# Quizbank/Electricity and Magnetism (calculus based)/c12

calcPhyEMq/c12 ID153287923206 (Study guide)

**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:Quizbank153287923206.pdf

*Contact me at* User talk:Guy vandegrift *if you need any help.*

### c12 A0[edit | edit source]

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.432 m and 0.402 T, then how much current (in the z-direction) flows through a circle of radius 0.275 m that is centered on the axis with its plane perpendicular to the axis?

- a) 3.277E+05 A
- b) 3.604E+05 A
- c) 3.965E+05 A
- d) 4.361E+05 A
- e) 4.797E+05 A

2) Two loops of wire carry the same current of 18 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.848 m while the other has a radius of 1.42 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.625 m from the first (smaller) loopif the disance between the loops is 1.55 m?

- a) 7.952E-03 T
- b) 8.747E-03 T
- c) 9.622E-03 T
- d) 1.058E-02 T
- e) 1.164E-02 T

3) Two parallel wires each carry a 3.8 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.74 cm, 1.47 cm), while the other is located at (5.26 cm, 5.87 cm). What is the force per unit length between the wires?

- a) 5.926E-11 N/m
- b) 6.518E-11 N/m
- c) 7.170E-11 N/m
- d) 7.887E-11 N/m
- e) 8.676E-11 N/m

4) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.18 mm from the center of a wire of radius 3 mm if the current is 1A?

- a) 1.791E-05 T
- b) 1.970E-05 T
- c) 2.167E-05 T
- d) 2.384E-05 T
- e) 2.622E-05 T

#### c12 A1[edit | edit source]

1) Two parallel wires each carry a 1.65 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.59 cm, 1.81 cm), while the other is located at (5.78 cm, 4.43 cm). What is the force per unit length between the wires?

- a) 1.422E-11 N/m
- b) 1.564E-11 N/m
- c) 1.720E-11 N/m
- d) 1.892E-11 N/m
- e) 2.081E-11 N/m

2) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.18 mm from the center of a wire of radius 3 mm if the current is 1A?

- a) 1.791E-05 T
- b) 1.970E-05 T
- c) 2.167E-05 T
- d) 2.384E-05 T
- e) 2.622E-05 T

3) Two loops of wire carry the same current of 67 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.847 m while the other has a radius of 1.15 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.408 m from the first (smaller) loopif the disance between the loops is 1.15 m?

- a) 4.799E-02 T
- b) 5.278E-02 T
- c) 5.806E-02 T
- d) 6.387E-02 T
- e) 7.026E-02 T

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.871 m and 0.427 T, then how much current (in the z-direction) flows through a circle of radius 0.688 m that is centered on the axis with its plane perpendicular to the axis?

- a) 1.404E+06 A
- b) 1.544E+06 A
- c) 1.699E+06 A
- d) 1.869E+06 A
- e) 2.056E+06 A

#### c12 A2[edit | edit source]

1) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.51 mm from the center of a wire of radius 5 mm if the current is 1A?

- a) 1.208E-05 T
- b) 1.329E-05 T
- c) 1.462E-05 T
- d) 1.608E-05 T
- e) 1.769E-05 T

2) Two parallel wires each carry a 2.83 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.15 cm, 1.13 cm), while the other is located at (5.14 cm, 4.22 cm). What is the force per unit length between the wires?

- a) 2.977E-11 N/m
- b) 3.274E-11 N/m
- c) 3.602E-11 N/m
- d) 3.962E-11 N/m
- e) 4.358E-11 N/m

3) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.645 m and 0.469 T, then how much current (in the z-direction) flows through a circle of radius 0.26 m that is centered on the axis with its plane perpendicular to the axis?

- a) 2.949E+05 A
- b) 3.244E+05 A
- c) 3.568E+05 A
- d) 3.925E+05 A
- e) 4.317E+05 A

4) Two loops of wire carry the same current of 88 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.655 m while the other has a radius of 1.11 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.531 m from the first (smaller) loopif the disance between the loops is 1.72 m?

- a) 4.162E-02 T
- b) 4.578E-02 T
- c) 5.036E-02 T
- d) 5.540E-02 T
- e) 6.094E-02 T

### c12 B0[edit | edit source]

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.571 m and 0.331 T, then how much current (in the z-direction) flows through a circle of radius 0.321 m that is centered on the axis with its plane perpendicular to the axis?

- a) 3.226E+05 A
- b) 3.549E+05 A
- c) 3.904E+05 A
- d) 4.294E+05 A
- e) 4.724E+05 A

2) Two parallel wires each carry a 2.12 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.67 cm, 1.25 cm), while the other is located at (4.69 cm, 4.27 cm). What is the force per unit length between the wires?

- a) 2.119E-11 N/m
- b) 2.331E-11 N/m
- c) 2.564E-11 N/m
- d) 2.820E-11 N/m
- e) 3.102E-11 N/m

_{1}, I

_{2}, I

_{2}) are (1.03 A, 1.95 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 6.545E-05 T - b) B
_{x}= 7.200E-05 T - c) B
_{x}= 7.919E-05 T - d) B
_{x}= 8.711E-05 T - e) B
_{x}= 9.583E-05 T

4) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.86 mm from the center of a wire of radius 3 mm if the current is 1A?

- a) 3.416E-05 T
- b) 3.758E-05 T
- c) 4.133E-05 T
- d) 4.547E-05 T
- e) 5.001E-05 T

#### c12 B1[edit | edit source]

1) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.66 mm from the center of a wire of radius 5 mm if the current is 1A?

- a) 1.935E-05 T
- b) 2.128E-05 T
- c) 2.341E-05 T
- d) 2.575E-05 T
- e) 2.832E-05 T

2) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.52 m and 0.657 T, then how much current (in the z-direction) flows through a circle of radius 0.295 m that is centered on the axis with its plane perpendicular to the axis?

- a) 7.876E+05 A
- b) 8.664E+05 A
- c) 9.530E+05 A
- d) 1.048E+06 A
- e) 1.153E+06 A

3) Two parallel wires each carry a 7.48 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.13 cm, 0.955 cm), while the other is located at (5.37 cm, 5.48 cm). What is the force per unit length between the wires?

- a) 2.015E-10 N/m
- b) 2.216E-10 N/m
- c) 2.438E-10 N/m
- d) 2.682E-10 N/m
- e) 2.950E-10 N/m

_{1}, I

_{2}, I

_{2}) are (1.16 A, 2.46 A, 2.15 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 9.053E-05 T - b) B
_{x}= 9.959E-05 T - c) B
_{x}= 1.095E-04 T - d) B
_{x}= 1.205E-04 T - e) B
_{x}= 1.325E-04 T

#### c12 B2[edit | edit source]

1) Three wires sit at the corners of a square of length 0.466 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I_{1}, I

_{2}, I

_{2}) are (1.4 A, 2.42 A, 1.9 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 1.335E-04 T - b) B
_{x}= 1.468E-04 T - c) B
_{x}= 1.615E-04 T - d) B
_{x}= 1.777E-04 T - e) B
_{x}= 1.954E-04 T

2) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.568 m and 0.214 T, then how much current (in the z-direction) flows through a circle of radius 0.387 m that is centered on the axis with its plane perpendicular to the axis?

- a) 3.382E+05 A
- b) 3.720E+05 A
- c) 4.092E+05 A
- d) 4.502E+05 A
- e) 4.952E+05 A

3) Two parallel wires each carry a 3.51 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.14 cm, 1.43 cm), while the other is located at (4.14 cm, 5.23 cm). What is the force per unit length between the wires?

- a) 6.484E-11 N/m
- b) 7.133E-11 N/m
- c) 7.846E-11 N/m
- d) 8.631E-11 N/m
- e) 9.494E-11 N/m

4) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.66 mm from the center of a wire of radius 5 mm if the current is 1A?

- a) 1.935E-05 T
- b) 2.128E-05 T
- c) 2.341E-05 T
- d) 2.575E-05 T
- e) 2.832E-05 T

### c12 C0[edit | edit source]

1) Three wires sit at the corners of a square of length 0.76 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I_{1}, I

_{2}, I

_{2}) are (1.91 A, 1.34 A, 1.05 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 5.611E-05 T - b) B
_{y}= 6.172E-05 T - c) B
_{y}= 6.789E-05 T - d) B
_{y}= 7.468E-05 T - e) B
_{y}= 8.215E-05 T

_{1}, I

_{2}, I

_{2}) are (1.4 A, 2.42 A, 1.9 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 1.335E-04 T - b) B
_{x}= 1.468E-04 T - c) B
_{x}= 1.615E-04 T - d) B
_{x}= 1.777E-04 T - e) B
_{x}= 1.954E-04 T

3) A wire carries a current of 266 A in a circular arc with radius 2.21 cm swept through 73 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 5.034E+00 Tesla
- b) 5.538E+00 Tesla
- c) 6.091E+00 Tesla
- d) 6.701E+00 Tesla
- e) 7.371E+00 Tesla

4) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.59 mm from the center of a wire of radius 5 mm if the current is 1A?

- a) 2.072E-05 T
- b) 2.279E-05 T
- c) 2.507E-05 T
- d) 2.758E-05 T
- e) 3.034E-05 T

#### c12 C1[edit | edit source]

1) A wire carries a current of 269 A in a circular arc with radius 2.35 cm swept through 36 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 1.613E+00 Tesla
- b) 1.774E+00 Tesla
- c) 1.951E+00 Tesla
- d) 2.146E+00 Tesla
- e) 2.361E+00 Tesla

_{1}, I

_{2}, I

_{2}) are (2.26 A, 1.75 A, 2.47 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 7.518E-05 T - b) B
_{y}= 8.270E-05 T - c) B
_{y}= 9.097E-05 T - d) B
_{y}= 1.001E-04 T - e) B
_{y}= 1.101E-04 T

3) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.81 mm from the center of a wire of radius 3 mm if the current is 1A?

- a) 3.324E-05 T
- b) 3.657E-05 T
- c) 4.022E-05 T
- d) 4.424E-05 T
- e) 4.867E-05 T

_{1}, I

_{2}, I

_{2}) are (1.03 A, 1.95 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 6.545E-05 T - b) B
_{x}= 7.200E-05 T - c) B
_{x}= 7.919E-05 T - d) B
_{x}= 8.711E-05 T - e) B
_{x}= 9.583E-05 T

#### c12 C2[edit | edit source]

1) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.18 mm from the center of a wire of radius 3 mm if the current is 1A?

- a) 1.791E-05 T
- b) 1.970E-05 T
- c) 2.167E-05 T
- d) 2.384E-05 T
- e) 2.622E-05 T

_{1}, I

_{2}, I

_{2}) are (1.76 A, 1.02 A, 1.08 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 3.394E-05 T - b) B
_{x}= 3.733E-05 T - c) B
_{x}= 4.106E-05 T - d) B
_{x}= 4.517E-05 T - e) B
_{x}= 4.969E-05 T

_{1}, I

_{2}, I

_{2}) are (2.24 A, 1.37 A, 2.3 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 7.576E-05 T - b) B
_{y}= 8.333E-05 T - c) B
_{y}= 9.167E-05 T - d) B
_{y}= 1.008E-04 T - e) B
_{y}= 1.109E-04 T

4) A wire carries a current of 250 A in a circular arc with radius 2.17 cm swept through 53 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 3.498E+00 Tesla
- b) 3.848E+00 Tesla
- c) 4.233E+00 Tesla
- d) 4.656E+00 Tesla
- e) 5.122E+00 Tesla

### c12 D0[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.81 kA, I

_{2}=1.2 kA, and I

_{3}=1.84 kA, take the path and evalulate the line integral,

:

- a) 3.583E-03 T-m
- b) 3.941E-03 T-m
- c) 4.335E-03 T-m
- d) 4.769E-03 T-m
- e) 5.246E-03 T-m

2) Two loops of wire carry the same current of 21 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.753 m while the other has a radius of 1.47 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.406 m from the first (smaller) loopif the disance between the loops is 1.38 m?

- a) 1.559E-02 T
- b) 1.715E-02 T
- c) 1.886E-02 T
- d) 2.075E-02 T
- e) 2.283E-02 T

3) A wire carries a current of 106 A in a circular arc with radius 1.32 cm swept through 38 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 1.589E+00 Tesla
- b) 1.748E+00 Tesla
- c) 1.923E+00 Tesla
- d) 2.116E+00 Tesla
- e) 2.327E+00 Tesla

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.432 m and 0.402 T, then how much current (in the z-direction) flows through a circle of radius 0.275 m that is centered on the axis with its plane perpendicular to the axis?

- a) 3.277E+05 A
- b) 3.604E+05 A
- c) 3.965E+05 A
- d) 4.361E+05 A
- e) 4.797E+05 A

#### c12 D1[edit | edit source]

1) A wire carries a current of 385 A in a circular arc with radius 1.53 cm swept through 58 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 5.711E+00 Tesla
- b) 6.283E+00 Tesla
- c) 6.911E+00 Tesla
- d) 7.602E+00 Tesla
- e) 8.362E+00 Tesla

2) Two loops of wire carry the same current of 20 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.776 m while the other has a radius of 1.2 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.517 m from the first (smaller) loopif the disance between the loops is 1.37 m?

- a) 1.127E-02 T
- b) 1.240E-02 T
- c) 1.364E-02 T
- d) 1.500E-02 T
- e) 1.650E-02 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.78 kA, I

_{2}=2.61 kA, and I

_{3}=3.76 kA, take the path and evalulate the line integral,

:

- a) 4.939E-03 T-m
- b) 5.432E-03 T-m
- c) 5.976E-03 T-m
- d) 6.573E-03 T-m
- e) 7.231E-03 T-m

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.248 m and 0.459 T, then how much current (in the z-direction) flows through a circle of radius 0.152 m that is centered on the axis with its plane perpendicular to the axis?

- a) 2.228E+05 A
- b) 2.451E+05 A
- c) 2.696E+05 A
- d) 2.966E+05 A
- e) 3.262E+05 A

#### c12 D2[edit | edit source]

1) Two loops of wire carry the same current of 24 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.53 m while the other has a radius of 1.38 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.485 m from the first (smaller) loopif the disance between the loops is 1.78 m?

- a) 1.294E-02 T
- b) 1.424E-02 T
- c) 1.566E-02 T
- d) 1.723E-02 T
- e) 1.895E-02 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.84 kA, I

_{2}=2.02 kA, and I

_{3}=4.24 kA, take the path and evalulate the line integral,

:

- a) 5.255E-03 T-m
- b) 5.781E-03 T-m
- c) 6.359E-03 T-m
- d) 6.994E-03 T-m
- e) 7.694E-03 T-m

3) A wire carries a current of 297 A in a circular arc with radius 2.31 cm swept through 75 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 3.774E+00 Tesla
- b) 4.151E+00 Tesla
- c) 4.566E+00 Tesla
- d) 5.023E+00 Tesla
- e) 5.525E+00 Tesla

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.407 m and 0.605 T, then how much current (in the z-direction) flows through a circle of radius 0.196 m that is centered on the axis with its plane perpendicular to the axis?

