079E+02 N/C
- -b) 2.287E+02 N/C
- -c) 2.516E+02 N/C
- -d) 2.767E+02 N/C
- -e) 3.044E+02 N/C
- -a) 8.457E+01 N·m2/C
- +b) 9.303E+01 N·m2/C
- -c) 1.023E+02 N·m2/C
- -d) 1.126E+02 N·m2/C
- -e) 1.238E+02 N·m2/C
8) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 4.489E+02
- -b) 5.438E+02
- -c) 6.589E+02
- -d) 7.983E+02
- +e) 9.671E+02
9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- +a) 1.017E+01 N/C
- -b) 1.118E+01 N/C
- -c) 1.230E+01 N/C
- -d) 1.353E+01 N/C
- -e) 1.488E+01 N/C
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
Key: M2[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
2) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 2.158E+03
- -b) 2.614E+03
- -c) 3.167E+03
- -d) 3.837E+03
- -e) 4.649E+03
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.6 m from the center of the shells?
- -a) 6.641E+00 N/C
- -b) 7.305E+00 N/C
- +c) 8.036E+00 N/C
- -d) 8.839E+00 N/C
- -e) 9.723E+00 N/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
- -a) 2.067E+03 V·m
- -b) 2.274E+03 V·m
- +c) 2.501E+03 V·m
- -d) 2.752E+03 V·m
- -e) 3.027E+03 V·m
5) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?
- +a) 3.604E+02 N/C
- -b) 3.964E+02 N/C
- -c) 4.360E+02 N/C
- -d) 4.796E+02 N/C
- -e) 5.276E+02 N/C
6) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
- -a) 8.457E+01 N·m2/C
- +b) 9.303E+01 N·m2/C
- -c) 1.023E+02 N·m2/C
- -d) 1.126E+02 N·m2/C
- -e) 1.238E+02 N·m2/C
8) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 3.742E+02
- -b) 4.534E+02
- -c) 5.493E+02
- -d) 6.655E+02
- +e) 8.063E+02
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- -c)
- +d)
- -e) none of these are correct
Key: N0[edit | edit source]
1) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?
- +a) 4.782E+02 N/C
- -b) 5.260E+02 N/C
- -c) 5.787E+02 N/C
- -d) 6.365E+02 N/C
- -e) 7.002E+02 N/C
- +a) 3.249E+01 N·m2/C
- -b) 3.574E+01 N·m2/C
- -c) 3.931E+01 N·m2/C
- -d) 4.324E+01 N·m2/C
- -e) 4.757E+01 N·m2/C
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
- +a) 7.200E+01 V·m
- -b) 7.920E+01 V·m
- -c) 8.712E+01 V·m
- -d) 9.583E+01 V·m
- -e) 1.054E+02 V·m
- +a) 7.793E+01 N·m2/C
- -b) 8.572E+01 N·m2/C
- -c) 9.429E+01 N·m2/C
- -d) 1.037E+02 N·m2/C
- -e) 1.141E+02 N·m2/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 2.420E+02
- -b) 2.931E+02
- -c) 3.551E+02
- +d) 4.303E+02
- -e) 5.213E+02
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 2.597E+03
- -b) 3.147E+03
- -c) 3.812E+03
- -d) 4.619E+03
- +e) 5.596E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
Key: N1[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.1 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- -a) 5.606E+01 N·m2/C
- -b) 6.167E+01 N·m2/C
- -c) 6.784E+01 N·m2/C
- +d) 7.462E+01 N·m2/C
- -e) 8.208E+01 N·m2/C
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
- +a) 7.200E+01 V·m
- -b) 7.920E+01 V·m
- -c) 8.712E+01 V·m
- -d) 9.583E+01 V·m
- -e) 1.054E+02 V·m
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
4) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 2.597E+03
- -b) 3.147E+03
- -c) 3.812E+03
- -d) 4.619E+03
- +e) 5.596E+03
- -a) 2.079E+01 N·m2/C
- -b) 2.287E+01 N·m2/C
- -c) 2.516E+01 N·m2/C
- +d) 2.768E+01 N·m2/C
- -e) 3.044E+01 N·m2/C
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
7) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 6.546E+02
- -b) 7.931E+02
- -c) 9.609E+02
- +d) 1.164E+03
- -e) 1.410E+03
8) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?
- +a) 4.782E+02 N/C
- -b) 5.260E+02 N/C
- -c) 5.787E+02 N/C
- -d) 6.365E+02 N/C
- -e) 7.002E+02 N/C
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a) none of these are correct
- -b)
- -c)
- +d)
- -e)
Key: N2[edit | edit source]
1) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 1.704E+03
- -b) 2.064E+03
- -c) 2.501E+03
- +d) 3.030E+03
- -e) 3.671E+03
2) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?
- +a) 2.285E+01 N/C
- -b) 2.514E+01 N/C
- -c) 2.765E+01 N/C
- -d) 3.042E+01 N/C
- -e) 3.346E+01 N/C
- +a) 5.978E+01 N·m2/C
- -b) 6.576E+01 N·m2/C
- -c) 7.233E+01 N·m2/C
- -d) 7.957E+01 N·m2/C
- -e) 8.752E+01 N·m2/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
7) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 2.318E+02
- -b) 2.808E+02
- -c) 3.402E+02
- +d) 4.122E+02
- -e) 4.994E+02
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- -a) 7.054E+03 V·m
- -b) 7.759E+03 V·m
- -c) 8.535E+03 V·m
- -d) 9.388E+03 V·m
- +e) 1.033E+04 V·m
- -a) 5.606E+01 N·m2/C
- -b) 6.167E+01 N·m2/C
- -c) 6.784E+01 N·m2/C
- +d) 7.462E+01 N·m2/C
- -e) 8.208E+01 N·m2/C
Key: O0[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
- -a) 2.210E+04 V·m
- +b) 2.431E+04 V·m
- -c) 2.674E+04 V·m
- -d) 2.941E+04 V·m
- -e) 3.235E+04 V·m
- -a) 3.662E+01 N·m2/C
- +b) 4.028E+01 N·m2/C
- -c) 4.430E+01 N·m2/C
- -d) 4.873E+01 N·m2/C
- -e) 5.361E+01 N·m2/C
- -a) 1.698E+01 N·m2/C
- -b) 1.868E+01 N·m2/C
- -c) 2.055E+01 N·m2/C
- -d) 2.260E+01 N·m2/C
- +e) 2.486E+01 N·m2/C
4) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?
- +a) 1.383E+02 N/C
- -b) 1.522E+02 N/C
- -c) 1.674E+02 N/C
- -d) 1.841E+02 N/C
- -e) 2.025E+02 N/C
5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 4.593E+03
- -b) 5.564E+03
- +c) 6.741E+03
- -d) 8.167E+03
- -e) 9.894E+03
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 9.41E+03
- -b) 1.14E+04
- +c) 1.38E+04
- -d) 1.67E+04
- -e) 2.03E+04
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b) none of these are correct
- -c)
- +d)
- -e)
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a) none of these are correct
- -b)
- -c)
- +d)
- -e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
Key: O1[edit | edit source]
1) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b)
- -c)
- -d) none of these are correct
- -e)
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
4) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 6.201E+02
- -b) 7.513E+02
- -c) 9.102E+02
- +d) 1.103E+03
- -e) 1.336E+03
6) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?
