Quizbank/Electricity and Magnetism (calculus based)/QBCh6

QB153086031104

QB:Ch 6:V1

QB153086031104

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=1.7 m, y=y₁=4.6 m, z=z₀=1.4 m, and z=z₁=4.5 m. The surfaces in the yz plane each have area 9.0m². Those in the xy plane have area 6.4m² ,and those in the zx plane have area 6.8m². An electric field of magnitude 15 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) 3.959E+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

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=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\vec {E}}=3y^{2.9}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.5}{\hat {k}}$

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

3) 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)=ar^1.5 (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