- a) 3.583E+05 A
- b) 3.941E+05 A
- c) 4.335E+05 A
- d) 4.769E+05 A
- e) 5.246E+05 A

### c12 E0[edit | edit source]

1) Three wires sit at the corners of a square of length 0.819 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I_{1}, I

_{2}, I

_{2}) are (2.01 A, 1.09 A, 1.56 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 4.688E-05 T - b) B
_{y}= 5.156E-05 T - c) B
_{y}= 5.672E-05 T - d) B
_{y}= 6.239E-05 T - e) B
_{y}= 6.863E-05 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.58 kA, I

_{2}=1.27 kA, and I

_{3}=1.99 kA, take the path and evalulate the line integral,

:

- a) 3.770E-03 T-m
- b) 4.147E-03 T-m
- c) 4.562E-03 T-m
- d) 5.018E-03 T-m
- e) 5.520E-03 T-m

3) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.03 mm from the center of a wire of radius 3 mm if the current is 1A?

- a) 1.720E-05 T
- b) 1.892E-05 T
- c) 2.081E-05 T
- d) 2.289E-05 T
- e) 2.518E-05 T

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 16 turns per centimeter and the current applied to the solenoid is 536 mA, the net magnetic field is measured to be 1.47 T. What is the magnetic susceptibility for this case?

- a) 9.310E+02
- b) 1.024E+03
- c) 1.126E+03
- d) 1.239E+03
- e) 1.363E+03

#### c12 E1[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.38 kA, I

_{2}=1.58 kA, and I

_{3}=4.31 kA, take the path and evalulate the line integral,

:

- a) 4.386E-03 T-m
- b) 4.825E-03 T-m
- c) 5.307E-03 T-m
- d) 5.838E-03 T-m
- e) 6.421E-03 T-m

2) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 17 turns per centimeter and the current applied to the solenoid is 455 mA, the net magnetic field is measured to be 1.14 T. What is the magnetic susceptibility for this case?

- a) 8.804E+02
- b) 9.685E+02
- c) 1.065E+03
- d) 1.172E+03
- e) 1.289E+03

_{1}, I

_{2}, I

_{2}) are (2.45 A, 1.66 A, 1.63 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 1.205E-04 T - b) B
_{y}= 1.325E-04 T - c) B
_{y}= 1.458E-04 T - d) B
_{y}= 1.604E-04 T - e) B
_{y}= 1.764E-04 T

4) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.86 mm from the center of a wire of radius 5 mm if the current is 1A?

- a) 1.488E-05 T
- b) 1.637E-05 T
- c) 1.800E-05 T
- d) 1.981E-05 T
- e) 2.179E-05 T

#### c12 E2[edit | edit source]

1) Three wires sit at the corners of a square of length 0.859 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I_{1}, I

_{2}, I

_{2}) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 4.028E-05 T - b) B
_{y}= 4.431E-05 T - c) B
_{y}= 4.874E-05 T - d) B
_{y}= 5.361E-05 T - e) B
_{y}= 5.897E-05 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.38 kA, I

_{2}=0.839 kA, and I

_{3}=2.27 kA, take the path and evalulate the line integral,

:

- a) 4.354E-03 T-m
- b) 4.789E-03 T-m
- c) 5.268E-03 T-m
- d) 5.795E-03 T-m
- e) 6.374E-03 T-m

3) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.43 mm from the center of a wire of radius 5 mm if the current is 1A?

- a) 1.944E-05 T
- b) 2.138E-05 T
- c) 2.352E-05 T
- d) 2.587E-05 T
- e) 2.846E-05 T

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 24 turns per centimeter and the current applied to the solenoid is 242 mA, the net magnetic field is measured to be 1.38 T. What is the magnetic susceptibility for this case?

- a) 1.718E+03
- b) 1.890E+03
- c) 2.079E+03
- d) 2.287E+03
- e) 2.515E+03

### c12 F0[edit | edit source]

1) A solenoid has 4.380E+04 turns wound around a cylinder of diameter 1.77 cm and length 16 m. The current through the coils is 0.916 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−4.39 cm to z=+4.26 cm

- a) 2.478E-04 T-m
- b) 2.726E-04 T-m
- c) 2.998E-04 T-m
- d) 3.298E-04 T-m
- e) 3.628E-04 T-m

2) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.259 m and 0.575 T, then how much current (in the z-direction) flows through a circle of radius 0.191 m that is centered on the axis with its plane perpendicular to the axis?

- a) 3.492E+05 A
- b) 3.841E+05 A
- c) 4.225E+05 A
- d) 4.648E+05 A
- e) 5.113E+05 A

3) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 16 turns per centimeter and the current applied to the solenoid is 536 mA, the net magnetic field is measured to be 1.47 T. What is the magnetic susceptibility for this case?

- a) 9.310E+02
- b) 1.024E+03
- c) 1.126E+03
- d) 1.239E+03
- e) 1.363E+03

_{1}, I

_{2}, I

_{2}) are (1.03 A, 1.95 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 6.545E-05 T - b) B
_{x}= 7.200E-05 T - c) B
_{x}= 7.919E-05 T - d) B
_{x}= 8.711E-05 T - e) B
_{x}= 9.583E-05 T

#### c12 F1[edit | edit source]

1) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 22 turns per centimeter and the current applied to the solenoid is 568 mA, the net magnetic field is measured to be 1.29 T. What is the magnetic susceptibility for this case?

- a) 8.205E+02
- b) 9.026E+02
- c) 9.928E+02
- d) 1.092E+03
- e) 1.201E+03

2) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.253 m and 0.489 T, then how much current (in the z-direction) flows through a circle of radius 0.112 m that is centered on the axis with its plane perpendicular to the axis?

- a) 1.289E+05 A
- b) 1.418E+05 A
- c) 1.560E+05 A
- d) 1.716E+05 A
- e) 1.888E+05 A

_{1}, I

_{2}, I

_{2}) are (1.57 A, 2.03 A, 2.08 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 7.270E-05 T - b) B
_{x}= 7.997E-05 T - c) B
_{x}= 8.797E-05 T - d) B
_{x}= 9.677E-05 T - e) B
_{x}= 1.064E-04 T

4) A solenoid has 3.950E+04 turns wound around a cylinder of diameter 1.64 cm and length 16 m. The current through the coils is 0.441 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−2.05 cm to z=+3.97 cm

- a) 6.807E-05 T-m
- b) 7.487E-05 T-m
- c) 8.236E-05 T-m
- d) 9.060E-05 T-m
- e) 9.966E-05 T-m

#### c12 F2[edit | edit source]

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.51 m and 0.649 T, then how much current (in the z-direction) flows through a circle of radius 0.376 m that is centered on the axis with its plane perpendicular to the axis?

- a) 9.388E+05 A
- b) 1.033E+06 A
- c) 1.136E+06 A
- d) 1.249E+06 A
- e) 1.374E+06 A

2) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 27 turns per centimeter and the current applied to the solenoid is 280 mA, the net magnetic field is measured to be 1.13 T. What is the magnetic susceptibility for this case?

- a) 1.188E+03
- b) 1.307E+03
- c) 1.438E+03
- d) 1.582E+03
- e) 1.740E+03

_{1}, I

_{2}, I

_{2}) are (1.03 A, 1.95 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 6.545E-05 T - b) B
_{x}= 7.200E-05 T - c) B
_{x}= 7.919E-05 T - d) B
_{x}= 8.711E-05 T - e) B
_{x}= 9.583E-05 T

4) A solenoid has 5.980E+04 turns wound around a cylinder of diameter 1.8 cm and length 17 m. The current through the coils is 0.933 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−3.68 cm to z=+1.29 cm

- a) 1.863E-04 T-m
- b) 2.050E-04 T-m
- c) 2.255E-04 T-m
- d) 2.480E-04 T-m
- e) 2.728E-04 T-m

### c12 G0[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.38 kA, I

_{2}=0.839 kA, and I

_{3}=2.27 kA, take the path and evalulate the line integral,

:

- a) 4.354E-03 T-m
- b) 4.789E-03 T-m
- c) 5.268E-03 T-m
- d) 5.795E-03 T-m
- e) 6.374E-03 T-m

2) Two loops of wire carry the same current of 66 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.485 m while the other has a radius of 1.27 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.507 m from the first (smaller) loopif the disance between the loops is 1.76 m?

- a) 2.733E-02 T
- b) 3.007E-02 T
- c) 3.307E-02 T
- d) 3.638E-02 T
- e) 4.002E-02 T

3) A solenoid has 3.950E+04 turns wound around a cylinder of diameter 1.64 cm and length 16 m. The current through the coils is 0.441 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−2.05 cm to z=+3.97 cm

- a) 6.807E-05 T-m
- b) 7.487E-05 T-m
- c) 8.236E-05 T-m
- d) 9.060E-05 T-m
- e) 9.966E-05 T-m

4) A wire carries a current of 343 A in a circular arc with radius 2.95 cm swept through 38 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 1.902E+00 Tesla
- b) 2.092E+00 Tesla
- c) 2.301E+00 Tesla
- d) 2.532E+00 Tesla
- e) 2.785E+00 Tesla

#### c12 G1[edit | edit source]

1) Two loops of wire carry the same current of 97 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.595 m while the other has a radius of 1.1 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.63 m from the first (smaller) loopif the disance between the loops is 1.72 m?

- a) 5.302E-02 T
- b) 5.832E-02 T
- c) 6.415E-02 T
- d) 7.056E-02 T
- e) 7.762E-02 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.42 kA, I

_{2}=0.904 kA, and I

_{3}=1.34 kA, take the path and evalulate the line integral,

:

- a) 2.696E-03 T-m
- b) 2.966E-03 T-m
- c) 3.263E-03 T-m
- d) 3.589E-03 T-m
- e) 3.948E-03 T-m

3) A wire carries a current of 293 A in a circular arc with radius 1.75 cm swept through 71 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 4.652E+00 Tesla
- b) 5.117E+00 Tesla
- c) 5.629E+00 Tesla
- d) 6.192E+00 Tesla
- e) 6.811E+00 Tesla

4) A solenoid has 7.610E+04 turns wound around a cylinder of diameter 1.21 cm and length 9 m. The current through the coils is 0.696 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−1.52 cm to z=+2.04 cm

- a) 2.176E-04 T-m
- b) 2.393E-04 T-m
- c) 2.633E-04 T-m
- d) 2.896E-04 T-m
- e) 3.186E-04 T-m

#### c12 G2[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.72 kA, I

_{2}=2.17 kA, and I

_{3}=3.21 kA, take the path and evalulate the line integral,

:

- a) 3.905E-03 T-m
- b) 4.295E-03 T-m
- c) 4.725E-03 T-m
- d) 5.197E-03 T-m
- e) 5.717E-03 T-m

2) A solenoid has 7.610E+04 turns wound around a cylinder of diameter 1.21 cm and length 9 m. The current through the coils is 0.696 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−1.52 cm to z=+2.04 cm

- a) 2.176E-04 T-m
- b) 2.393E-04 T-m
- c) 2.633E-04 T-m
- d) 2.896E-04 T-m
- e) 3.186E-04 T-m

3) Two loops of wire carry the same current of 18 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.848 m while the other has a radius of 1.42 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.625 m from the first (smaller) loopif the disance between the loops is 1.55 m?

- a) 7.952E-03 T
- b) 8.747E-03 T
- c) 9.622E-03 T
- d) 1.058E-02 T
- e) 1.164E-02 T

4) A wire carries a current of 266 A in a circular arc with radius 2.21 cm swept through 73 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 5.034E+00 Tesla
- b) 5.538E+00 Tesla
- c) 6.091E+00 Tesla
- d) 6.701E+00 Tesla
- e) 7.371E+00 Tesla

### c12 H0[edit | edit source]

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.432 m and 0.402 T, then how much current (in the z-direction) flows through a circle of radius 0.275 m that is centered on the axis with its plane perpendicular to the axis?

- a) 3.277E+05 A
- b) 3.604E+05 A
- c) 3.965E+05 A
- d) 4.361E+05 A
- e) 4.797E+05 A

_{1}, I

_{2}, I

_{2}) are (1.57 A, 2.03 A, 2.08 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 7.270E-05 T - b) B
_{x}= 7.997E-05 T - c) B
_{x}= 8.797E-05 T - d) B
_{x}= 9.677E-05 T - e) B
_{x}= 1.064E-04 T

_{1}, I

_{2}, I

_{2}) are (1.32 A, 1.4 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 3.480E-05 T - b) B
_{y}= 3.828E-05 T - c) B
_{y}= 4.210E-05 T - d) B
_{y}= 4.631E-05 T - e) B
_{y}= 5.095E-05 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.89 kA, I

_{2}=1.19 kA, and I

_{3}=3.5 kA, take the path and evalulate the line integral,

:

- a) 6.535E-03 T-m
- b) 7.188E-03 T-m
- c) 7.907E-03 T-m
- d) 8.697E-03 T-m
- e) 9.567E-03 T-m

#### c12 H1[edit | edit source]

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.52 m and 0.657 T, then how much current (in the z-direction) flows through a circle of radius 0.295 m that is centered on the axis with its plane perpendicular to the axis?

- a) 7.876E+05 A
- b) 8.664E+05 A
- c) 9.530E+05 A
- d) 1.048E+06 A
- e) 1.153E+06 A

_{1}, I

_{2}, I

_{2}) are (1.32 A, 1.4 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 3.480E-05 T - b) B
_{y}= 3.828E-05 T - c) B
_{y}= 4.210E-05 T - d) B
_{y}= 4.631E-05 T - e) B
_{y}= 5.095E-05 T

_{1}, I

_{2}, I

_{2}) are (2.23 A, 1.52 A, 1.86 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 4.559E-05 T - b) B
_{x}= 5.015E-05 T - c) B
_{x}= 5.517E-05 T - d) B
_{x}= 6.068E-05 T - e) B
_{x}= 6.675E-05 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.38 kA, I

_{2}=0.839 kA, and I

_{3}=2.27 kA, take the path and evalulate the line integral,

:

- a) 4.354E-03 T-m
- b) 4.789E-03 T-m
- c) 5.268E-03 T-m
- d) 5.795E-03 T-m
- e) 6.374E-03 T-m

#### c12 H2[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.57 kA, I

_{2}=0.708 kA, and I

_{3}=1.48 kA, take the path and evalulate the line integral,

:

- a) 4.200E-03 T-m
- b) 4.620E-03 T-m
- c) 5.082E-03 T-m
- d) 5.590E-03 T-m
- e) 6.149E-03 T-m

_{1}, I

_{2}, I

_{2}) are (1.87 A, 2.18 A, 1.34 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 6.999E-05 T - b) B
_{y}= 7.699E-05 T - c) B
_{y}= 8.469E-05 T - d) B
_{y}= 9.316E-05 T - e) B
_{y}= 1.025E-04 T

_{1}, I

_{2}, I

_{2}) are (2.17 A, 2.25 A, 2.22 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 1.037E-04 T - b) B
_{x}= 1.141E-04 T - c) B
_{x}= 1.255E-04 T - d) B
_{x}= 1.381E-04 T - e) B
_{x}= 1.519E-04 T

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.259 m and 0.575 T, then how much current (in the z-direction) flows through a circle of radius 0.191 m that is centered on the axis with its plane perpendicular to the axis?