- +a) 1.383E+02 N/C
- -b) 1.522E+02 N/C
- -c) 1.674E+02 N/C
- -d) 1.841E+02 N/C
- -e) 2.025E+02 N/C
- -a) 2.012E+01 N·m2/C
- -b) 2.213E+01 N·m2/C
- -c) 2.435E+01 N·m2/C
- -d) 2.678E+01 N·m2/C
- +e) 2.946E+01 N·m2/C
8) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 3.18E+03
- -b) 3.85E+03
- -c) 4.66E+03
- +d) 5.65E+03
- -e) 6.84E+03
9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- -a) 1.128E+04 V·m
- -b) 1.241E+04 V·m
- -c) 1.365E+04 V·m
- +d) 1.502E+04 V·m
- -e) 1.652E+04 V·m
- -a) 4.521E+01 N·m2/C
- -b) 4.973E+01 N·m2/C
- -c) 5.470E+01 N·m2/C
- -d) 6.017E+01 N·m2/C
- +e) 6.619E+01 N·m2/C
Key: O2[edit | edit source]
1) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 4.522E+02
- -b) 5.478E+02
- -c) 6.637E+02
- +d) 8.041E+02
- -e) 9.742E+02
- -a) 4.809E+01 N·m2/C
- -b) 5.290E+01 N·m2/C
- +c) 5.819E+01 N·m2/C
- -d) 6.401E+01 N·m2/C
- -e) 7.041E+01 N·m2/C
- +a) 8.314E+01 N·m2/C
- -b) 9.146E+01 N·m2/C
- -c) 1.006E+02 N·m2/C
- -d) 1.107E+02 N·m2/C
- -e) 1.217E+02 N·m2/C
4) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?
- +a) 4.782E+02 N/C
- -b) 5.260E+02 N/C
- -c) 5.787E+02 N/C
- -d) 6.365E+02 N/C
- -e) 7.002E+02 N/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- +a) 5.91E+02
- -b) 7.16E+02
- -c) 8.68E+02
- -d) 1.05E+03
- -e) 1.27E+03
6) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- -a) 7.054E+03 V·m
- -b) 7.759E+03 V·m
- -c) 8.535E+03 V·m
- -d) 9.388E+03 V·m
- +e) 1.033E+04 V·m
Key: P0[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.3 m, z=z0=1.2 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 7.7m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- -a) 5.989E+01 N·m2/C
- -b) 6.588E+01 N·m2/C
- -c) 7.247E+01 N·m2/C
- +d) 7.971E+01 N·m2/C
- -e) 8.769E+01 N·m2/C
2) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?
- -a) 3.821E+02 N/C
- -b) 4.203E+02 N/C
- -c) 4.624E+02 N/C
- +d) 5.086E+02 N/C
- -e) 5.594E+02 N/C
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
- +a) 3.429E+03 V·m
- -b) 3.771E+03 V·m
- -c) 4.149E+03 V·m
- -d) 4.564E+03 V·m
- -e) 5.020E+03 V·m
- +a) 7.793E+01 N·m2/C
- -b) 8.572E+01 N·m2/C
- -c) 9.429E+01 N·m2/C
- -d) 1.037E+02 N·m2/C
- -e) 1.141E+02 N·m2/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 3.356E+02
- -b) 4.066E+02
- +c) 4.926E+02
- -d) 5.968E+02
- -e) 7.230E+02
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 3.742E+02
- -b) 4.534E+02
- -c) 5.493E+02
- -d) 6.655E+02
- +e) 8.063E+02
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
Key: P1[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
- -a) 3.695E+01 N·m2/C
- -b) 4.065E+01 N·m2/C
- -c) 4.472E+01 N·m2/C
- -d) 4.919E+01 N·m2/C
- +e) 5.411E+01 N·m2/C
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
4) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?
- +a) 4.782E+02 N/C
- -b) 5.260E+02 N/C
- -c) 5.787E+02 N/C
- -d) 6.365E+02 N/C
- -e) 7.002E+02 N/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 5.043E+02
- -b) 6.109E+02
- -c) 7.402E+02
- +d) 8.967E+02
- -e) 1.086E+03
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
- -a) 3.959E+01 N·m2/C
- -b) 4.354E+01 N·m2/C
- -c) 4.790E+01 N·m2/C
- +d) 5.269E+01 N·m2/C
- -e) 5.796E+01 N·m2/C
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
9) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 2.454E+02
- -b) 2.973E+02
- -c) 3.601E+02
- +d) 4.363E+02
- -e) 5.286E+02
10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
- -a) 8.545E+01 V·m
- -b) 9.400E+01 V·m
- -c) 1.034E+02 V·m
- -d) 1.137E+02 V·m
- +e) 1.251E+02 V·m
Key: P2[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.4 m, z=z0=1.5 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 4.6m2 ,and those in the zx plane have area 6.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- +a) 3.222E+01 N·m2/C
- -b) 3.544E+01 N·m2/C
- -c) 3.899E+01 N·m2/C
- -d) 4.289E+01 N·m2/C
- -e) 4.718E+01 N·m2/C
2) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 1.304E+03
- -b) 1.579E+03
- +c) 1.914E+03
- -d) 2.318E+03
- -e) 2.809E+03
- -a) 3.695E+01 N·m2/C
- -b) 4.065E+01 N·m2/C
- -c) 4.472E+01 N·m2/C
- -d) 4.919E+01 N·m2/C
- +e) 5.411E+01 N·m2/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- +a)
- -b) none of these are correct
- -c)
- -d)
- -e)
6) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
- -a) 2.210E+04 V·m
- +b) 2.431E+04 V·m
- -c) 2.674E+04 V·m
- -d) 2.941E+04 V·m
- -e) 3.235E+04 V·m
7) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.3 m from the center?
- -a) 2.777E+02 N/C
- -b) 3.055E+02 N/C
- +c) 3.361E+02 N/C
- -d) 3.697E+02 N/C
- -e) 4.066E+02 N/C
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- -c) none of these are correct
- -d)
- +e)
9) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 4.162E+02
- -b) 5.042E+02
- -c) 6.109E+02
- -d) 7.401E+02
- -e) 8.967E+02
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
Key: Q0[edit | edit source]
1) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?