- a) 3.492E+05 A
- b) 3.841E+05 A
- c) 4.225E+05 A
- d) 4.648E+05 A
- e) 5.113E+05 A

### c12 I0[edit | edit source]

1) Two loops of wire carry the same current of 67 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.847 m while the other has a radius of 1.15 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.408 m from the first (smaller) loopif the disance between the loops is 1.15 m?

- a) 4.799E-02 T
- b) 5.278E-02 T
- c) 5.806E-02 T
- d) 6.387E-02 T
- e) 7.026E-02 T

2) Two parallel wires each carry a 7.68 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.36 cm, 1.58 cm), while the other is located at (5.29 cm, 5.18 cm). What is the force per unit length between the wires?

- a) 1.973E-10 N/m
- b) 2.170E-10 N/m
- c) 2.387E-10 N/m
- d) 2.625E-10 N/m
- e) 2.888E-10 N/m

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.32 kA, I

_{2}=2.0 kA, and I

_{3}=3.66 kA, take the path and evalulate the line integral,

:

- a) 1.724E-03 T-m
- b) 1.896E-03 T-m
- c) 2.086E-03 T-m
- d) 2.295E-03 T-m
- e) 2.524E-03 T-m

_{1}, I

_{2}, I

_{2}) are (1.38 A, 1.87 A, 2.03 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 7.134E-05 T - b) B
_{x}= 7.847E-05 T - c) B
_{x}= 8.632E-05 T - d) B
_{x}= 9.495E-05 T - e) B
_{x}= 1.044E-04 T

#### c12 I1[edit | edit source]

1) Two parallel wires each carry a 2.58 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.79 cm, 1.03 cm), while the other is located at (5.64 cm, 5.12 cm). What is the force per unit length between the wires?

- a) 2.634E-11 N/m
- b) 2.897E-11 N/m
- c) 3.187E-11 N/m
- d) 3.506E-11 N/m
- e) 3.856E-11 N/m

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.51 kA, I

_{2}=2.33 kA, and I

_{3}=5.35 kA, take the path and evalulate the line integral,

:

- a) 3.795E-03 T-m
- b) 4.175E-03 T-m
- c) 4.592E-03 T-m
- d) 5.051E-03 T-m
- e) 5.556E-03 T-m

_{1}, I

_{2}, I

_{2}) are (2.29 A, 1.77 A, 1.48 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 8.371E-05 T - b) B
_{x}= 9.208E-05 T - c) B
_{x}= 1.013E-04 T - d) B
_{x}= 1.114E-04 T - e) B
_{x}= 1.226E-04 T

4) Two loops of wire carry the same current of 85 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.854 m while the other has a radius of 1.18 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.5 m from the first (smaller) loopif the disance between the loops is 1.66 m?

- a) 4.253E-02 T
- b) 4.678E-02 T
- c) 5.146E-02 T
- d) 5.661E-02 T
- e) 6.227E-02 T

#### c12 I2[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.66 kA, I

_{2}=1.25 kA, and I

_{3}=2.74 kA, take the path and evalulate the line integral,

:

- a) 1.547E-03 T-m
- b) 1.702E-03 T-m
- c) 1.872E-03 T-m
- d) 2.060E-03 T-m
- e) 2.266E-03 T-m

2) Two loops of wire carry the same current of 85 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.854 m while the other has a radius of 1.18 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.5 m from the first (smaller) loopif the disance between the loops is 1.66 m?

- a) 4.253E-02 T
- b) 4.678E-02 T
- c) 5.146E-02 T
- d) 5.661E-02 T
- e) 6.227E-02 T

3) Two parallel wires each carry a 4.15 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.19 cm, 1.78 cm), while the other is located at (3.73 cm, 4.12 cm). What is the force per unit length between the wires?

- a) 1.434E-10 N/m
- b) 1.578E-10 N/m
- c) 1.736E-10 N/m
- d) 1.909E-10 N/m
- e) 2.100E-10 N/m

_{1}, I

_{2}, I

_{2}) are (1.73 A, 1.37 A, 1.65 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 6.171E-05 T - b) B
_{x}= 6.788E-05 T - c) B
_{x}= 7.467E-05 T - d) B
_{x}= 8.213E-05 T - e) B
_{x}= 9.035E-05 T

### c12 J0[edit | edit source]

1) Two loops of wire carry the same current of 14 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.835 m while the other has a radius of 1.29 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.607 m from the first (smaller) loopif the disance between the loops is 1.61 m?

- a) 6.099E-03 T
- b) 6.709E-03 T
- c) 7.380E-03 T
- d) 8.118E-03 T
- e) 8.930E-03 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.51 kA, I

_{2}=2.33 kA, and I

_{3}=5.35 kA, take the path and evalulate the line integral,

:

- a) 3.795E-03 T-m
- b) 4.175E-03 T-m
- c) 4.592E-03 T-m
- d) 5.051E-03 T-m
- e) 5.556E-03 T-m

_{1}, I

_{2}, I

_{2}) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 4.028E-05 T - b) B
_{y}= 4.431E-05 T - c) B
_{y}= 4.874E-05 T - d) B
_{y}= 5.361E-05 T - e) B
_{y}= 5.897E-05 T

4) Two parallel wires each carry a 7.48 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.13 cm, 0.955 cm), while the other is located at (5.37 cm, 5.48 cm). What is the force per unit length between the wires?

- a) 2.015E-10 N/m
- b) 2.216E-10 N/m
- c) 2.438E-10 N/m
- d) 2.682E-10 N/m
- e) 2.950E-10 N/m

#### c12 J1[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.51 kA, I

_{2}=1.32 kA, and I

_{3}=2.73 kA, take the path and evalulate the line integral,

:

- a) 1.331E-03 T-m
- b) 1.464E-03 T-m
- c) 1.611E-03 T-m
- d) 1.772E-03 T-m
- e) 1.949E-03 T-m

_{1}, I

_{2}, I

_{2}) are (1.91 A, 1.34 A, 1.05 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 5.611E-05 T - b) B
_{y}= 6.172E-05 T - c) B
_{y}= 6.789E-05 T - d) B
_{y}= 7.468E-05 T - e) B
_{y}= 8.215E-05 T

3) Two parallel wires each carry a 7.59 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.98 cm, 0.969 cm), while the other is located at (5.13 cm, 5.53 cm). What is the force per unit length between the wires?

- a) 1.840E-10 N/m
- b) 2.024E-10 N/m
- c) 2.227E-10 N/m
- d) 2.449E-10 N/m
- e) 2.694E-10 N/m

4) Two loops of wire carry the same current of 12 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.751 m while the other has a radius of 1.42 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.493 m from the first (smaller) loopif the disance between the loops is 1.26 m?

- a) 7.836E-03 T
- b) 8.620E-03 T
- c) 9.482E-03 T
- d) 1.043E-02 T
- e) 1.147E-02 T

#### c12 J2[edit | edit source]

1) Two loops of wire carry the same current of 20 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.776 m while the other has a radius of 1.2 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.517 m from the first (smaller) loopif the disance between the loops is 1.37 m?

- a) 1.127E-02 T
- b) 1.240E-02 T
- c) 1.364E-02 T
- d) 1.500E-02 T
- e) 1.650E-02 T

_{1}, I

_{2}, I

_{2}) are (2.24 A, 1.37 A, 2.3 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 7.576E-05 T - b) B
_{y}= 8.333E-05 T - c) B
_{y}= 9.167E-05 T - d) B
_{y}= 1.008E-04 T - e) B
_{y}= 1.109E-04 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.55 kA, I

_{2}=1.02 kA, and I

_{3}=1.81 kA, take the path and evalulate the line integral,

:

- a) 8.204E-04 T-m
- b) 9.025E-04 T-m
- c) 9.927E-04 T-m
- d) 1.092E-03 T-m
- e) 1.201E-03 T-m

4) Two parallel wires each carry a 8.75 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.66 cm, 1.4 cm), while the other is located at (5.64 cm, 5.66 cm). What is the force per unit length between the wires?

- a) 2.449E-10 N/m
- b) 2.694E-10 N/m
- c) 2.963E-10 N/m
- d) 3.260E-10 N/m
- e) 3.586E-10 N/m

### c12 K0[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.57 kA, I

_{2}=0.708 kA, and I

_{3}=1.48 kA, take the path and evalulate the line integral,

:

- a) 4.200E-03 T-m
- b) 4.620E-03 T-m
- c) 5.082E-03 T-m
- d) 5.590E-03 T-m
- e) 6.149E-03 T-m

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.84 kA, I

_{2}=0.476 kA, and I

_{3}=1.57 kA, take the path and evalulate the line integral,

:

- a) 1.250E-03 T-m
- b) 1.375E-03 T-m
- c) 1.512E-03 T-m
- d) 1.663E-03 T-m
- e) 1.830E-03 T-m

3) Two loops of wire carry the same current of 18 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.848 m while the other has a radius of 1.42 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.625 m from the first (smaller) loopif the disance between the loops is 1.55 m?

- a) 7.952E-03 T
- b) 8.747E-03 T
- c) 9.622E-03 T
- d) 1.058E-02 T
- e) 1.164E-02 T

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.37 m and 0.556 T, then how much current (in the z-direction) flows through a circle of radius 0.14 m that is centered on the axis with its plane perpendicular to the axis?

- a) 2.171E+05 A
- b) 2.388E+05 A
- c) 2.627E+05 A
- d) 2.890E+05 A
- e) 3.179E+05 A

#### c12 K1[edit | edit source]

1) Two loops of wire carry the same current of 12 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.751 m while the other has a radius of 1.42 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.493 m from the first (smaller) loopif the disance between the loops is 1.26 m?

- a) 7.836E-03 T
- b) 8.620E-03 T
- c) 9.482E-03 T
- d) 1.043E-02 T
- e) 1.147E-02 T

2) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.547 m and 0.597 T, then how much current (in the z-direction) flows through a circle of radius 0.158 m that is centered on the axis with its plane perpendicular to the axis?

- a) 1.751E+05 A
- b) 1.927E+05 A
- c) 2.119E+05 A
- d) 2.331E+05 A
- e) 2.564E+05 A

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.61 kA, I

_{2}=2.2 kA, and I

_{3}=5.1 kA, take the path and evalulate the line integral,

:

- a) 3.644E-03 T-m
- b) 4.009E-03 T-m
- c) 4.410E-03 T-m
- d) 4.850E-03 T-m
- e) 5.336E-03 T-m

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.38 kA, I

_{2}=1.58 kA, and I

_{3}=4.31 kA, take the path and evalulate the line integral,

:

- a) 4.386E-03 T-m
- b) 4.825E-03 T-m
- c) 5.307E-03 T-m
- d) 5.838E-03 T-m
- e) 6.421E-03 T-m

#### c12 K2[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.84 kA, I

_{2}=2.02 kA, and I

_{3}=4.24 kA, take the path and evalulate the line integral,

:

- a) 5.255E-03 T-m
- b) 5.781E-03 T-m
- c) 6.359E-03 T-m
- d) 6.994E-03 T-m
- e) 7.694E-03 T-m

2) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.549 m and 0.599 T, then how much current (in the z-direction) flows through a circle of radius 0.29 m that is centered on the axis with its plane perpendicular to the axis?

- a) 5.581E+05 A
- b) 6.139E+05 A
- c) 6.752E+05 A
- d) 7.428E+05 A
- e) 8.170E+05 A

3) Two loops of wire carry the same current of 44 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.678 m while the other has a radius of 1.14 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.508 m from the first (smaller) loopif the disance between the loops is 1.16 m?

- a) 3.342E-02 T
- b) 3.676E-02 T
- c) 4.044E-02 T
- d) 4.448E-02 T
- e) 4.893E-02 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.48 kA, I

_{2}=1.47 kA, and I

_{3}=2.6 kA, take the path and evalulate the line integral,

:

- a) 1.420E-03 T-m
- b) 1.562E-03 T-m
- c) 1.718E-03 T-m
- d) 1.890E-03 T-m
- e) 2.079E-03 T-m

### c12 L0[edit | edit source]

1) A solenoid has 7.610E+04 turns wound around a cylinder of diameter 1.21 cm and length 9 m. The current through the coils is 0.696 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−1.52 cm to z=+2.04 cm

- a) 2.176E-04 T-m
- b) 2.393E-04 T-m
- c) 2.633E-04 T-m
- d) 2.896E-04 T-m
- e) 3.186E-04 T-m

2) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.51 mm from the center of a wire of radius 5 mm if the current is 1A?

- a) 1.208E-05 T
- b) 1.329E-05 T
- c) 1.462E-05 T
- d) 1.608E-05 T
- e) 1.769E-05 T

_{1}, I

_{2}, I

_{2}) are (1.11 A, 1.25 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 5.930E-05 T - b) B
_{y}= 6.523E-05 T - c) B
_{y}= 7.175E-05 T - d) B
_{y}= 7.892E-05 T - e) B
_{y}= 8.682E-05 T

4) Two parallel wires each carry a 9.59 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.97 cm, 1.4 cm), while the other is located at (4.02 cm, 5.19 cm). What is the force per unit length between the wires?

- a) 4.412E-10 N/m
- b) 4.853E-10 N/m
- c) 5.338E-10 N/m
- d) 5.872E-10 N/m
- e) 6.459E-10 N/m

#### c12 L1[edit | edit source]

1) Two parallel wires each carry a 2.83 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.15 cm, 1.13 cm), while the other is located at (5.14 cm, 4.22 cm). What is the force per unit length between the wires?

- a) 2.977E-11 N/m
- b) 3.274E-11 N/m
- c) 3.602E-11 N/m
- d) 3.962E-11 N/m
- e) 4.358E-11 N/m

2) A solenoid has 7.690E+04 turns wound around a cylinder of diameter 1.63 cm and length 11 m. The current through the coils is 0.728 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−2.76 cm to z=+1.99 cm

- a) 2.762E-04 T-m
- b) 3.038E-04 T-m
- c) 3.342E-04 T-m
- d) 3.676E-04 T-m
- e) 4.043E-04 T-m

_{1}, I

_{2}, I

_{2}) are (2.24 A, 1.37 A, 2.3 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 7.576E-05 T - b) B
_{y}= 8.333E-05 T - c) B
_{y}= 9.167E-05 T - d) B
_{y}= 1.008E-04 T - e) B
_{y}= 1.109E-04 T

4) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.51 mm from the center of a wire of radius 5 mm if the current is 1A?

- a) 1.098E-05 T
- b) 1.208E-05 T
- c) 1.329E-05 T
- d) 1.462E-05 T
- e) 1.608E-05 T

#### c12 L2[edit | edit source]

1) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.64 mm from the center of a wire of radius 5 mm if the current is 1A?

- a) 1.920E-05 T
- b) 2.112E-05 T
- c) 2.323E-05 T
- d) 2.556E-05 T
- e) 2.811E-05 T

_{1}, I

_{2}, I

_{2}) are (1.78 A, 1.34 A, 1.64 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 6.118E-05 T - b) B
_{y}= 6.730E-05 T - c) B
_{y}= 7.403E-05 T - d) B
_{y}= 8.144E-05 T - e) B
_{y}= 8.958E-05 T

3) A solenoid has 5.500E+04 turns wound around a cylinder of diameter 1.45 cm and length 15 m. The current through the coils is 0.395 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−4.19 cm to z=+2.16 cm

- a) 7.894E-05 T-m
- b) 8.683E-05 T-m
- c) 9.551E-05 T-m
- d) 1.051E-04 T-m
- e) 1.156E-04 T-m

4) Two parallel wires each carry a 2.12 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.67 cm, 1.25 cm), while the other is located at (4.69 cm, 4.27 cm). What is the force per unit length between the wires?

- a) 2.119E-11 N/m
- b) 2.331E-11 N/m
- c) 2.564E-11 N/m
- d) 2.820E-11 N/m
- e) 3.102E-11 N/m

### c12 M0[edit | edit source]

1) Three wires sit at the corners of a square of length 0.834 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I_{1}, I

_{2}, I

_{2}) are (2.26 A, 1.75 A, 2.47 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 7.518E-05 T - b) B
_{y}= 8.270E-05 T - c) B
_{y}= 9.097E-05 T - d) B
_{y}= 1.001E-04 T - e) B
_{y}= 1.101E-04 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.35 kA, I

_{2}=0.809 kA, and I

_{3}=2.34 kA, take the path and evalulate the line integral,

:

- a) 4.031E-03 T-m
- b) 4.434E-03 T-m
- c) 4.877E-03 T-m
- d) 5.365E-03 T-m
- e) 5.901E-03 T-m

3) Two loops of wire carry the same current of 39 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.49 m while the other has a radius of 1.11 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.552 m from the first (smaller) loopif the disance between the loops is 1.62 m?

- a) 1.564E-02 T
- b) 1.720E-02 T
- c) 1.892E-02 T
- d) 2.081E-02 T
- e) 2.289E-02 T

4) Two parallel wires each carry a 9.08 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.17 cm, 1.32 cm), while the other is located at (5.72 cm, 4.47 cm). What is the force per unit length between the wires?

- a) 3.882E-10 N/m
- b) 4.270E-10 N/m
- c) 4.697E-10 N/m
- d) 5.167E-10 N/m
- e) 5.683E-10 N/m

#### c12 M1[edit | edit source]

1) Two loops of wire carry the same current of 39 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.49 m while the other has a radius of 1.11 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.552 m from the first (smaller) loopif the disance between the loops is 1.62 m?

- a) 1.564E-02 T
- b) 1.720E-02 T
- c) 1.892E-02 T
- d) 2.081E-02 T
- e) 2.289E-02 T

_{1}, I

_{2}, I

_{2}) are (2.18 A, 1.82 A, 1.35 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 7.035E-05 T - b) B
_{y}= 7.739E-05 T - c) B
_{y}= 8.512E-05 T - d) B
_{y}= 9.364E-05 T - e) B
_{y}= 1.030E-04 T

3) Two parallel wires each carry a 2.83 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.15 cm, 1.13 cm), while the other is located at (5.14 cm, 4.22 cm). What is the force per unit length between the wires?

- a) 2.977E-11 N/m
- b) 3.274E-11 N/m
- c) 3.602E-11 N/m
- d) 3.962E-11 N/m
- e) 4.358E-11 N/m

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.33 kA, I

_{2}=0.741 kA, and I

_{3}=2.21 kA, take the path and evalulate the line integral,

:

- a) 3.261E-03 T-m
- b) 3.587E-03 T-m
- c) 3.945E-03 T-m
- d) 4.340E-03 T-m
- e) 4.774E-03 T-m

#### c12 M2[edit | edit source]

1) Two loops of wire carry the same current of 12 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.751 m while the other has a radius of 1.42 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.493 m from the first (smaller) loopif the disance between the loops is 1.26 m?

- a) 7.836E-03 T
- b) 8.620E-03 T
- c) 9.482E-03 T
- d) 1.043E-02 T
- e) 1.147E-02 T

_{1}, I

_{2}, I

_{2}) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 4.028E-05 T - b) B
_{y}= 4.431E-05 T - c) B
_{y}= 4.874E-05 T - d) B
_{y}= 5.361E-05 T - e) B
_{y}= 5.897E-05 T

3) Two parallel wires each carry a 7.75 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.62 cm, 1.31 cm), while the other is located at (4.63 cm, 5.53 cm). What is the force per unit length between the wires?

- a) 2.588E-10 N/m
- b) 2.847E-10 N/m
- c) 3.131E-10 N/m
- d) 3.444E-10 N/m
- e) 3.789E-10 N/m

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.58 kA, I

_{2}=1.27 kA, and I

_{3}=1.99 kA, take the path and evalulate the line integral,

:

- a) 3.770E-03 T-m
- b) 4.147E-03 T-m
- c) 4.562E-03 T-m
- d) 5.018E-03 T-m
- e) 5.520E-03 T-m

### c12 N0[edit | edit source]

1) Two loops of wire carry the same current of 11 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.424 m while the other has a radius of 1.32 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.52 m from the first (smaller) loopif the disance between the loops is 1.25 m?

- a) 7.623E-03 T
- b) 8.385E-03 T
- c) 9.223E-03 T
- d) 1.015E-02 T
- e) 1.116E-02 T

2) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.18 mm from the center of a wire of radius 3 mm if the current is 1A?

- a) 1.791E-05 T
- b) 1.970E-05 T
- c) 2.167E-05 T
- d) 2.384E-05 T
- e) 2.622E-05 T

_{1}, I

_{2}, I

_{2}) are (1.57 A, 2.03 A, 2.08 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 7.270E-05 T - b) B
_{x}= 7.997E-05 T - c) B
_{x}= 8.797E-05 T - d) B
_{x}= 9.677E-05 T - e) B
_{x}= 1.064E-04 T

4) A solenoid has 4.730E+04 turns wound around a cylinder of diameter 1.46 cm and length 15 m. The current through the coils is 0.754 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−3.4 cm to z=+1.14 cm

- a) 1.121E-04 T-m
- b) 1.233E-04 T-m
- c) 1.356E-04 T-m
- d) 1.492E-04 T-m
- e) 1.641E-04 T-m

#### c12 N1[edit | edit source]

1) A solenoid has 7.920E+04 turns wound around a cylinder of diameter 1.45 cm and length 11 m. The current through the coils is 0.702 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−4.27 cm to z=+1.36 cm

- a) 2.687E-04 T-m
- b) 2.955E-04 T-m
- c) 3.251E-04 T-m
- d) 3.576E-04 T-m
- e) 3.934E-04 T-m

_{1}, I

_{2}, I

_{2}) are (2.48 A, 1.4 A, 1.47 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 4.506E-05 T - b) B
_{x}= 4.957E-05 T - c) B
_{x}= 5.452E-05 T - d) B
_{x}= 5.997E-05 T - e) B
_{x}= 6.597E-05 T

3) Two loops of wire carry the same current of 20 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.776 m while the other has a radius of 1.2 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.517 m from the first (smaller) loopif the disance between the loops is 1.37 m?

- a) 1.127E-02 T
- b) 1.240E-02 T
- c) 1.364E-02 T
- d) 1.500E-02 T
- e) 1.650E-02 T

4) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 3.33 mm from the center of a wire of radius 5 mm if the current is 1A?

- a) 2.202E-05 T
- b) 2.422E-05 T
- c) 2.664E-05 T
- d) 2.930E-05 T
- e) 3.223E-05 T

#### c12 N2[edit | edit source]

1) A solenoid has 7.610E+04 turns wound around a cylinder of diameter 1.21 cm and length 9 m. The current through the coils is 0.696 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−1.52 cm to z=+2.04 cm

- a) 2.176E-04 T-m
- b) 2.393E-04 T-m
- c) 2.633E-04 T-m
- d) 2.896E-04 T-m
- e) 3.186E-04 T-m

2) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.26 mm from the center of a wire of radius 5 mm if the current is 1A?

- a) 1.494E-05 T
- b) 1.644E-05 T
- c) 1.808E-05 T
- d) 1.989E-05 T
- e) 2.188E-05 T

_{1}, I

_{2}, I

_{2}) are (2.29 A, 1.77 A, 1.48 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 8.371E-05 T - b) B
_{x}= 9.208E-05 T - c) B
_{x}= 1.013E-04 T - d) B
_{x}= 1.114E-04 T - e) B
_{x}= 1.226E-04 T

4) Two loops of wire carry the same current of 99 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.798 m while the other has a radius of 1.29 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.394 m from the first (smaller) loopif the disance between the loops is 1.29 m?

- a) 8.291E-02 T
- b) 9.120E-02 T
- c) 1.003E-01 T
- d) 1.104E-01 T
- e) 1.214E-01 T

### c12 O0[edit | edit source]

1) Three wires sit at the corners of a square of length 0.467 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I_{1}, I

_{2}, I

_{2}) are (2.29 A, 1.77 A, 1.48 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 8.371E-05 T - b) B
_{x}= 9.208E-05 T - c) B
_{x}= 1.013E-04 T - d) B
_{x}= 1.114E-04 T - e) B
_{x}= 1.226E-04 T

2) A solenoid has 4.730E+04 turns wound around a cylinder of diameter 1.46 cm and length 15 m. The current through the coils is 0.754 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−3.4 cm to z=+1.14 cm

- a) 1.121E-04 T-m
- b) 1.233E-04 T-m
- c) 1.356E-04 T-m
- d) 1.492E-04 T-m
- e) 1.641E-04 T-m

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.49 kA, I

_{2}=0.996 kA, and I

_{3}=2.61 kA, take the path and evalulate the line integral,

:

- a) 1.385E-03 T-m
- b) 1.524E-03 T-m
- c) 1.676E-03 T-m
- d) 1.844E-03 T-m
- e) 2.028E-03 T-m

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.51 m and 0.649 T, then how much current (in the z-direction) flows through a circle of radius 0.376 m that is centered on the axis with its plane perpendicular to the axis?

- a) 9.388E+05 A
- b) 1.033E+06 A
- c) 1.136E+06 A
- d) 1.249E+06 A
- e) 1.374E+06 A

#### c12 O1[edit | edit source]

1) Three wires sit at the corners of a square of length 0.774 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I_{1}, I

_{2}, I

_{2}) are (1.57 A, 2.03 A, 2.08 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 7.270E-05 T - b) B
_{x}= 7.997E-05 T - c) B
_{x}= 8.797E-05 T - d) B
_{x}= 9.677E-05 T - e) B
_{x}= 1.064E-04 T

2) A solenoid has 9.160E+04 turns wound around a cylinder of diameter 1.64 cm and length 16 m. The current through the coils is 0.873 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−1.74 cm to z=+4.75 cm

- a) 3.369E-04 T-m
- b) 3.706E-04 T-m
- c) 4.076E-04 T-m
- d) 4.484E-04 T-m
- e) 4.932E-04 T-m

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.55 kA, I

_{2}=1.02 kA, and I

_{3}=1.81 kA, take the path and evalulate the line integral,

:

- a) 8.204E-04 T-m
- b) 9.025E-04 T-m
- c) 9.927E-04 T-m
- d) 1.092E-03 T-m
- e) 1.201E-03 T-m

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.619 m and 0.215 T, then how much current (in the z-direction) flows through a circle of radius 0.351 m that is centered on the axis with its plane perpendicular to the axis?

- a) 2.534E+05 A
- b) 2.787E+05 A
- c) 3.066E+05 A
- d) 3.373E+05 A
- e) 3.710E+05 A

#### c12 O2[edit | edit source]

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.37 m and 0.556 T, then how much current (in the z-direction) flows through a circle of radius 0.14 m that is centered on the axis with its plane perpendicular to the axis?

- a) 2.171E+05 A
- b) 2.388E+05 A
- c) 2.627E+05 A
- d) 2.890E+05 A
- e) 3.179E+05 A

_{1}, I

_{2}, I

_{2}) are (1.19 A, 1.51 A, 2.18 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 7.487E-05 T - b) B
_{x}= 8.236E-05 T - c) B
_{x}= 9.060E-05 T - d) B
_{x}= 9.966E-05 T - e) B
_{x}= 1.096E-04 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.43 kA, I

_{2}=1.64 kA, and I

_{3}=4.81 kA, take the path and evalulate the line integral,

:

- a) 2.721E-03 T-m
- b) 2.993E-03 T-m
- c) 3.292E-03 T-m
- d) 3.621E-03 T-m
- e) 3.984E-03 T-m

4) A solenoid has 5.980E+04 turns wound around a cylinder of diameter 1.8 cm and length 17 m. The current through the coils is 0.933 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−3.68 cm to z=+1.29 cm

- a) 1.863E-04 T-m
- b) 2.050E-04 T-m
- c) 2.255E-04 T-m
- d) 2.480E-04 T-m
- e) 2.728E-04 T-m

### c12 P0[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.66 kA, I

_{2}=1.25 kA, and I

_{3}=2.74 kA, take the path and evalulate the line integral,

:

- a) 1.547E-03 T-m
- b) 1.702E-03 T-m
- c) 1.872E-03 T-m
- d) 2.060E-03 T-m
- e) 2.266E-03 T-m

2) A wire carries a current of 303 A in a circular arc with radius 2.2 cm swept through 72 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 3.881E+00 Tesla
- b) 4.269E+00 Tesla
- c) 4.696E+00 Tesla
- d) 5.165E+00 Tesla
- e) 5.682E+00 Tesla

_{1}, I

_{2}, I

_{2}) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 4.028E-05 T - b) B
_{y}= 4.431E-05 T - c) B
_{y}= 4.874E-05 T - d) B
_{y}= 5.361E-05 T - e) B
_{y}= 5.897E-05 T

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 18 turns per centimeter and the current applied to the solenoid is 582 mA, the net magnetic field is measured to be 1.15 T. What is the magnetic susceptibility for this case?