- +a) 7.825E+02 N/C
- -b) 8.607E+02 N/C
- -c) 9.468E+02 N/C
- -d) 1.041E+03 N/C
- -e) 1.146E+03 N/C
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
- +a) 7.200E+01 V·m
- -b) 7.920E+01 V·m
- -c) 8.712E+01 V·m
- -d) 9.583E+01 V·m
- -e) 1.054E+02 V·m
- -a) 8.457E+01 N·m2/C
- +b) 9.303E+01 N·m2/C
- -c) 1.023E+02 N·m2/C
- -d) 1.126E+02 N·m2/C
- -e) 1.238E+02 N·m2/C
- +a) 5.978E+01 N·m2/C
- -b) 6.576E+01 N·m2/C
- -c) 7.233E+01 N·m2/C
- -d) 7.957E+01 N·m2/C
- -e) 8.752E+01 N·m2/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 3.742E+02
- -b) 4.534E+02
- -c) 5.493E+02
- -d) 6.655E+02
- +e) 8.063E+02
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 2.93E+02
- -b) 3.55E+02
- +c) 4.30E+02
- -d) 5.21E+02
- -e) 6.32E+02
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
8) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b)
- -c)
- +d)
- -e) none of these are correct
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- -c)
- +d)
- -e) none of these are correct
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
Key: Q1[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.8 m, z=z0=1.8 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 8.9m2 ,and those in the zx plane have area 7.2m2. An electric field has the xyz components (0, 5.9, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- -a) 2.901E+01 N·m2/C
- -b) 3.192E+01 N·m2/C
- -c) 3.511E+01 N·m2/C
- -d) 3.862E+01 N·m2/C
- +e) 4.248E+01 N·m2/C
2) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?
- +a) 7.825E+02 N/C
- -b) 8.607E+02 N/C
- -c) 9.468E+02 N/C
- -d) 1.041E+03 N/C
- -e) 1.146E+03 N/C
3) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 3.417E+03
- -b) 4.140E+03
- -c) 5.016E+03
- +d) 6.077E+03
- -e) 7.362E+03
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- -c)
- +d)
- -e) none of these are correct
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.59E+03
- -b) 1.93E+03
- +c) 2.34E+03
- -d) 2.83E+03
- -e) 3.43E+03
6) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
- -a) 4.521E+01 N·m2/C
- -b) 4.973E+01 N·m2/C
- -c) 5.470E+01 N·m2/C
- -d) 6.017E+01 N·m2/C
- +e) 6.619E+01 N·m2/C
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- -c)
- +d)
- -e) none of these are correct
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a) none of these are correct
- +b)
- -c)
- -d)
- -e)
10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
- +a) 3.429E+03 V·m
- -b) 3.771E+03 V·m
- -c) 4.149E+03 V·m
- -d) 4.564E+03 V·m
- -e) 5.020E+03 V·m
Key: Q2[edit | edit source]
1) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 9.41E+03
- -b) 1.14E+04
- +c) 1.38E+04
- -d) 1.67E+04
- -e) 2.03E+04
- +a) 7.876E+01 N·m2/C
- -b) 8.664E+01 N·m2/C
- -c) 9.531E+01 N·m2/C
- -d) 1.048E+02 N·m2/C
- -e) 1.153E+02 N·m2/C
3) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b) none of these are correct
- -c)
- +d)
- -e)
4) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- -c) none of these are correct
- -d)
- +e)
- +a) 5.978E+01 N·m2/C
- -b) 6.576E+01 N·m2/C
- -c) 7.233E+01 N·m2/C
- -d) 7.957E+01 N·m2/C
- -e) 8.752E+01 N·m2/C
8) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 1.248E+03
- -b) 1.512E+03
- +c) 1.832E+03
- -d) 2.220E+03
- -e) 2.689E+03
9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
- -a) 2.694E+03 V·m
- -b) 2.963E+03 V·m
- -c) 3.259E+03 V·m
- +d) 3.585E+03 V·m
- -e) 3.944E+03 V·m
10) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?
- -a) 2.274E+02 N/C
- -b) 2.501E+02 N/C
- +c) 2.751E+02 N/C
- -d) 3.026E+02 N/C
- -e) 3.329E+02 N/C
Key: R0[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.7 m, z=z0=1.4 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 33° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- -a) 6.920E+01 N·m2/C
- -b) 7.612E+01 N·m2/C
- -c) 8.373E+01 N·m2/C
- +d) 9.210E+01 N·m2/C
- -e) 1.013E+02 N·m2/C
2) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.7 m from the center?
- -a) 2.579E+02 N/C
- +b) 2.837E+02 N/C
- -c) 3.121E+02 N/C
- -d) 3.433E+02 N/C
- -e) 3.776E+02 N/C
- +a) 5.978E+01 N·m2/C
- -b) 6.576E+01 N·m2/C
- -c) 7.233E+01 N·m2/C
- -d) 7.957E+01 N·m2/C
- -e) 8.752E+01 N·m2/C
- +a) 8.921E+01 N·m2/C
- -b) 9.813E+01 N·m2/C
- -c) 1.079E+02 N·m2/C
- -d) 1.187E+02 N·m2/C
- -e) 1.306E+02 N·m2/C
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 3.96E+02
- -b) 4.79E+02
- -c) 5.81E+02
- -d) 7.04E+02
- +e) 8.53E+02
6) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- +a) 8.528E+02
- -b) 1.033E+03
- -c) 1.252E+03
- -d) 1.516E+03
- -e) 1.837E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- -c) none of these are correct
- -d)
- +e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
Key: R1[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
2) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 3.041E+02
- -b) 3.684E+02
- +c) 4.464E+02
- -d) 5.408E+02
- -e) 6.552E+02
- -a) 2.756E+01 N·m2/C
- -b) 3.032E+01 N·m2/C
- -c) 3.335E+01 N·m2/C
- -d) 3.668E+01 N·m2/C
- +e) 4.035E+01 N·m2/C
- -a) 4.024E+01 N·m2/C
- +b) 4.426E+01 N·m2/C
- -c) 4.868E+01 N·m2/C
- -d) 5.355E+01 N·m2/C
- -e) 5.891E+01 N·m2/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 4.63E+02
- +b) 5.61E+02
- -c) 6.80E+02
- -d) 8.23E+02
- -e) 9.98E+02
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
- -a) 1.388E+01 N·m2/C
- +b) 1.526E+01 N·m2/C
- -c) 1.679E+01 N·m2/C
- -d) 1.847E+01 N·m2/C
- -e) 2.032E+01 N·m2/C
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- -c)
- +d)
- -e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a) none of these are correct
- -b)
- -c)
- +d)
- -e)
10) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?
- +a) 3.604E+02 N/C
- -b) 3.964E+02 N/C
- -c) 4.360E+02 N/C
- -d) 4.796E+02 N/C
- -e) 5.276E+02 N/C
Key: R2[edit | edit source]
1) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 5.311E+02
- -b) 6.434E+02
- -c) 7.795E+02
- +d) 9.444E+02
- -e) 1.144E+03
2) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.59E+03
- -b) 1.93E+03
- +c) 2.34E+03
- -d) 2.83E+03
- -e) 3.43E+03
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
4) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
- +a) 7.793E+01 N·m2/C
- -b) 8.572E+01 N·m2/C
- -c) 9.429E+01 N·m2/C
- -d) 1.037E+02 N·m2/C
- -e) 1.141E+02 N·m2/C
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
- -a) 4.953E+01 N·m2/C
- -b) 5.449E+01 N·m2/C
- -c) 5.993E+01 N·m2/C
- -d) 6.593E+01 N·m2/C
- +e) 7.252E+01 N·m2/C
9) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?