- a) 7.211E+02
- b) 7.932E+02
- c) 8.726E+02
- d) 9.598E+02
- e) 1.056E+03

#### c12 P1[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.84 kA, I

_{2}=0.476 kA, and I

_{3}=1.57 kA, take the path and evalulate the line integral,

:

- a) 1.250E-03 T-m
- b) 1.375E-03 T-m
- c) 1.512E-03 T-m
- d) 1.663E-03 T-m
- e) 1.830E-03 T-m

_{1}, I

_{2}, I

_{2}) are (2.26 A, 1.75 A, 2.47 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 7.518E-05 T - b) B
_{y}= 8.270E-05 T - c) B
_{y}= 9.097E-05 T - d) B
_{y}= 1.001E-04 T - e) B
_{y}= 1.101E-04 T

3) A wire carries a current of 266 A in a circular arc with radius 2.21 cm swept through 73 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 5.034E+00 Tesla
- b) 5.538E+00 Tesla
- c) 6.091E+00 Tesla
- d) 6.701E+00 Tesla
- e) 7.371E+00 Tesla

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 26 turns per centimeter and the current applied to the solenoid is 359 mA, the net magnetic field is measured to be 1.32 T. What is the magnetic susceptibility for this case?

- a) 1.124E+03
- b) 1.237E+03
- c) 1.360E+03
- d) 1.497E+03
- e) 1.646E+03

#### c12 P2[edit | edit source]

1) A wire carries a current of 385 A in a circular arc with radius 1.53 cm swept through 58 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 5.711E+00 Tesla
- b) 6.283E+00 Tesla
- c) 6.911E+00 Tesla
- d) 7.602E+00 Tesla
- e) 8.362E+00 Tesla

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.49 kA, I

_{2}=0.996 kA, and I

_{3}=2.61 kA, take the path and evalulate the line integral,

:

- a) 1.385E-03 T-m
- b) 1.524E-03 T-m
- c) 1.676E-03 T-m
- d) 1.844E-03 T-m
- e) 2.028E-03 T-m

_{1}, I

_{2}, I

_{2}) are (1.94 A, 2.04 A, 2.41 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 6.833E-05 T - b) B
_{y}= 7.517E-05 T - c) B
_{y}= 8.268E-05 T - d) B
_{y}= 9.095E-05 T - e) B
_{y}= 1.000E-04 T

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 26 turns per centimeter and the current applied to the solenoid is 359 mA, the net magnetic field is measured to be 1.32 T. What is the magnetic susceptibility for this case?

- a) 1.124E+03
- b) 1.237E+03
- c) 1.360E+03
- d) 1.497E+03
- e) 1.646E+03

### c12 Q0[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.84 kA, I

_{2}=2.02 kA, and I

_{3}=4.24 kA, take the path and evalulate the line integral,

:

- a) 5.255E-03 T-m
- b) 5.781E-03 T-m
- c) 6.359E-03 T-m
- d) 6.994E-03 T-m
- e) 7.694E-03 T-m

2) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.619 m and 0.215 T, then how much current (in the z-direction) flows through a circle of radius 0.351 m that is centered on the axis with its plane perpendicular to the axis?

- a) 2.534E+05 A
- b) 2.787E+05 A
- c) 3.066E+05 A
- d) 3.373E+05 A
- e) 3.710E+05 A

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.55 kA, I

_{2}=1.02 kA, and I

_{3}=1.81 kA, take the path and evalulate the line integral,

:

- a) 8.204E-04 T-m
- b) 9.025E-04 T-m
- c) 9.927E-04 T-m
- d) 1.092E-03 T-m
- e) 1.201E-03 T-m

4) Two parallel wires each carry a 9.59 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.97 cm, 1.4 cm), while the other is located at (4.02 cm, 5.19 cm). What is the force per unit length between the wires?

- a) 4.412E-10 N/m
- b) 4.853E-10 N/m
- c) 5.338E-10 N/m
- d) 5.872E-10 N/m
- e) 6.459E-10 N/m

#### c12 Q1[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.66 kA, I

_{2}=1.25 kA, and I

_{3}=2.74 kA, take the path and evalulate the line integral,

:

- a) 1.547E-03 T-m
- b) 1.702E-03 T-m
- c) 1.872E-03 T-m
- d) 2.060E-03 T-m
- e) 2.266E-03 T-m

2) Two parallel wires each carry a 1.65 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.59 cm, 1.81 cm), while the other is located at (5.78 cm, 4.43 cm). What is the force per unit length between the wires?

- a) 1.422E-11 N/m
- b) 1.564E-11 N/m
- c) 1.720E-11 N/m
- d) 1.892E-11 N/m
- e) 2.081E-11 N/m

3) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.568 m and 0.214 T, then how much current (in the z-direction) flows through a circle of radius 0.387 m that is centered on the axis with its plane perpendicular to the axis?

- a) 3.382E+05 A
- b) 3.720E+05 A
- c) 4.092E+05 A
- d) 4.502E+05 A
- e) 4.952E+05 A

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.58 kA, I

_{2}=1.27 kA, and I

_{3}=1.99 kA, take the path and evalulate the line integral,

:

- a) 3.770E-03 T-m
- b) 4.147E-03 T-m
- c) 4.562E-03 T-m
- d) 5.018E-03 T-m
- e) 5.520E-03 T-m

#### c12 Q2[edit | edit source]

1) Two parallel wires each carry a 2.58 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.79 cm, 1.03 cm), while the other is located at (5.64 cm, 5.12 cm). What is the force per unit length between the wires?

- a) 2.634E-11 N/m
- b) 2.897E-11 N/m
- c) 3.187E-11 N/m
- d) 3.506E-11 N/m
- e) 3.856E-11 N/m

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.58 kA, I

_{2}=1.27 kA, and I

_{3}=1.99 kA, take the path and evalulate the line integral,

:

- a) 3.770E-03 T-m
- b) 4.147E-03 T-m
- c) 4.562E-03 T-m
- d) 5.018E-03 T-m
- e) 5.520E-03 T-m

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.45 kA, I

_{2}=2.68 kA, and I

_{3}=5.5 kA, take the path and evalulate the line integral,

:

- a) 3.544E-03 T-m
- b) 3.898E-03 T-m
- c) 4.288E-03 T-m
- d) 4.717E-03 T-m
- e) 5.188E-03 T-m

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.353 m and 0.697 T, then how much current (in the z-direction) flows through a circle of radius 0.196 m that is centered on the axis with its plane perpendicular to the axis?

- a) 5.479E+05 A
- b) 6.027E+05 A
- c) 6.630E+05 A
- d) 7.293E+05 A
- e) 8.022E+05 A

### c12 R0[edit | edit source]

1) Two parallel wires each carry a 3.38 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.46 cm, 1.76 cm), while the other is located at (5.13 cm, 5.5 cm). What is the force per unit length between the wires?

- a) 3.810E-11 N/m
- b) 4.191E-11 N/m
- c) 4.610E-11 N/m
- d) 5.071E-11 N/m
- e) 5.578E-11 N/m

2) Two loops of wire carry the same current of 14 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.835 m while the other has a radius of 1.29 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.607 m from the first (smaller) loopif the disance between the loops is 1.61 m?

- a) 6.099E-03 T
- b) 6.709E-03 T
- c) 7.380E-03 T
- d) 8.118E-03 T
- e) 8.930E-03 T

_{1}, I

_{2}, I

_{2}) are (1.73 A, 1.37 A, 1.65 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 6.171E-05 T - b) B
_{x}= 6.788E-05 T - c) B
_{x}= 7.467E-05 T - d) B
_{x}= 8.213E-05 T - e) B
_{x}= 9.035E-05 T

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.248 m and 0.459 T, then how much current (in the z-direction) flows through a circle of radius 0.152 m that is centered on the axis with its plane perpendicular to the axis?

- a) 2.228E+05 A
- b) 2.451E+05 A
- c) 2.696E+05 A
- d) 2.966E+05 A
- e) 3.262E+05 A

#### c12 R1[edit | edit source]

1) Two parallel wires each carry a 8.75 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.66 cm, 1.4 cm), while the other is located at (5.64 cm, 5.66 cm). What is the force per unit length between the wires?

- a) 2.449E-10 N/m
- b) 2.694E-10 N/m
- c) 2.963E-10 N/m
- d) 3.260E-10 N/m
- e) 3.586E-10 N/m

_{1}, I

_{2}, I

_{2}) are (2.23 A, 1.52 A, 1.86 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 4.559E-05 T - b) B
_{x}= 5.015E-05 T - c) B
_{x}= 5.517E-05 T - d) B
_{x}= 6.068E-05 T - e) B
_{x}= 6.675E-05 T

3) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.253 m and 0.489 T, then how much current (in the z-direction) flows through a circle of radius 0.112 m that is centered on the axis with its plane perpendicular to the axis?

- a) 1.289E+05 A
- b) 1.418E+05 A
- c) 1.560E+05 A
- d) 1.716E+05 A
- e) 1.888E+05 A

4) Two loops of wire carry the same current of 88 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.655 m while the other has a radius of 1.11 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.531 m from the first (smaller) loopif the disance between the loops is 1.72 m?

- a) 4.162E-02 T
- b) 4.578E-02 T
- c) 5.036E-02 T
- d) 5.540E-02 T
- e) 6.094E-02 T

#### c12 R2[edit | edit source]

1) Two parallel wires each carry a 3.8 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.74 cm, 1.47 cm), while the other is located at (5.26 cm, 5.87 cm). What is the force per unit length between the wires?

- a) 5.926E-11 N/m
- b) 6.518E-11 N/m
- c) 7.170E-11 N/m
- d) 7.887E-11 N/m
- e) 8.676E-11 N/m

2) Two loops of wire carry the same current of 21 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.753 m while the other has a radius of 1.47 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.406 m from the first (smaller) loopif the disance between the loops is 1.38 m?

- a) 1.559E-02 T
- b) 1.715E-02 T
- c) 1.886E-02 T
- d) 2.075E-02 T
- e) 2.283E-02 T

_{1}, I

_{2}, I

_{2}) are (1.16 A, 2.46 A, 2.15 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 9.053E-05 T - b) B
_{x}= 9.959E-05 T - c) B
_{x}= 1.095E-04 T - d) B
_{x}= 1.205E-04 T - e) B
_{x}= 1.325E-04 T

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.619 m and 0.215 T, then how much current (in the z-direction) flows through a circle of radius 0.351 m that is centered on the axis with its plane perpendicular to the axis?

- a) 2.534E+05 A
- b) 2.787E+05 A
- c) 3.066E+05 A
- d) 3.373E+05 A
- e) 3.710E+05 A

### c12 S0[edit | edit source]

1) A wire carries a current of 250 A in a circular arc with radius 2.17 cm swept through 53 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 3.498E+00 Tesla
- b) 3.848E+00 Tesla
- c) 4.233E+00 Tesla
- d) 4.656E+00 Tesla
- e) 5.122E+00 Tesla

2) Two loops of wire carry the same current of 97 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.595 m while the other has a radius of 1.1 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.63 m from the first (smaller) loopif the disance between the loops is 1.72 m?

- a) 5.302E-02 T
- b) 5.832E-02 T
- c) 6.415E-02 T
- d) 7.056E-02 T
- e) 7.762E-02 T

_{1}, I

_{2}, I

_{2}) are (2.41 A, 1.87 A, 2.21 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 6.718E-05 T - b) B
_{y}= 7.390E-05 T - c) B
_{y}= 8.129E-05 T - d) B
_{y}= 8.942E-05 T - e) B
_{y}= 9.836E-05 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.84 kA, I

_{2}=3.3 kA, and I

_{3}=5.85 kA, take the path and evalulate the line integral,

:

- a) 5.598E-03 T-m
- b) 6.158E-03 T-m
- c) 6.773E-03 T-m
- d) 7.451E-03 T-m
- e) 8.196E-03 T-m

#### c12 S1[edit | edit source]

1) Three wires sit at the corners of a square of length 0.591 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I_{1}, I

_{2}, I

_{2}) are (2.47 A, 2.1 A, 2.24 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 1.191E-04 T - b) B
_{y}= 1.310E-04 T - c) B
_{y}= 1.441E-04 T - d) B
_{y}= 1.585E-04 T - e) B
_{y}= 1.744E-04 T

2) A wire carries a current of 338 A in a circular arc with radius 2.62 cm swept through 79 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 4.387E+00 Tesla
- b) 4.826E+00 Tesla
- c) 5.309E+00 Tesla
- d) 5.839E+00 Tesla
- e) 6.423E+00 Tesla

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.46 kA, I

_{2}=2.14 kA, and I

_{3}=4.44 kA, take the path and evalulate the line integral,

:

- a) 4.943E-03 T-m
- b) 5.438E-03 T-m
- c) 5.982E-03 T-m
- d) 6.580E-03 T-m
- e) 7.238E-03 T-m

4) Two loops of wire carry the same current of 29 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.76 m while the other has a radius of 1.12 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.544 m from the first (smaller) loopif the disance between the loops is 1.56 m?

- a) 1.950E-02 T
- b) 2.145E-02 T
- c) 2.360E-02 T
- d) 2.596E-02 T
- e) 2.855E-02 T

#### c12 S2[edit | edit source]

1) Three wires sit at the corners of a square of length 0.823 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I_{1}, I

_{2}, I

_{2}) are (2.41 A, 1.87 A, 2.21 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 6.718E-05 T - b) B
_{y}= 7.390E-05 T - c) B
_{y}= 8.129E-05 T - d) B
_{y}= 8.942E-05 T - e) B
_{y}= 9.836E-05 T

2) A wire carries a current of 353 A in a circular arc with radius 2.44 cm swept through 86 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 5.891E+00 Tesla
- b) 6.481E+00 Tesla
- c) 7.129E+00 Tesla
- d) 7.841E+00 Tesla
- e) 8.626E+00 Tesla

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.84 kA, I

_{2}=3.3 kA, and I

_{3}=5.85 kA, take the path and evalulate the line integral,

:

- a) 5.598E-03 T-m
- b) 6.158E-03 T-m
- c) 6.773E-03 T-m
- d) 7.451E-03 T-m
- e) 8.196E-03 T-m

4) Two loops of wire carry the same current of 64 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.838 m while the other has a radius of 1.17 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.528 m from the first (smaller) loopif the disance between the loops is 1.62 m?

- a) 3.863E-02 T
- b) 4.249E-02 T
- c) 4.674E-02 T
- d) 5.141E-02 T
- e) 5.655E-02 T

### c12 T0[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.43 kA, I

_{2}=1.64 kA, and I

_{3}=4.81 kA, take the path and evalulate the line integral,

:

- a) 2.721E-03 T-m
- b) 2.993E-03 T-m
- c) 3.292E-03 T-m
- d) 3.621E-03 T-m
- e) 3.984E-03 T-m

2) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.37 m and 0.556 T, then how much current (in the z-direction) flows through a circle of radius 0.14 m that is centered on the axis with its plane perpendicular to the axis?

- a) 2.171E+05 A
- b) 2.388E+05 A
- c) 2.627E+05 A
- d) 2.890E+05 A
- e) 3.179E+05 A

3) Two parallel wires each carry a 6.53 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.82 cm, 1.17 cm), while the other is located at (4.07 cm, 5.5 cm). What is the force per unit length between the wires?

- a) 1.788E-10 N/m
- b) 1.966E-10 N/m
- c) 2.163E-10 N/m
- d) 2.379E-10 N/m
- e) 2.617E-10 N/m

4) A wire carries a current of 202 A in a circular arc with radius 2.17 cm swept through 51 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 2.473E+00 Tesla
- b) 2.720E+00 Tesla
- c) 2.992E+00 Tesla
- d) 3.291E+00 Tesla
- e) 3.620E+00 Tesla

#### c12 T1[edit | edit source]

1) A wire carries a current of 297 A in a circular arc with radius 2.31 cm swept through 75 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 3.774E+00 Tesla
- b) 4.151E+00 Tesla
- c) 4.566E+00 Tesla
- d) 5.023E+00 Tesla
- e) 5.525E+00 Tesla

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.31 kA, I

_{2}=1.08 kA, and I

_{3}=1.77 kA, take the path and evalulate the line integral,

:

- a) 7.166E-04 T-m
- b) 7.883E-04 T-m
- c) 8.671E-04 T-m
- d) 9.538E-04 T-m
- e) 1.049E-03 T-m

3) Two parallel wires each carry a 6.26 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.4 cm, 1.42 cm), while the other is located at (5.56 cm, 4.99 cm). What is the force per unit length between the wires?

- a) 1.283E-10 N/m
- b) 1.411E-10 N/m
- c) 1.552E-10 N/m
- d) 1.708E-10 N/m
- e) 1.878E-10 N/m

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.547 m and 0.597 T, then how much current (in the z-direction) flows through a circle of radius 0.158 m that is centered on the axis with its plane perpendicular to the axis?

- a) 1.751E+05 A
- b) 1.927E+05 A
- c) 2.119E+05 A
- d) 2.331E+05 A
- e) 2.564E+05 A

#### c12 T2[edit | edit source]

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.619 m and 0.215 T, then how much current (in the z-direction) flows through a circle of radius 0.351 m that is centered on the axis with its plane perpendicular to the axis?

- a) 2.534E+05 A
- b) 2.787E+05 A
- c) 3.066E+05 A
- d) 3.373E+05 A
- e) 3.710E+05 A

2) A wire carries a current of 303 A in a circular arc with radius 2.2 cm swept through 72 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 3.881E+00 Tesla
- b) 4.269E+00 Tesla
- c) 4.696E+00 Tesla
- d) 5.165E+00 Tesla
- e) 5.682E+00 Tesla

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.43 kA, I

_{2}=1.81 kA, and I

_{3}=3.23 kA, take the path and evalulate the line integral,

:

- a) 1.622E-03 T-m
- b) 1.784E-03 T-m
- c) 1.963E-03 T-m
- d) 2.159E-03 T-m
- e) 2.375E-03 T-m

4) Two parallel wires each carry a 8.75 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.66 cm, 1.4 cm), while the other is located at (5.64 cm, 5.66 cm). What is the force per unit length between the wires?

- a) 2.449E-10 N/m
- b) 2.694E-10 N/m
- c) 2.963E-10 N/m
- d) 3.260E-10 N/m
- e) 3.586E-10 N/m

### c12 U0[edit | edit source]

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.407 m and 0.605 T, then how much current (in the z-direction) flows through a circle of radius 0.196 m that is centered on the axis with its plane perpendicular to the axis?

- a) 3.583E+05 A
- b) 3.941E+05 A
- c) 4.335E+05 A
- d) 4.769E+05 A
- e) 5.246E+05 A

2) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 20 turns per centimeter and the current applied to the solenoid is 344 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

- a) 1.185E+03
- b) 1.303E+03
- c) 1.433E+03
- d) 1.577E+03
- e) 1.734E+03

3) Two parallel wires each carry a 4.15 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.19 cm, 1.78 cm), while the other is located at (3.73 cm, 4.12 cm). What is the force per unit length between the wires?

- a) 1.434E-10 N/m
- b) 1.578E-10 N/m
- c) 1.736E-10 N/m
- d) 1.909E-10 N/m
- e) 2.100E-10 N/m

4) A solenoid has 4.730E+04 turns wound around a cylinder of diameter 1.46 cm and length 15 m. The current through the coils is 0.754 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−3.4 cm to z=+1.14 cm

- a) 1.121E-04 T-m
- b) 1.233E-04 T-m
- c) 1.356E-04 T-m
- d) 1.492E-04 T-m
- e) 1.641E-04 T-m

#### c12 U1[edit | edit source]

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.619 m and 0.215 T, then how much current (in the z-direction) flows through a circle of radius 0.351 m that is centered on the axis with its plane perpendicular to the axis?

- a) 2.534E+05 A
- b) 2.787E+05 A
- c) 3.066E+05 A
- d) 3.373E+05 A
- e) 3.710E+05 A

2) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 26 turns per centimeter and the current applied to the solenoid is 533 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?

- a) 7.512E+02
- b) 8.264E+02
- c) 9.090E+02
- d) 9.999E+02
- e) 1.100E+03

3) A solenoid has 7.690E+04 turns wound around a cylinder of diameter 1.63 cm and length 11 m. The current through the coils is 0.728 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−2.76 cm to z=+1.99 cm

- a) 2.762E-04 T-m
- b) 3.038E-04 T-m
- c) 3.342E-04 T-m
- d) 3.676E-04 T-m
- e) 4.043E-04 T-m

4) Two parallel wires each carry a 6.26 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.4 cm, 1.42 cm), while the other is located at (5.56 cm, 4.99 cm). What is the force per unit length between the wires?

- a) 1.283E-10 N/m
- b) 1.411E-10 N/m
- c) 1.552E-10 N/m
- d) 1.708E-10 N/m
- e) 1.878E-10 N/m

#### c12 U2[edit | edit source]

1) A solenoid has 5.160E+04 turns wound around a cylinder of diameter 1.55 cm and length 18 m. The current through the coils is 0.57 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−2.88 cm to z=+1.52 cm

- a) 6.788E-05 T-m
- b) 7.467E-05 T-m
- c) 8.213E-05 T-m
- d) 9.035E-05 T-m
- e) 9.938E-05 T-m

2) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 27 turns per centimeter and the current applied to the solenoid is 280 mA, the net magnetic field is measured to be 1.13 T. What is the magnetic susceptibility for this case?

- a) 1.188E+03
- b) 1.307E+03
- c) 1.438E+03
- d) 1.582E+03
- e) 1.740E+03

3) Two parallel wires each carry a 2.58 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.79 cm, 1.03 cm), while the other is located at (5.64 cm, 5.12 cm). What is the force per unit length between the wires?

- a) 2.634E-11 N/m
- b) 2.897E-11 N/m
- c) 3.187E-11 N/m
- d) 3.506E-11 N/m
- e) 3.856E-11 N/m

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.852 m and 0.476 T, then how much current (in the z-direction) flows through a circle of radius 0.212 m that is centered on the axis with its plane perpendicular to the axis?

- a) 1.502E+05 A
- b) 1.652E+05 A
- c) 1.817E+05 A
- d) 1.999E+05 A
- e) 2.199E+05 A

### c12 V0[edit | edit source]

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.353 m and 0.697 T, then how much current (in the z-direction) flows through a circle of radius 0.196 m that is centered on the axis with its plane perpendicular to the axis?

- a) 5.479E+05 A
- b) 6.027E+05 A
- c) 6.630E+05 A
- d) 7.293E+05 A
- e) 8.022E+05 A

2) Two loops of wire carry the same current of 14 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.835 m while the other has a radius of 1.29 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.607 m from the first (smaller) loopif the disance between the loops is 1.61 m?

- a) 6.099E-03 T
- b) 6.709E-03 T
- c) 7.380E-03 T
- d) 8.118E-03 T
- e) 8.930E-03 T

3) A solenoid has 4.730E+04 turns wound around a cylinder of diameter 1.46 cm and length 15 m. The current through the coils is 0.754 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−3.4 cm to z=+1.14 cm

- a) 1.121E-04 T-m
- b) 1.233E-04 T-m
- c) 1.356E-04 T-m
- d) 1.492E-04 T-m
- e) 1.641E-04 T-m

_{1}, I

_{2}, I

_{2}) are (1.94 A, 2.04 A, 2.41 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 6.833E-05 T - b) B
_{y}= 7.517E-05 T - c) B
_{y}= 8.268E-05 T - d) B
_{y}= 9.095E-05 T - e) B
_{y}= 1.000E-04 T

#### c12 V1[edit | edit source]

1) A solenoid has 9.560E+04 turns wound around a cylinder of diameter 1.18 cm and length 12 m. The current through the coils is 0.664 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−4.49 cm to z=+3.61 cm

- a) 4.895E-04 T-m
- b) 5.384E-04 T-m
- c) 5.923E-04 T-m
- d) 6.515E-04 T-m
- e) 7.167E-04 T-m

2) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.52 m and 0.657 T, then how much current (in the z-direction) flows through a circle of radius 0.295 m that is centered on the axis with its plane perpendicular to the axis?

- a) 7.876E+05 A
- b) 8.664E+05 A
- c) 9.530E+05 A
- d) 1.048E+06 A
- e) 1.153E+06 A

_{1}, I

_{2}, I

_{2}) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 4.028E-05 T - b) B
_{y}= 4.431E-05 T - c) B
_{y}= 4.874E-05 T - d) B
_{y}= 5.361E-05 T - e) B
_{y}= 5.897E-05 T

4) Two loops of wire carry the same current of 39 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.49 m while the other has a radius of 1.11 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.552 m from the first (smaller) loopif the disance between the loops is 1.62 m?

- a) 1.564E-02 T
- b) 1.720E-02 T
- c) 1.892E-02 T
- d) 2.081E-02 T
- e) 2.289E-02 T

#### c12 V2[edit | edit source]

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.353 m and 0.697 T, then how much current (in the z-direction) flows through a circle of radius 0.196 m that is centered on the axis with its plane perpendicular to the axis?

- a) 5.479E+05 A
- b) 6.027E+05 A
- c) 6.630E+05 A
- d) 7.293E+05 A
- e) 8.022E+05 A

_{1}, I

_{2}, I

_{2}) are (1.32 A, 1.4 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 3.480E-05 T - b) B
_{y}= 3.828E-05 T - c) B
_{y}= 4.210E-05 T - d) B
_{y}= 4.631E-05 T - e) B
_{y}= 5.095E-05 T

3) A solenoid has 5.980E+04 turns wound around a cylinder of diameter 1.8 cm and length 17 m. The current through the coils is 0.933 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−3.68 cm to z=+1.29 cm

- a) 1.863E-04 T-m
- b) 2.050E-04 T-m
- c) 2.255E-04 T-m
- d) 2.480E-04 T-m
- e) 2.728E-04 T-m

4) Two loops of wire carry the same current of 12 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.751 m while the other has a radius of 1.42 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.493 m from the first (smaller) loopif the disance between the loops is 1.26 m?

- a) 7.836E-03 T
- b) 8.620E-03 T
- c) 9.482E-03 T
- d) 1.043E-02 T
- e) 1.147E-02 T

### c12 W0[edit | edit source]

1) Two loops of wire carry the same current of 64 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.838 m while the other has a radius of 1.17 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.528 m from the first (smaller) loopif the disance between the loops is 1.62 m?

- a) 3.863E-02 T
- b) 4.249E-02 T
- c) 4.674E-02 T
- d) 5.141E-02 T
- e) 5.655E-02 T

2) Two parallel wires each carry a 9.59 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.97 cm, 1.4 cm), while the other is located at (4.02 cm, 5.19 cm). What is the force per unit length between the wires?

- a) 4.412E-10 N/m
- b) 4.853E-10 N/m
- c) 5.338E-10 N/m
- d) 5.872E-10 N/m
- e) 6.459E-10 N/m

_{1}, I

_{2}, I

_{2}) are (2.41 A, 1.87 A, 2.21 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 6.718E-05 T - b) B
_{y}= 7.390E-05 T - c) B
_{y}= 8.129E-05 T - d) B
_{y}= 8.942E-05 T - e) B
_{y}= 9.836E-05 T

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.353 m and 0.697 T, then how much current (in the z-direction) flows through a circle of radius 0.196 m that is centered on the axis with its plane perpendicular to the axis?

- a) 5.479E+05 A
- b) 6.027E+05 A
- c) 6.630E+05 A
- d) 7.293E+05 A
- e) 8.022E+05 A

#### c12 W1[edit | edit source]

1) Three wires sit at the corners of a square of length 0.66 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I_{1}, I

_{2}, I

_{2}) are (2.18 A, 1.82 A, 1.35 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 7.035E-05 T - b) B
_{y}= 7.739E-05 T - c) B
_{y}= 8.512E-05 T - d) B
_{y}= 9.364E-05 T - e) B
_{y}= 1.030E-04 T

2) Two loops of wire carry the same current of 29 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.76 m while the other has a radius of 1.12 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.544 m from the first (smaller) loopif the disance between the loops is 1.56 m?

- a) 1.950E-02 T
- b) 2.145E-02 T
- c) 2.360E-02 T
- d) 2.596E-02 T
- e) 2.855E-02 T

3) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.37 m and 0.556 T, then how much current (in the z-direction) flows through a circle of radius 0.14 m that is centered on the axis with its plane perpendicular to the axis?

- a) 2.171E+05 A
- b) 2.388E+05 A
- c) 2.627E+05 A
- d) 2.890E+05 A
- e) 3.179E+05 A

4) Two parallel wires each carry a 9.08 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.17 cm, 1.32 cm), while the other is located at (5.72 cm, 4.47 cm). What is the force per unit length between the wires?