- +a) 7.825E+02 N/C
- -b) 8.607E+02 N/C
- -c) 9.468E+02 N/C
- -d) 1.041E+03 N/C
- -e) 1.146E+03 N/C
- -a) 3.959E+01 N·m2/C
- -b) 4.354E+01 N·m2/C
- -c) 4.790E+01 N·m2/C
- +d) 5.269E+01 N·m2/C
- -e) 5.796E+01 N·m2/C
Key: S0[edit | edit source]
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
- -a) 2.610E+03 V·m
- -b) 2.871E+03 V·m
- +c) 3.158E+03 V·m
- -d) 3.474E+03 V·m
- -e) 3.822E+03 V·m
- -a) 6.270E+01 N·m2/C
- -b) 6.897E+01 N·m2/C
- -c) 7.586E+01 N·m2/C
- -d) 8.345E+01 N·m2/C
- +e) 9.179E+01 N·m2/C
- -a) 7.081E+01 N·m2/C
- -b) 7.789E+01 N·m2/C
- +c) 8.568E+01 N·m2/C
- -d) 9.425E+01 N·m2/C
- -e) 1.037E+02 N·m2/C
- -a) 2.214E+01 N·m2/C
- -b) 2.436E+01 N·m2/C
- -c) 2.679E+01 N·m2/C
- -d) 2.947E+01 N·m2/C
- +e) 3.242E+01 N·m2/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 3.799E+02
- -b) 4.603E+02
- -c) 5.576E+02
- +d) 6.756E+02
- -e) 8.185E+02
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 9.41E+03
- -b) 1.14E+04
- +c) 1.38E+04
- -d) 1.67E+04
- -e) 2.03E+04
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- -c)
- +d)
- -e) none of these are correct
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b) none of these are correct
- -c)
- +d)
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
Key: S1[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- -c)
- -d) none of these are correct
- +e)
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
- -a) 4.521E+01 N·m2/C
- -b) 4.973E+01 N·m2/C
- -c) 5.470E+01 N·m2/C
- -d) 6.017E+01 N·m2/C
- +e) 6.619E+01 N·m2/C
4) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 3.60E+02
- +b) 4.36E+02
- -c) 5.29E+02
- -d) 6.40E+02
- -e) 7.76E+02
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- -c) none of these are correct
- -d)
- +e)
- +a) 8.921E+01 N·m2/C
- -b) 9.813E+01 N·m2/C
- -c) 1.079E+02 N·m2/C
- -d) 1.187E+02 N·m2/C
- -e) 1.306E+02 N·m2/C
- -a) 1.388E+01 N·m2/C
- +b) 1.526E+01 N·m2/C
- -c) 1.679E+01 N·m2/C
- -d) 1.847E+01 N·m2/C
- -e) 2.032E+01 N·m2/C
9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
- +a) 7.200E+01 V·m
- -b) 7.920E+01 V·m
- -c) 8.712E+01 V·m
- -d) 9.583E+01 V·m
- -e) 1.054E+02 V·m
10) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 7.465E+02
- -b) 9.044E+02
- -c) 1.096E+03
- -d) 1.327E+03
- +e) 1.608E+03
Key: S2[edit | edit source]
1) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 5.40E+02
- -b) 6.55E+02
- -c) 7.93E+02
- -d) 9.61E+02
- +e) 1.16E+03
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
- -a) 9.952E+03 V·m
- -b) 1.095E+04 V·m
- -c) 1.204E+04 V·m
- +d) 1.325E+04 V·m
- -e) 1.457E+04 V·m
- -a) 6.614E+01 N·m2/C
- +b) 7.275E+01 N·m2/C
- -c) 8.003E+01 N·m2/C
- -d) 8.803E+01 N·m2/C
- -e) 9.683E+01 N·m2/C
4) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
- -a) 2.214E+01 N·m2/C
- -b) 2.436E+01 N·m2/C
- -c) 2.679E+01 N·m2/C
- -d) 2.947E+01 N·m2/C
- +e) 3.242E+01 N·m2/C
- -a) 9.823E+00 N·m2/C
- +b) 1.080E+01 N·m2/C
- -c) 1.189E+01 N·m2/C
- -d) 1.307E+01 N·m2/C
- -e) 1.438E+01 N·m2/C
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
8) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 2.454E+02
- -b) 2.973E+02
- -c) 3.601E+02
- +d) 4.363E+02
- -e) 5.286E+02
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a) none of these are correct
- -b)
- -c)
- +d)
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a) none of these are correct
- -b)
- -c)
- +d)
- -e)
Key: T0[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.3 m, z=z0=1.2 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 4.3m2 ,and those in the zx plane have area 5.1m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- -a) 3.750E+01 N·m2/C
- -b) 4.125E+01 N·m2/C
- -c) 4.537E+01 N·m2/C
- +d) 4.991E+01 N·m2/C
- -e) 5.490E+01 N·m2/C
2) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.7 m from the center?
- -a) 2.579E+02 N/C
- +b) 2.837E+02 N/C
- -c) 3.121E+02 N/C
- -d) 3.433E+02 N/C
- -e) 3.776E+02 N/C
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?
- -a) 2.964E+00 N/C
- -b) 3.260E+00 N/C
- -c) 3.586E+00 N/C
- +d) 3.944E+00 N/C
- -e) 4.339E+00 N/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
- -a) 2.067E+03 V·m
- -b) 2.274E+03 V·m
- +c) 2.501E+03 V·m
- -d) 2.752E+03 V·m
- -e) 3.027E+03 V·m
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 5.311E+02
- -b) 6.434E+02
- -c) 7.795E+02
- +d) 9.444E+02
- -e) 1.144E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 4.162E+02
- -b) 5.042E+02
- -c) 6.109E+02
- -d) 7.401E+02
- -e) 8.967E+02
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
8) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
Key: T1[edit | edit source]
1) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 4.489E+02
- -b) 5.438E+02
- -c) 6.589E+02
- -d) 7.983E+02
- +e) 9.671E+02
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
- -a) 3.750E+01 N·m2/C
- -b) 4.125E+01 N·m2/C
- -c) 4.537E+01 N·m2/C
- +d) 4.991E+01 N·m2/C
- -e) 5.490E+01 N·m2/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- +a)
- -b)
- -c)
- -d) none of these are correct
- -e)
5) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.4 m from the center of the shells?
- -a) 8.580E+00 N/C
- -b) 9.438E+00 N/C
- -c) 1.038E+01 N/C
- +d) 1.142E+01 N/C
- -e) 1.256E+01 N/C
6) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?
- +a) 7.825E+02 N/C
- -b) 8.607E+02 N/C
- -c) 9.468E+02 N/C
- -d) 1.041E+03 N/C
- -e) 1.146E+03 N/C
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
8) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 4.162E+02
- -b) 5.042E+02
- -c) 6.109E+02
- -d) 7.401E+02
- -e) 8.967E+02
9) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- -a) 7.054E+03 V·m
- -b) 7.759E+03 V·m
- -c) 8.535E+03 V·m
- -d) 9.388E+03 V·m
- +e) 1.033E+04 V·m
Key: T2[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
2) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 3.417E+03
- -b) 4.140E+03
- -c) 5.016E+03
- +d) 6.077E+03
- -e) 7.362E+03
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- -c)
- -d) none of these are correct
- +e)
4) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
5) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.3 m from the center?
- -a) 2.777E+02 N/C
- -b) 3.055E+02 N/C
- +c) 3.361E+02 N/C
- -d) 3.697E+02 N/C
- -e) 4.066E+02 N/C
6) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?
- -a) 2.964E+00 N/C
- -b) 3.260E+00 N/C
- -c) 3.586E+00 N/C
- +d) 3.944E+00 N/C
- -e) 4.339E+00 N/C
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
8) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 3.799E+02
- -b) 4.603E+02
- -c) 5.576E+02
- +d) 6.756E+02
- -e) 8.185E+02
9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- -a) 1.997E+03 V·m
- +b) 2.197E+03 V·m
- -c) 2.417E+03 V·m
- -d) 2.659E+03 V·m
- -e) 2.924E+03 V·m
- -a) 2.012E+01 N·m2/C
- -b) 2.213E+01 N·m2/C
- -c) 2.435E+01 N·m2/C
- -d) 2.678E+01 N·m2/C
- +e) 2.946E+01 N·m2/C
Key: U0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?
- -a) 2.988E+00 N/C
- -b) 3.287E+00 N/C
- -c) 3.616E+00 N/C
- -d) 3.977E+00 N/C
- +e) 4.375E+00 N/C
- -a) 2.012E+01 N·m2/C
- -b) 2.213E+01 N·m2/C
- -c) 2.435E+01 N·m2/C
- -d) 2.678E+01 N·m2/C
- +e) 2.946E+01 N·m2/C
3) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?
- -a) 6.411E+02 N/C
- -b) 7.052E+02 N/C
- +c) 7.757E+02 N/C
- -d) 8.533E+02 N/C
- -e) 9.386E+02 N/C
- +a) 7.793E+01 N·m2/C
- -b) 8.572E+01 N·m2/C
- -c) 9.429E+01 N·m2/C
- -d) 1.037E+02 N·m2/C
- -e) 1.141E+02 N·m2/C
5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 9.41E+03
- -b) 1.14E+04
- +c) 1.38E+04
- -d) 1.67E+04
- -e) 2.03E+04
6) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 1.248E+03
- -b) 1.512E+03
- +c) 1.832E+03
- -d) 2.220E+03
- -e) 2.689E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
8) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
Key: U1[edit | edit source]
1) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 4.593E+03
- -b) 5.564E+03
- +c) 6.741E+03
- -d) 8.167E+03
- -e) 9.894E+03
2) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?
- +a) 7.825E+02 N/C
- -b) 8.607E+02 N/C
- -c) 9.468E+02 N/C
- -d) 1.041E+03 N/C
- -e) 1.146E+03 N/C
- -a) 2.012E+01 N·m2/C
- -b) 2.213E+01 N·m2/C
- -c) 2.435E+01 N·m2/C
- -d) 2.678E+01 N·m2/C
- +e) 2.946E+01 N·m2/C
4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- -a) 1.096E+00 N/C
- -b) 1.206E+00 N/C
- -c) 1.327E+00 N/C
- -d) 1.459E+00 N/C
- +e) 1.605E+00 N/C
5) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b)
- -c)
- +d)
- -e) none of these are correct
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
- +a) 5.385E+01 N·m2/C
- -b) 5.923E+01 N·m2/C
- -c) 6.516E+01 N·m2/C
- -d) 7.167E+01 N·m2/C
- -e) 7.884E+01 N·m2/C
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
9) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 3.18E+03
- -b) 3.85E+03
- -c) 4.66E+03
- +d) 5.65E+03
- -e) 6.84E+03
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
Key: U2[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.3 m, z=z0=1.2 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 4.3m2 ,and those in the zx plane have area 5.1m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- -a) 3.750E+01 N·m2/C
- -b) 4.125E+01 N·m2/C
- -c) 4.537E+01 N·m2/C
- +d) 4.991E+01 N·m2/C
- -e) 5.490E+01 N·m2/C
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- -a) 1.096E+00 N/C
- -b) 1.206E+00 N/C
- -c) 1.327E+00 N/C
- -d) 1.459E+00 N/C
- +e) 1.605E+00 N/C
4) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 4.63E+02
- +b) 5.61E+02
- -c) 6.80E+02
- -d) 8.23E+02
- -e) 9.98E+02
5) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- +a) 8.528E+02
- -b) 1.033E+03
- -c) 1.252E+03
- -d) 1.516E+03
- -e) 1.837E+03
6) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?
- +a) 2.285E+01 N/C
- -b) 2.514E+01 N/C
- -c) 2.765E+01 N/C
- -d) 3.042E+01 N/C
- -e) 3.346E+01 N/C
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- +a)
- -b)
- -c)
- -d) none of these are correct
- -e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
- -a) 3.712E+01 N·m2/C
- -b) 4.083E+01 N·m2/C
- +c) 4.491E+01 N·m2/C
- -d) 4.940E+01 N·m2/C
- -e) 5.434E+01 N·m2/C
10) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
Key: V0[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.2 m, z=z0=1.1 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 8.5m2. Those in the xy plane have area 2.8m2 ,and those in the zx plane have area 3.7m2. An electric field has the xyz components (0, 7.4, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- -a) 2.079E+01 N·m2/C
- -b) 2.287E+01 N·m2/C
- -c) 2.516E+01 N·m2/C
- +d) 2.768E+01 N·m2/C
- -e) 3.044E+01 N·m2/C
- -a) 5.989E+01 N·m2/C
- -b) 6.588E+01 N·m2/C
- -c) 7.247E+01 N·m2/C
- +d) 7.971E+01 N·m2/C
- -e) 8.769E+01 N·m2/C
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
- -a) 2.067E+03 V·m
- -b) 2.274E+03 V·m
- +c) 2.501E+03 V·m
- -d) 2.752E+03 V·m
- -e) 3.027E+03 V·m
4) A non-conducting sphere of radius R=1.2 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.6 (r≤R) where a=2 nC·m-1.4. What is the magnitude of the electric field at a distance of 0.76 m from the center?