- a) 3.882E-10 N/m
- b) 4.270E-10 N/m
- c) 4.697E-10 N/m
- d) 5.167E-10 N/m
- e) 5.683E-10 N/m

#### c12 W2[edit | edit source]

1) Three wires sit at the corners of a square of length 0.534 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I_{1}, I

_{2}, I

_{2}) are (2.45 A, 2.44 A, 1.61 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 9.388E-05 T - b) B
_{y}= 1.033E-04 T - c) B
_{y}= 1.136E-04 T - d) B
_{y}= 1.250E-04 T - e) B
_{y}= 1.375E-04 T

2) Two loops of wire carry the same current of 67 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.847 m while the other has a radius of 1.15 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.408 m from the first (smaller) loopif the disance between the loops is 1.15 m?

- a) 4.799E-02 T
- b) 5.278E-02 T
- c) 5.806E-02 T
- d) 6.387E-02 T
- e) 7.026E-02 T

3) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.619 m and 0.215 T, then how much current (in the z-direction) flows through a circle of radius 0.351 m that is centered on the axis with its plane perpendicular to the axis?

- a) 2.534E+05 A
- b) 2.787E+05 A
- c) 3.066E+05 A
- d) 3.373E+05 A
- e) 3.710E+05 A

4) Two parallel wires each carry a 7.75 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.62 cm, 1.31 cm), while the other is located at (4.63 cm, 5.53 cm). What is the force per unit length between the wires?

- a) 2.588E-10 N/m
- b) 2.847E-10 N/m
- c) 3.131E-10 N/m
- d) 3.444E-10 N/m
- e) 3.789E-10 N/m

### c12 X0[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.32 kA, I

_{2}=2.0 kA, and I

_{3}=3.66 kA, take the path and evalulate the line integral,

:

- a) 1.724E-03 T-m
- b) 1.896E-03 T-m
- c) 2.086E-03 T-m
- d) 2.295E-03 T-m
- e) 2.524E-03 T-m

2) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.81 mm from the center of a wire of radius 3 mm if the current is 1A?

- a) 3.324E-05 T
- b) 3.657E-05 T
- c) 4.022E-05 T
- d) 4.424E-05 T
- e) 4.867E-05 T

3) Two parallel wires each carry a 9.59 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.97 cm, 1.4 cm), while the other is located at (4.02 cm, 5.19 cm). What is the force per unit length between the wires?

- a) 4.412E-10 N/m
- b) 4.853E-10 N/m
- c) 5.338E-10 N/m
- d) 5.872E-10 N/m
- e) 6.459E-10 N/m

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.852 m and 0.476 T, then how much current (in the z-direction) flows through a circle of radius 0.212 m that is centered on the axis with its plane perpendicular to the axis?

- a) 1.502E+05 A
- b) 1.652E+05 A
- c) 1.817E+05 A
- d) 1.999E+05 A
- e) 2.199E+05 A

#### c12 X1[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.4 kA, I

_{2}=2.64 kA, and I

_{3}=3.96 kA, take the path and evalulate the line integral,

:

- a) 1.133E-03 T-m
- b) 1.246E-03 T-m
- c) 1.371E-03 T-m
- d) 1.508E-03 T-m
- e) 1.659E-03 T-m

2) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.81 mm from the center of a wire of radius 3 mm if the current is 1A?

- a) 3.324E-05 T
- b) 3.657E-05 T
- c) 4.022E-05 T
- d) 4.424E-05 T
- e) 4.867E-05 T

3) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.568 m and 0.214 T, then how much current (in the z-direction) flows through a circle of radius 0.387 m that is centered on the axis with its plane perpendicular to the axis?

- a) 3.382E+05 A
- b) 3.720E+05 A
- c) 4.092E+05 A
- d) 4.502E+05 A
- e) 4.952E+05 A

4) Two parallel wires each carry a 9.08 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.17 cm, 1.32 cm), while the other is located at (5.72 cm, 4.47 cm). What is the force per unit length between the wires?

- a) 3.882E-10 N/m
- b) 4.270E-10 N/m
- c) 4.697E-10 N/m
- d) 5.167E-10 N/m
- e) 5.683E-10 N/m

#### c12 X2[edit | edit source]

1) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.86 mm from the center of a wire of radius 5 mm if the current is 1A?

- a) 1.488E-05 T
- b) 1.637E-05 T
- c) 1.800E-05 T
- d) 1.981E-05 T
- e) 2.179E-05 T

2) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.52 m and 0.657 T, then how much current (in the z-direction) flows through a circle of radius 0.295 m that is centered on the axis with its plane perpendicular to the axis?

- a) 7.876E+05 A
- b) 8.664E+05 A
- c) 9.530E+05 A
- d) 1.048E+06 A
- e) 1.153E+06 A

3) Two parallel wires each carry a 6.26 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.4 cm, 1.42 cm), while the other is located at (5.56 cm, 4.99 cm). What is the force per unit length between the wires?

- a) 1.283E-10 N/m
- b) 1.411E-10 N/m
- c) 1.552E-10 N/m
- d) 1.708E-10 N/m
- e) 1.878E-10 N/m

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.44 kA, I

_{2}=1.1 kA, and I

_{3}=1.99 kA, take the path and evalulate the line integral,

:

- a) 1.017E-03 T-m
- b) 1.118E-03 T-m
- c) 1.230E-03 T-m
- d) 1.353E-03 T-m
- e) 1.489E-03 T-m

### c12 Y0[edit | edit source]

1) Three wires sit at the corners of a square of length 0.66 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I_{1}, I

_{2}, I

_{2}) are (2.18 A, 1.82 A, 1.35 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 7.035E-05 T - b) B
_{y}= 7.739E-05 T - c) B
_{y}= 8.512E-05 T - d) B
_{y}= 9.364E-05 T - e) B
_{y}= 1.030E-04 T

2) Two parallel wires each carry a 3.8 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.74 cm, 1.47 cm), while the other is located at (5.26 cm, 5.87 cm). What is the force per unit length between the wires?

- a) 5.926E-11 N/m
- b) 6.518E-11 N/m
- c) 7.170E-11 N/m
- d) 7.887E-11 N/m
- e) 8.676E-11 N/m

3) A solenoid has 3.950E+04 turns wound around a cylinder of diameter 1.64 cm and length 16 m. The current through the coils is 0.441 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−2.05 cm to z=+3.97 cm

- a) 6.807E-05 T-m
- b) 7.487E-05 T-m
- c) 8.236E-05 T-m
- d) 9.060E-05 T-m
- e) 9.966E-05 T-m

_{1}, I

_{2}, I

_{2}) are (1.03 A, 1.95 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 6.545E-05 T - b) B
_{x}= 7.200E-05 T - c) B
_{x}= 7.919E-05 T - d) B
_{x}= 8.711E-05 T - e) B
_{x}= 9.583E-05 T

#### c12 Y1[edit | edit source]

1) Two parallel wires each carry a 6.26 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.4 cm, 1.42 cm), while the other is located at (5.56 cm, 4.99 cm). What is the force per unit length between the wires?

- a) 1.283E-10 N/m
- b) 1.411E-10 N/m
- c) 1.552E-10 N/m
- d) 1.708E-10 N/m
- e) 1.878E-10 N/m

_{1}, I

_{2}, I

_{2}) are (2.01 A, 1.09 A, 1.56 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 4.688E-05 T - b) B
_{y}= 5.156E-05 T - c) B
_{y}= 5.672E-05 T - d) B
_{y}= 6.239E-05 T - e) B
_{y}= 6.863E-05 T

_{1}, I

_{2}, I

_{2}) are (2.28 A, 1.27 A, 1.61 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 5.409E-05 T - b) B
_{x}= 5.950E-05 T - c) B
_{x}= 6.545E-05 T - d) B
_{x}= 7.200E-05 T - e) B
_{x}= 7.920E-05 T

4) A solenoid has 4.900E+04 turns wound around a cylinder of diameter 1.74 cm and length 19 m. The current through the coils is 0.432 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−4.18 cm to z=+1.77 cm

- a) 6.884E-05 T-m
- b) 7.573E-05 T-m
- c) 8.330E-05 T-m
- d) 9.163E-05 T-m
- e) 1.008E-04 T-m

#### c12 Y2[edit | edit source]

1) Two parallel wires each carry a 1.65 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.59 cm, 1.81 cm), while the other is located at (5.78 cm, 4.43 cm). What is the force per unit length between the wires?

- a) 1.422E-11 N/m
- b) 1.564E-11 N/m
- c) 1.720E-11 N/m
- d) 1.892E-11 N/m
- e) 2.081E-11 N/m

2) A solenoid has 5.160E+04 turns wound around a cylinder of diameter 1.55 cm and length 18 m. The current through the coils is 0.57 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral alongthe axis from z=−2.88 cm to z=+1.52 cm

- a) 6.788E-05 T-m
- b) 7.467E-05 T-m
- c) 8.213E-05 T-m
- d) 9.035E-05 T-m
- e) 9.938E-05 T-m

_{1}, I

_{2}, I

_{2}) are (1.78 A, 1.34 A, 1.64 A), respectively. What is the y-component of the magnetic field at point P?

- a) B
_{y}= 6.118E-05 T - b) B
_{y}= 6.730E-05 T - c) B
_{y}= 7.403E-05 T - d) B
_{y}= 8.144E-05 T - e) B
_{y}= 8.958E-05 T

_{1}, I

_{2}, I

_{2}) are (1.57 A, 2.03 A, 2.08 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 7.270E-05 T - b) B
_{x}= 7.997E-05 T - c) B
_{x}= 8.797E-05 T - d) B
_{x}= 9.677E-05 T - e) B
_{x}= 1.064E-04 T

### c12 Z0[edit | edit source]

1) A wire carries a current of 109 A in a circular arc with radius 1.26 cm swept through 71 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 2.908E+00 Tesla
- b) 3.199E+00 Tesla
- c) 3.519E+00 Tesla
- d) 3.871E+00 Tesla
- e) 4.258E+00 Tesla

_{1}, I

_{2}, I

_{2}) are (1.19 A, 1.51 A, 2.18 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 7.487E-05 T - b) B
_{x}= 8.236E-05 T - c) B
_{x}= 9.060E-05 T - d) B
_{x}= 9.966E-05 T - e) B
_{x}= 1.096E-04 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.5 kA, I

_{2}=1.53 kA, and I

_{3}=2.34 kA, take the path and evalulate the line integral,

:

- a) 1.018E-03 T-m
- b) 1.120E-03 T-m
- c) 1.232E-03 T-m
- d) 1.355E-03 T-m
- e) 1.490E-03 T-m

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.31 kA, I

_{2}=1.16 kA, and I

_{3}=2.13 kA, take the path and evalulate the line integral,

:

- a) 2.815E-03 T-m
- b) 3.097E-03 T-m
- c) 3.406E-03 T-m
- d) 3.747E-03 T-m
- e) 4.122E-03 T-m

#### c12 Z1[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.31 kA, I

_{2}=1.16 kA, and I

_{3}=2.13 kA, take the path and evalulate the line integral,

:

- a) 2.815E-03 T-m
- b) 3.097E-03 T-m
- c) 3.406E-03 T-m
- d) 3.747E-03 T-m
- e) 4.122E-03 T-m

2) A wire carries a current of 385 A in a circular arc with radius 1.53 cm swept through 58 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 5.711E+00 Tesla
- b) 6.283E+00 Tesla
- c) 6.911E+00 Tesla
- d) 7.602E+00 Tesla
- e) 8.362E+00 Tesla

_{1}, I

_{2}, I

_{2}) are (2.23 A, 1.52 A, 1.86 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 4.559E-05 T - b) B
_{x}= 5.015E-05 T - c) B
_{x}= 5.517E-05 T - d) B
_{x}= 6.068E-05 T - e) B
_{x}= 6.675E-05 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.48 kA, I

_{2}=1.47 kA, and I

_{3}=2.6 kA, take the path and evalulate the line integral,

:

- a) 1.420E-03 T-m
- b) 1.562E-03 T-m
- c) 1.718E-03 T-m
- d) 1.890E-03 T-m
- e) 2.079E-03 T-m

#### c12 Z2[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.5 kA, I

_{2}=1.28 kA, and I

_{3}=3.4 kA, take the path and evalulate the line integral,

:

- a) 4.362E-03 T-m
- b) 4.798E-03 T-m
- c) 5.278E-03 T-m
- d) 5.806E-03 T-m
- e) 6.386E-03 T-m

2) A wire carries a current of 250 A in a circular arc with radius 2.17 cm swept through 53 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- a) 3.498E+00 Tesla
- b) 3.848E+00 Tesla
- c) 4.233E+00 Tesla
- d) 4.656E+00 Tesla
- e) 5.122E+00 Tesla

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.61 kA, I

_{2}=2.2 kA, and I

_{3}=5.1 kA, take the path and evalulate the line integral,

:

- a) 3.644E-03 T-m
- b) 4.009E-03 T-m
- c) 4.410E-03 T-m
- d) 4.850E-03 T-m
- e) 5.336E-03 T-m

_{1}, I

_{2}, I

_{2}) are (1.57 A, 2.03 A, 2.08 A), respectively. What is the x-component of the magnetic field at point P?

- a) B
_{x}= 7.270E-05 T - b) B
_{x}= 7.997E-05 T - c) B
_{x}= 8.797E-05 T - d) B
_{x}= 9.677E-05 T - e) B
_{x}= 1.064E-04 T

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### Key: A0[edit | edit source]

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.432 m and 0.402 T, then how much current (in the z-direction) flows through a circle of radius 0.275 m that is centered on the axis with its plane perpendicular to the axis?

- -a) 3.277E+05 A
- -b) 3.604E+05 A
- -c) 3.965E+05 A
- -d) 4.361E+05 A
- +e) 4.797E+05 A

2) Two loops of wire carry the same current of 18 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.848 m while the other has a radius of 1.42 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.625 m from the first (smaller) loopif the disance between the loops is 1.55 m?

- -a) 7.952E-03 T
- -b) 8.747E-03 T
- -c) 9.622E-03 T
- -d) 1.058E-02 T
- +e) 1.164E-02 T

3) Two parallel wires each carry a 3.8 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.74 cm, 1.47 cm), while the other is located at (5.26 cm, 5.87 cm). What is the force per unit length between the wires?

- -a) 5.926E-11 N/m
- +b) 6.518E-11 N/m
- -c) 7.170E-11 N/m
- -d) 7.887E-11 N/m
- -e) 8.676E-11 N/m

4) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.18 mm from the center of a wire of radius 3 mm if the current is 1A?