- +a) 2.406E+01 N/C
- -b) 2.646E+01 N/C
- -c) 2.911E+01 N/C
- -d) 3.202E+01 N/C
- -e) 3.522E+01 N/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 6.546E+02
- -b) 7.931E+02
- -c) 9.609E+02
- +d) 1.164E+03
- -e) 1.410E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 7.933E+02
- +b) 9.611E+02
- -c) 1.164E+03
- -d) 1.411E+03
- -e) 1.709E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- -c)
- -d) none of these are correct
- +e)
10) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a) none of these are correct
- +b)
- -c)
- -d)
- -e)
Key: V1[edit | edit source]
1) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- +a) 8.528E+02
- -b) 1.033E+03
- -c) 1.252E+03
- -d) 1.516E+03
- -e) 1.837E+03
2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
- -a) 9.952E+03 V·m
- -b) 1.095E+04 V·m
- -c) 1.204E+04 V·m
- +d) 1.325E+04 V·m
- -e) 1.457E+04 V·m
3) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
4) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 4.021E+02
- -b) 4.872E+02
- -c) 5.902E+02
- -d) 7.151E+02
- -e) 8.663E+02
- +a) 6.529E+01 N·m2/C
- -b) 7.181E+01 N·m2/C
- -c) 7.900E+01 N·m2/C
- -d) 8.690E+01 N·m2/C
- -e) 9.559E+01 N·m2/C
6) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?
- +a) 3.604E+02 N/C
- -b) 3.964E+02 N/C
- -c) 4.360E+02 N/C
- -d) 4.796E+02 N/C
- -e) 5.276E+02 N/C
- -a) 9.823E+00 N·m2/C
- +b) 1.080E+01 N·m2/C
- -c) 1.189E+01 N·m2/C
- -d) 1.307E+01 N·m2/C
- -e) 1.438E+01 N·m2/C
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- -c)
- +d)
- -e) none of these are correct
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b) none of these are correct
- -c)
- +d)
- -e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a) none of these are correct
- +b)
- -c)
- -d)
- -e)
Key: V2[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.4 m, z=z0=1.5 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 4.6m2 ,and those in the zx plane have area 6.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- +a) 3.222E+01 N·m2/C
- -b) 3.544E+01 N·m2/C
- -c) 3.899E+01 N·m2/C
- -d) 4.289E+01 N·m2/C
- -e) 4.718E+01 N·m2/C
2) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 6.546E+02
- -b) 7.931E+02
- -c) 9.609E+02
- +d) 1.164E+03
- -e) 1.410E+03
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
- +a) 7.200E+01 V·m
- -b) 7.920E+01 V·m
- -c) 8.712E+01 V·m
- -d) 9.583E+01 V·m
- -e) 1.054E+02 V·m
4) A non-conducting sphere of radius R=2.2 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=3 nC·m-1.6. What is the magnitude of the electric field at a distance of 0.86 m from the center?
- -a) 4.874E+01 N/C
- +b) 5.362E+01 N/C
- -c) 5.898E+01 N/C
- -d) 6.488E+01 N/C
- -e) 7.137E+01 N/C
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b) none of these are correct
- -c)
- +d)
- -e)
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- +a)
- -b) none of these are correct
- -c)
- -d)
- -e)
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
8) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 5.043E+02
- -b) 6.109E+02
- -c) 7.402E+02
- +d) 8.967E+02
- -e) 1.086E+03
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
- +a) 5.978E+01 N·m2/C
- -b) 6.576E+01 N·m2/C
- -c) 7.233E+01 N·m2/C
- -d) 7.957E+01 N·m2/C
- -e) 8.752E+01 N·m2/C
Key: W0[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.9 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.1 m, z=z0=1.3 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.6m2 ,and those in the zx plane have area 6.5m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 46° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- +a) 5.385E+01 N·m2/C
- -b) 5.923E+01 N·m2/C
- -c) 6.516E+01 N·m2/C
- -d) 7.167E+01 N·m2/C
- -e) 7.884E+01 N·m2/C
- -a) 4.730E+01 N·m2/C
- +b) 5.203E+01 N·m2/C
- -c) 5.723E+01 N·m2/C
- -d) 6.295E+01 N·m2/C
- -e) 6.925E+01 N·m2/C
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?
- -a) 2.988E+00 N/C
- -b) 3.287E+00 N/C
- -c) 3.616E+00 N/C
- -d) 3.977E+00 N/C
- +e) 4.375E+00 N/C
4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
- -a) 4.820E+03 V·m
- -b) 5.302E+03 V·m
- +c) 5.832E+03 V·m
- -d) 6.415E+03 V·m
- -e) 7.057E+03 V·m
5) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 5.043E+02
- -b) 6.109E+02
- -c) 7.402E+02
- +d) 8.967E+02
- -e) 1.086E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.59E+03
- -b) 1.93E+03
- +c) 2.34E+03
- -d) 2.83E+03
- -e) 3.43E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a) none of these are correct
- -b)
- -c)
- +d)
- -e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
10) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- -c)
- +d)
- -e) none of these are correct
Key: W1[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
2) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- -a) 1.096E+00 N/C
- -b) 1.206E+00 N/C
- -c) 1.327E+00 N/C
- -d) 1.459E+00 N/C
- +e) 1.605E+00 N/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- +a) 2.769E+03
- -b) 3.354E+03
- -c) 4.064E+03
- -d) 4.923E+03
- -e) 5.965E+03
- -a) 3.328E+01 N·m2/C
- -b) 3.660E+01 N·m2/C
- -c) 4.026E+01 N·m2/C
- -d) 4.429E+01 N·m2/C
- +e) 4.872E+01 N·m2/C
7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
- -a) 2.210E+04 V·m
- +b) 2.431E+04 V·m
- -c) 2.674E+04 V·m
- -d) 2.941E+04 V·m
- -e) 3.235E+04 V·m
- -a) 3.924E+01 N·m2/C
- -b) 4.316E+01 N·m2/C
- -c) 4.748E+01 N·m2/C
- +d) 5.222E+01 N·m2/C
- -e) 5.745E+01 N·m2/C
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- +a)
- -b)
- -c)
- -d) none of these are correct
- -e)
10) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.13E+03
- -b) 1.37E+03
- -c) 1.66E+03
- +d) 2.01E+03
- -e) 2.44E+03
Key: W2[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?
- -a) 2.837E+01 N/C
- -b) 3.121E+01 N/C
- -c) 3.433E+01 N/C
- -d) 3.776E+01 N/C
- +e) 4.154E+01 N/C
2) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.09E+03
- -b) 1.32E+03
- -c) 1.60E+03
- -d) 1.94E+03
- +e) 2.35E+03
- -a) 8.457E+01 N·m2/C
- +b) 9.303E+01 N·m2/C
- -c) 1.023E+02 N·m2/C
- -d) 1.126E+02 N·m2/C
- -e) 1.238E+02 N·m2/C
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b) none of these are correct
- -c)
- +d)
- -e)
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 7.933E+02
- +b) 9.611E+02
- -c) 1.164E+03
- -d) 1.411E+03
- -e) 1.709E+03
- -a) 2.901E+01 N·m2/C
- -b) 3.192E+01 N·m2/C
- -c) 3.511E+01 N·m2/C
- -d) 3.862E+01 N·m2/C
- +e) 4.248E+01 N·m2/C
8) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
- -a) 1.128E+04 V·m
- -b) 1.241E+04 V·m
- -c) 1.365E+04 V·m
- +d) 1.502E+04 V·m
- -e) 1.652E+04 V·m
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
Key: X0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?
- +a) 5.058E+00 N/C
- -b) 5.564E+00 N/C
- -c) 6.120E+00 N/C
- -d) 6.732E+00 N/C
- -e) 7.405E+00 N/C
- +a) 8.921E+01 N·m2/C
- -b) 9.813E+01 N·m2/C
- -c) 1.079E+02 N·m2/C
- -d) 1.187E+02 N·m2/C
- -e) 1.306E+02 N·m2/C
3) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?
- -a) 3.821E+02 N/C
- -b) 4.203E+02 N/C
- -c) 4.624E+02 N/C
- +d) 5.086E+02 N/C
- -e) 5.594E+02 N/C
- -a) 1.992E+01 N·m2/C
- -b) 2.192E+01 N·m2/C
- +c) 2.411E+01 N·m2/C
- -d) 2.652E+01 N·m2/C
- -e) 2.917E+01 N·m2/C
5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- -a) 1.08E+03
- -b) 1.30E+03
- -c) 1.58E+03
- +d) 1.91E+03
- -e) 2.32E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 3.742E+02
- -b) 4.534E+02
- -c) 5.493E+02
- -d) 6.655E+02
- +e) 8.063E+02
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- +b)
- -c) none of these are correct
- -d)
- -e)
Key: X1[edit | edit source]
1) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
- -a) 3.695E+01 N·m2/C
- -b) 4.065E+01 N·m2/C
- -c) 4.472E+01 N·m2/C
- -d) 4.919E+01 N·m2/C
- +e) 5.411E+01 N·m2/C
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
4) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?
- +a) 3.797E+01 N/C
- -b) 4.177E+01 N/C
- -c) 4.595E+01 N/C
- -d) 5.054E+01 N/C
- -e) 5.560E+01 N/C
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a) none of these are correct
- -b)
- -c)
- +d)
- -e)
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- +b)
- -c)
- -d)
- -e) none of these are correct
7) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- +a) 1.017E+01 N/C
- -b) 1.118E+01 N/C
- -c) 1.230E+01 N/C
- -d) 1.353E+01 N/C
- -e) 1.488E+01 N/C
8) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- +a) 5.91E+02
- -b) 7.16E+02
- -c) 8.68E+02
- -d) 1.05E+03
- -e) 1.27E+03
- -a) 2.134E+01 N·m2/C
- -b) 2.347E+01 N·m2/C
- +c) 2.582E+01 N·m2/C
- -d) 2.840E+01 N·m2/C
- -e) 3.124E+01 N·m2/C
10) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 5.043E+02
- -b) 6.109E+02
- -c) 7.402E+02
- +d) 8.967E+02
- -e) 1.086E+03
Key: X2[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.6 m from the center of the shells?
- -a) 1.114E+01 N/C
- +b) 1.225E+01 N/C
- -c) 1.347E+01 N/C
- -d) 1.482E+01 N/C
- -e) 1.630E+01 N/C
3) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
4) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
5) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- +c)
- -d)
- -e) none of these are correct
- -a) 4.420E+01 N·m2/C
- -b) 4.862E+01 N·m2/C
- -c) 5.348E+01 N·m2/C
- -d) 5.882E+01 N·m2/C
- +e) 6.471E+01 N·m2/C
7) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 2.597E+03
- -b) 3.147E+03
- -c) 3.812E+03
- -d) 4.619E+03
- +e) 5.596E+03
8) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?
- -a) 6.411E+02 N/C
- -b) 7.052E+02 N/C
- +c) 7.757E+02 N/C
- -d) 8.533E+02 N/C
- -e) 9.386E+02 N/C
- -a) 3.959E+01 N·m2/C
- -b) 4.354E+01 N·m2/C
- -c) 4.790E+01 N·m2/C
- +d) 5.269E+01 N·m2/C
- -e) 5.796E+01 N·m2/C
10) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the entire surface of the cylinder.
- +a) 5.91E+02
- -b) 7.16E+02
- -c) 8.68E+02
- -d) 1.05E+03
- -e) 1.27E+03
Key: Y0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?
- -a) 3.251E+01 N/C
- -b) 3.577E+01 N/C
- -c) 3.934E+01 N/C
- -d) 4.328E+01 N/C
- +e) 4.760E+01 N/C
- -a) 4.125E+01 N·m2/C
- -b) 4.537E+01 N·m2/C
- -c) 4.991E+01 N·m2/C
- +d) 5.490E+01 N·m2/C
- -e) 6.039E+01 N·m2/C
- -a) 4.809E+01 N·m2/C
- -b) 5.290E+01 N·m2/C
- +c) 5.819E+01 N·m2/C
- -d) 6.401E+01 N·m2/C
- -e) 7.041E+01 N·m2/C
4) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?
- +a) 4.782E+02 N/C
- -b) 5.260E+02 N/C
- -c) 5.787E+02 N/C
- -d) 6.365E+02 N/C
- -e) 7.002E+02 N/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 1.704E+03
- -b) 2.064E+03
- -c) 2.501E+03
- +d) 3.030E+03
- -e) 3.671E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 2.454E+02
- -b) 2.973E+02
- -c) 3.601E+02
- +d) 4.363E+02
- -e) 5.286E+02
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b)
- -c)
- -d) none of these are correct
- +e)
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b)
- -c)
- -d) none of these are correct
- +e)
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- +a)
- -b)
- -c)
- -d) none of these are correct
- -e)
Key: Y1[edit | edit source]
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=4.3 m, z=z0=1.7 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 4.1m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 27° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?- +a) 7.876E+01 N·m2/C
- -b) 8.664E+01 N·m2/C
- -c) 9.531E+01 N·m2/C
- -d) 1.048E+02 N·m2/C
- -e) 1.153E+02 N·m2/C
2) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- +a) 5.664E+03
- -b) 6.863E+03
- -c) 8.314E+03
- -d) 1.007E+04
- -e) 1.220E+04
- -a) 2.079E+01 N·m2/C
- -b) 2.287E+01 N·m2/C
- -c) 2.516E+01 N·m2/C
- +d) 2.768E+01 N·m2/C
- -e) 3.044E+01 N·m2/C
4) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- +a)
- -b) none of these are correct
- -c)
- -d)
- -e)
5) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?