- -a) 1.791E-05 T
- -b) 1.970E-05 T
- -c) 2.167E-05 T
- -d) 2.384E-05 T
- +e) 2.622E-05 T

Click these links for the keys:

#### Key: A1[edit | edit source]

1) Two parallel wires each carry a 1.65 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.59 cm, 1.81 cm), while the other is located at (5.78 cm, 4.43 cm). What is the force per unit length between the wires?

- -a) 1.422E-11 N/m
- -b) 1.564E-11 N/m
- -c) 1.720E-11 N/m
- +d) 1.892E-11 N/m
- -e) 2.081E-11 N/m

2) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.18 mm from the center of a wire of radius 3 mm if the current is 1A?

- -a) 1.791E-05 T
- -b) 1.970E-05 T
- -c) 2.167E-05 T
- -d) 2.384E-05 T
- +e) 2.622E-05 T

3) Two loops of wire carry the same current of 67 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.847 m while the other has a radius of 1.15 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.408 m from the first (smaller) loopif the disance between the loops is 1.15 m?

- -a) 4.799E-02 T
- -b) 5.278E-02 T
- +c) 5.806E-02 T
- -d) 6.387E-02 T
- -e) 7.026E-02 T

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.871 m and 0.427 T, then how much current (in the z-direction) flows through a circle of radius 0.688 m that is centered on the axis with its plane perpendicular to the axis?

- +a) 1.404E+06 A
- -b) 1.544E+06 A
- -c) 1.699E+06 A
- -d) 1.869E+06 A
- -e) 2.056E+06 A

Click these links for the keys:

#### Key: A2[edit | edit source]

1) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.51 mm from the center of a wire of radius 5 mm if the current is 1A?

- +a) 1.208E-05 T
- -b) 1.329E-05 T
- -c) 1.462E-05 T
- -d) 1.608E-05 T
- -e) 1.769E-05 T

2) Two parallel wires each carry a 2.83 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.15 cm, 1.13 cm), while the other is located at (5.14 cm, 4.22 cm). What is the force per unit length between the wires?

- -a) 2.977E-11 N/m
- -b) 3.274E-11 N/m
- -c) 3.602E-11 N/m
- -d) 3.962E-11 N/m
- +e) 4.358E-11 N/m

3) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.645 m and 0.469 T, then how much current (in the z-direction) flows through a circle of radius 0.26 m that is centered on the axis with its plane perpendicular to the axis?

- -a) 2.949E+05 A
- -b) 3.244E+05 A
- -c) 3.568E+05 A
- +d) 3.925E+05 A
- -e) 4.317E+05 A

4) Two loops of wire carry the same current of 88 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.655 m while the other has a radius of 1.11 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.531 m from the first (smaller) loopif the disance between the loops is 1.72 m?

- -a) 4.162E-02 T
- -b) 4.578E-02 T
- -c) 5.036E-02 T
- +d) 5.540E-02 T
- -e) 6.094E-02 T

Click these links for the keys:

### Key: B0[edit | edit source]

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.571 m and 0.331 T, then how much current (in the z-direction) flows through a circle of radius 0.321 m that is centered on the axis with its plane perpendicular to the axis?

- -a) 3.226E+05 A
- -b) 3.549E+05 A
- -c) 3.904E+05 A
- +d) 4.294E+05 A
- -e) 4.724E+05 A

2) Two parallel wires each carry a 2.12 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.67 cm, 1.25 cm), while the other is located at (4.69 cm, 4.27 cm). What is the force per unit length between the wires?

- -a) 2.119E-11 N/m
- -b) 2.331E-11 N/m
- -c) 2.564E-11 N/m
- +d) 2.820E-11 N/m
- -e) 3.102E-11 N/m

_{1}, I

_{2}, I

_{2}) are (1.03 A, 1.95 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?

- -a) B
_{x}= 6.545E-05 T - +b) B
_{x}= 7.200E-05 T - -c) B
_{x}= 7.919E-05 T - -d) B
_{x}= 8.711E-05 T - -e) B
_{x}= 9.583E-05 T

4) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.86 mm from the center of a wire of radius 3 mm if the current is 1A?

- -a) 3.416E-05 T
- -b) 3.758E-05 T
- +c) 4.133E-05 T
- -d) 4.547E-05 T
- -e) 5.001E-05 T

Click these links for the keys:

#### Key: B1[edit | edit source]

1) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.66 mm from the center of a wire of radius 5 mm if the current is 1A?

- -a) 1.935E-05 T
- +b) 2.128E-05 T
- -c) 2.341E-05 T
- -d) 2.575E-05 T
- -e) 2.832E-05 T

,

where is the maximum magnetic field (at ). If 0.52 m and 0.657 T, then how much current (in the z-direction) flows through a circle of radius 0.295 m that is centered on the axis with its plane perpendicular to the axis?

- +a) 7.876E+05 A
- -b) 8.664E+05 A
- -c) 9.530E+05 A
- -d) 1.048E+06 A
- -e) 1.153E+06 A

3) Two parallel wires each carry a 7.48 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.13 cm, 0.955 cm), while the other is located at (5.37 cm, 5.48 cm). What is the force per unit length between the wires?

- -a) 2.015E-10 N/m
- +b) 2.216E-10 N/m
- -c) 2.438E-10 N/m
- -d) 2.682E-10 N/m
- -e) 2.950E-10 N/m

_{1}, I

_{2}, I

_{2}) are (1.16 A, 2.46 A, 2.15 A), respectively. What is the x-component of the magnetic field at point P?

- -a) B
_{x}= 9.053E-05 T - -b) B
_{x}= 9.959E-05 T - -c) B
_{x}= 1.095E-04 T - -d) B
_{x}= 1.205E-04 T - +e) B
_{x}= 1.325E-04 T

Click these links for the keys:

#### Key: B2[edit | edit source]

1) Three wires sit at the corners of a square of length 0.466 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I_{1}, I

_{2}, I

_{2}) are (1.4 A, 2.42 A, 1.9 A), respectively. What is the x-component of the magnetic field at point P?

- +a) B
_{x}= 1.335E-04 T - -b) B
_{x}= 1.468E-04 T - -c) B
_{x}= 1.615E-04 T - -d) B
_{x}= 1.777E-04 T - -e) B
_{x}= 1.954E-04 T

2) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.568 m and 0.214 T, then how much current (in the z-direction) flows through a circle of radius 0.387 m that is centered on the axis with its plane perpendicular to the axis?

- -a) 3.382E+05 A
- +b) 3.720E+05 A
- -c) 4.092E+05 A
- -d) 4.502E+05 A
- -e) 4.952E+05 A

3) Two parallel wires each carry a 3.51 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.14 cm, 1.43 cm), while the other is located at (4.14 cm, 5.23 cm). What is the force per unit length between the wires?

- +a) 6.484E-11 N/m
- -b) 7.133E-11 N/m
- -c) 7.846E-11 N/m
- -d) 8.631E-11 N/m
- -e) 9.494E-11 N/m

4) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.66 mm from the center of a wire of radius 5 mm if the current is 1A?

- -a) 1.935E-05 T
- +b) 2.128E-05 T
- -c) 2.341E-05 T
- -d) 2.575E-05 T
- -e) 2.832E-05 T

Click these links for the keys:

### Key: C0[edit | edit source]

1) Three wires sit at the corners of a square of length 0.76 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I_{1}, I

_{2}, I

_{2}) are (1.91 A, 1.34 A, 1.05 A), respectively. What is the y-component of the magnetic field at point P?

- -a) B
_{y}= 5.611E-05 T - -b) B
_{y}= 6.172E-05 T - +c) B
_{y}= 6.789E-05 T - -d) B
_{y}= 7.468E-05 T - -e) B
_{y}= 8.215E-05 T

_{1}, I

_{2}, I

_{2}) are (1.4 A, 2.42 A, 1.9 A), respectively. What is the x-component of the magnetic field at point P?

- +a) B
_{x}= 1.335E-04 T - -b) B
_{x}= 1.468E-04 T - -c) B
_{x}= 1.615E-04 T - -d) B
_{x}= 1.777E-04 T - -e) B
_{x}= 1.954E-04 T

3) A wire carries a current of 266 A in a circular arc with radius 2.21 cm swept through 73 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- +a) 5.034E+00 Tesla
- -b) 5.538E+00 Tesla
- -c) 6.091E+00 Tesla
- -d) 6.701E+00 Tesla
- -e) 7.371E+00 Tesla

4) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.59 mm from the center of a wire of radius 5 mm if the current is 1A?

- +a) 2.072E-05 T
- -b) 2.279E-05 T
- -c) 2.507E-05 T
- -d) 2.758E-05 T
- -e) 3.034E-05 T

Click these links for the keys:

#### Key: C1[edit | edit source]

1) A wire carries a current of 269 A in a circular arc with radius 2.35 cm swept through 36 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- -a) 1.613E+00 Tesla
- -b) 1.774E+00 Tesla
- -c) 1.951E+00 Tesla
- -d) 2.146E+00 Tesla
- +e) 2.361E+00 Tesla

_{1}, I

_{2}, I

_{2}) are (2.26 A, 1.75 A, 2.47 A), respectively. What is the y-component of the magnetic field at point P?

- +a) B
_{y}= 7.518E-05 T - -b) B
_{y}= 8.270E-05 T - -c) B
_{y}= 9.097E-05 T - -d) B
_{y}= 1.001E-04 T - -e) B
_{y}= 1.101E-04 T

3) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.81 mm from the center of a wire of radius 3 mm if the current is 1A?

- -a) 3.324E-05 T
- -b) 3.657E-05 T
- +c) 4.022E-05 T
- -d) 4.424E-05 T
- -e) 4.867E-05 T

_{1}, I

_{2}, I

_{2}) are (1.03 A, 1.95 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?

- -a) B
_{x}= 6.545E-05 T - +b) B
_{x}= 7.200E-05 T - -c) B
_{x}= 7.919E-05 T - -d) B
_{x}= 8.711E-05 T - -e) B
_{x}= 9.583E-05 T

Click these links for the keys:

#### Key: C2[edit | edit source]

1) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.18 mm from the center of a wire of radius 3 mm if the current is 1A?

- -a) 1.791E-05 T
- -b) 1.970E-05 T
- -c) 2.167E-05 T
- -d) 2.384E-05 T
- +e) 2.622E-05 T

_{1}, I

_{2}, I

_{2}) are (1.76 A, 1.02 A, 1.08 A), respectively. What is the x-component of the magnetic field at point P?

- -a) B
_{x}= 3.394E-05 T - -b) B
_{x}= 3.733E-05 T - -c) B
_{x}= 4.106E-05 T - -d) B
_{x}= 4.517E-05 T - +e) B
_{x}= 4.969E-05 T

_{1}, I

_{2}, I

_{2}) are (2.24 A, 1.37 A, 2.3 A), respectively. What is the y-component of the magnetic field at point P?

- -a) B
_{y}= 7.576E-05 T - +b) B
_{y}= 8.333E-05 T - -c) B
_{y}= 9.167E-05 T - -d) B
_{y}= 1.008E-04 T - -e) B
_{y}= 1.109E-04 T

4) A wire carries a current of 250 A in a circular arc with radius 2.17 cm swept through 53 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- +a) 3.498E+00 Tesla
- -b) 3.848E+00 Tesla
- -c) 4.233E+00 Tesla
- -d) 4.656E+00 Tesla
- -e) 5.122E+00 Tesla

Click these links for the keys:

### Key: D0[edit | edit source]

1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.81 kA, I

_{2}=1.2 kA, and I

_{3}=1.84 kA, take the path and evalulate the line integral,

:

- -a) 3.583E-03 T-m
- -b) 3.941E-03 T-m
- +c) 4.335E-03 T-m
- -d) 4.769E-03 T-m
- -e) 5.246E-03 T-m

2) Two loops of wire carry the same current of 21 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.753 m while the other has a radius of 1.47 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.406 m from the first (smaller) loopif the disance between the loops is 1.38 m?

- -a) 1.559E-02 T
- +b) 1.715E-02 T
- -c) 1.886E-02 T
- -d) 2.075E-02 T
- -e) 2.283E-02 T

3) A wire carries a current of 106 A in a circular arc with radius 1.32 cm swept through 38 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- -a) 1.589E+00 Tesla
- +b) 1.748E+00 Tesla
- -c) 1.923E+00 Tesla
- -d) 2.116E+00 Tesla
- -e) 2.327E+00 Tesla

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.432 m and 0.402 T, then how much current (in the z-direction) flows through a circle of radius 0.275 m that is centered on the axis with its plane perpendicular to the axis?

- -a) 3.277E+05 A
- -b) 3.604E+05 A
- -c) 3.965E+05 A
- -d) 4.361E+05 A
- +e) 4.797E+05 A

Click these links for the keys:

#### Key: D1[edit | edit source]

1) A wire carries a current of 385 A in a circular arc with radius 1.53 cm swept through 58 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

- -a) 5.711E+00 Tesla
- -b) 6.283E+00 Tesla
- -c) 6.911E+00 Tesla
- -d) 7.602E+00 Tesla
- +e) 8.362E+00 Tesla

2) Two loops of wire carry the same current of 20 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.776 m while the other has a radius of 1.2 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.517 m from the first (smaller) loopif the disance between the loops is 1.37 m?

- -a) 1.127E-02 T
- -b) 1.240E-02 T
- -c) 1.364E-02 T
- +d) 1.500E-02 T
- -e) 1.650E-02 T

_{1}and I

_{3}flow out of the page, and I

_{2}flows into the page, as shown. Two closed paths are shown, labeled and . If I

_{1}=2.78 kA, I

_{2}=2.61 kA, and I

_{3}=3.76 kA, take the path and evalulate the line integral,

:

- +a) 4.939E-03 T-m
- -b) 5.432E-03 T-m
- -c) 5.976E-03 T-m
- -d) 6.573E-03 T-m
- -e) 7.231E-03 T-m

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for is,

,

where is the maximum magnetic field (at ). If 0.248 m and 0.459 T, then how much current (in the z-direction) flows through a circle of radius 0.152 m that is centered on the axis with its plane perpendicular to the axis?

- -a) 2.228E+05 A
- -b) 2.451E+05 A
- -c) 2.696E+05 A
- +d) 2.966E+05 A
- -e) 3.262E+05 A

Click these links for the keys:

#### Key: D2[edit | edit source]

1) Two loops of wire carry the same current of 24 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.53 m while the other has a radius of 1.38 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.485 m from the first (smaller) loopif the disance between the loops is 1.78 m?

- -a) 1.294E-02 T
- -b) 1.424E-02 T
- +c) 1.566E-02 T
- -d) 1.723E-02 T
- -e) 1.895E-02 T