- -a) 3.251E+01 N/C
- -b) 3.577E+01 N/C
- -c) 3.934E+01 N/C
- -d) 4.328E+01 N/C
- +e) 4.760E+01 N/C
6) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
7) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 3.799E+02
- -b) 4.603E+02
- -c) 5.576E+02
- +d) 6.756E+02
- -e) 8.185E+02
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b)
- -c) none of these are correct
- -d)
- +e)
9) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?
- -a) 2.039E+01 N/C
- -b) 2.243E+01 N/C
- +c) 2.467E+01 N/C
- -d) 2.714E+01 N/C
- -e) 2.985E+01 N/C
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- -a)
- -b)
- -c) none of these are correct
- +d)
- -e)
Key: Y2[edit | edit source]
1) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
- +a)
- -b)
- -c) none of these are correct
- -d)
- -e)
- -a) 4.420E+01 N·m2/C
- -b) 4.862E+01 N·m2/C
- -c) 5.348E+01 N·m2/C
- -d) 5.882E+01 N·m2/C
- +e) 6.471E+01 N·m2/C
3) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 6.546E+02
- -b) 7.931E+02
- -c) 9.609E+02
- +d) 1.164E+03
- -e) 1.410E+03
4) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 4.522E+02
- -b) 5.478E+02
- -c) 6.637E+02
- +d) 8.041E+02
- -e) 9.742E+02
- +a) 5.978E+01 N·m2/C
- -b) 6.576E+01 N·m2/C
- -c) 7.233E+01 N·m2/C
- -d) 7.957E+01 N·m2/C
- -e) 8.752E+01 N·m2/C
6) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?
- -a) 6.411E+02 N/C
- -b) 7.052E+02 N/C
- +c) 7.757E+02 N/C
- -d) 8.533E+02 N/C
- -e) 9.386E+02 N/C
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
8) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
9) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- +a)
- -b) none of these are correct
- -c)
- -d)
- -e)
10) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.9 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.1 m from the center of the shells?
- -a) 5.297E+00 N/C
- -b) 5.827E+00 N/C
- -c) 6.409E+00 N/C
- -d) 7.050E+00 N/C
- +e) 7.755E+00 N/C
Key: Z0[edit | edit source]
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?
- +a) 1.017E+01 N/C
- -b) 1.118E+01 N/C
- -c) 1.230E+01 N/C
- -d) 1.353E+01 N/C
- -e) 1.488E+01 N/C
- +a) 3.249E+01 N·m2/C
- -b) 3.574E+01 N·m2/C
- -c) 3.931E+01 N·m2/C
- -d) 4.324E+01 N·m2/C
- -e) 4.757E+01 N·m2/C
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
- +a) 7.200E+01 V·m
- -b) 7.920E+01 V·m
- -c) 8.712E+01 V·m
- -d) 9.583E+01 V·m
- -e) 1.054E+02 V·m
- +a) 8.314E+01 N·m2/C
- -b) 9.146E+01 N·m2/C
- -c) 1.006E+02 N·m2/C
- -d) 1.107E+02 N·m2/C
- -e) 1.217E+02 N·m2/C
5) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 3.232E+03
- -b) 3.915E+03
- -c) 4.743E+03
- -d) 5.747E+03
- +e) 6.962E+03
6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 5.043E+02
- -b) 6.109E+02
- -c) 7.402E+02
- +d) 8.967E+02
- -e) 1.086E+03
7) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b)
- +c)
- -d) none of these are correct
- -e)
8) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
9) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- +b)
- -c)
- -d) none of these are correct
- -e)
10) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
Key: Z1[edit | edit source]
1) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- +a)
- -b)
- -c)
- -d)
- -e) none of these are correct
2) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- +a) 5.610E+02
- -b) 6.796E+02
- -c) 8.234E+02
- -d) 9.975E+02
- -e) 1.209E+03
3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
- -a) 9.952E+03 V·m
- -b) 1.095E+04 V·m
- -c) 1.204E+04 V·m
- +d) 1.325E+04 V·m
- -e) 1.457E+04 V·m
4) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 5.311E+02
- -b) 6.434E+02
- -c) 7.795E+02
- +d) 9.444E+02
- -e) 1.144E+03
5) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
- -a) 5.989E+01 N·m2/C
- -b) 6.588E+01 N·m2/C
- -c) 7.247E+01 N·m2/C
- +d) 7.971E+01 N·m2/C
- -e) 8.769E+01 N·m2/C
7) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
8) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?
- -a) 9.144E+00 N/C
- -b) 1.006E+01 N/C
- -c) 1.106E+01 N/C
- -d) 1.217E+01 N/C
- +e) 1.339E+01 N/C
- -a) 5.000E+01 N·m2/C
- -b) 5.500E+01 N·m2/C
- -c) 6.050E+01 N·m2/C
- +d) 6.656E+01 N·m2/C
- -e) 7.321E+01 N·m2/C
10) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a) none of these are correct
- -b)
- +c)
- -d)
- -e)
Key: Z2[edit | edit source]
1) A sphere has a uniform charge density of , and a radius or R. What formula describes the electric field at a distance r > R?
- +a)
- -b)
- -c)
- -d) none of these are correct
- -e)
2) A cylinder of radius, R, and height H has a uniform charge density of . The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
- -a)
- -b) none of these are correct
- -c)
- -d)
- +e)
3) A sphere has a uniform charge density of , and a radius equal to R. What formula describes the electric field at a distance r < R?
- -a)
- -b) none of these are correct
- +c)
- -d)
- -e)
- +a) 8.314E+01 N·m2/C
- -b) 9.146E+01 N·m2/C
- -c) 1.006E+02 N·m2/C
- -d) 1.107E+02 N·m2/C
- -e) 1.217E+02 N·m2/C
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the curved side surface of the cylinder.
- -a) 6.546E+02
- -b) 7.931E+02
- -c) 9.609E+02
- +d) 1.164E+03
- -e) 1.410E+03
6) A cylinder of radius, R, and height H has a uniform charge density of . The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
- -a) none of these are correct
- -b)
- -c)
- -d)
- +e)
7) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
Let be the outward unit normal to this cylinder and evaluate ,
over the top surface of the cylinder.
- -a) 5.311E+02
- -b) 6.434E+02
- -c) 7.795E+02
- +d) 9.444E+02
- -e) 1.144E+03
8) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
- -a) 7.054E+03 V·m
- -b) 7.759E+03 V·m
- -c) 8.535E+03 V·m
- -d) 9.388E+03 V·m
- +e) 1.033E+04 V·m
9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?
- -a) 9.144E+00 N/C
- -b) 1.006E+01 N/C
- -c) 1.106E+01 N/C
- -d) 1.217E+01 N/C
- +e) 1.339E+01 N/C
- -a) 1.891E+01 N·m2/C
- -b) 2.080E+01 N·m2/C
- +c) 2.288E+01 N·m2/C
- -d) 2.517E+01 N·m2/C
- -e) 2.768E+01 N·m2/C