# Quizbank/calcPhyEMqAll/c12

calcPhyEMqAll/c12 ID153478379917

Exams:

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.

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### c12 A0

1) 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
2)
Three wires sit at the corners of a square of length 0.832 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.03 A, 1.95 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.545E-05 T
b) Bx= 7.200E-05 T
c) Bx= 7.919E-05 T
d) Bx= 8.711E-05 T
e) Bx= 9.583E-05 T
3)
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 (I1, I2, I2) are (2.18 A, 1.82 A, 1.35 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 7.035E-05 T
b) By= 7.739E-05 T
c) By= 8.512E-05 T
d) By= 9.364E-05 T
e) By= 1.030E-04 T

4) 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

5) 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

6) 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

7) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.619 m and ${\displaystyle B_{max}=\,}$ 0.215 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.32 kA, I2=2.0 kA, and I3=3.66 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
9)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.57 kA, I2=0.708 kA, and I3=1.48 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

10) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

11) 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) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.512E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.264E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.090E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.999E+02
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.100E+03

#### c12 A1

1)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.42 kA, I2=0.904 kA, and I3=1.34 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

2) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.14 mm from the center of a wire of radius 3 mm if the current is 1A?

a) 2.533E-05 T
b) 2.787E-05 T
c) 3.065E-05 T
d) 3.372E-05 T
e) 3.709E-05 T
3)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.84 kA, I2=0.476 kA, and I3=1.57 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

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

5) 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

6) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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
7)
Three wires sit at the corners of a square of length 0.832 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.03 A, 1.95 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.545E-05 T
b) Bx= 7.200E-05 T
c) Bx= 7.919E-05 T
d) Bx= 8.711E-05 T
e) Bx= 9.583E-05 T

8) 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

9) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 23 turns per centimeter and the current applied to the solenoid is 534 mA, the net magnetic field is measured to be 1.48 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.917E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.708E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.579E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.054E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.159E+03

10) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.353 m and ${\displaystyle B_{max}=\,}$ 0.697 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
11)
Three wires sit at the corners of a square of length 0.699 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.87 A, 2.18 A, 1.34 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 6.999E-05 T
b) By= 7.699E-05 T
c) By= 8.469E-05 T
d) By= 9.316E-05 T
e) By= 1.025E-04 T

#### c12 A2

1) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 23 turns per centimeter and the current applied to the solenoid is 534 mA, the net magnetic field is measured to be 1.48 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.917E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.708E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.579E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.054E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.159E+03

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)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.89 kA, I2=1.19 kA, and I3=3.5 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
4)
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 (I1, I2, I2) are (2.18 A, 1.82 A, 1.35 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 7.035E-05 T
b) By= 7.739E-05 T
c) By= 8.512E-05 T
d) By= 9.364E-05 T
e) By= 1.030E-04 T

5) 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
6)
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 (I1, I2, I2) are (1.57 A, 2.03 A, 2.08 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 7.270E-05 T
b) Bx= 7.997E-05 T
c) Bx= 8.797E-05 T
d) Bx= 9.677E-05 T
e) Bx= 1.064E-04 T
7)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.44 kA, I2=1.1 kA, and I3=1.99 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

8) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

9) 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

10) 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

11) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.248 m and ${\displaystyle B_{max}=\,}$ 0.459 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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 B0

1) A wire carries a current of 306 A in a circular arc with radius 2.04 cm swept through 55 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) 3.551E+00 Tesla
b) 3.907E+00 Tesla
c) 4.297E+00 Tesla
d) 4.727E+00 Tesla
e) 5.200E+00 Tesla
2)
Three wires sit at the corners of a square of length 0.688 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.73 A, 1.37 A, 1.65 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.171E-05 T
b) Bx= 6.788E-05 T
c) Bx= 7.467E-05 T
d) Bx= 8.213E-05 T
e) Bx= 9.035E-05 T
3)
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 (I1, I2, I2) are (2.41 A, 1.87 A, 2.21 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 6.718E-05 T
b) By= 7.390E-05 T
c) By= 8.129E-05 T
d) By= 8.942E-05 T
e) By= 9.836E-05 T

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

5) 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

6) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 3.07 mm from the center of a wire of radius 5 mm if the current is 1A?

a) 1.677E-05 T
b) 1.845E-05 T
c) 2.030E-05 T
d) 2.233E-05 T
e) 2.456E-05 T

7) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.253 m and ${\displaystyle B_{max}=\,}$ 0.489 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.32 kA, I2=2.0 kA, and I3=3.66 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
9)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.33 kA, I2=0.741 kA, and I3=2.21 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

10) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

11) 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) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.211E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.932E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.726E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.598E+02
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.056E+03

#### c12 B1

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
2)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.43 kA, I2=1.81 kA, and I3=3.23 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

3) 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 525 mA, the net magnetic field is measured to be 1.44 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 5.515E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 6.066E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 6.673E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.340E+02
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.074E+02

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

5) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.407 m and ${\displaystyle B_{max}=\,}$ 0.605 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
6)
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 (I1, I2, I2) are (2.29 A, 1.77 A, 1.48 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 8.371E-05 T
b) Bx= 9.208E-05 T
c) Bx= 1.013E-04 T
d) Bx= 1.114E-04 T
e) Bx= 1.226E-04 T

7) A wire carries a current of 193 A in a circular arc with radius 3.13 cm swept through 40 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) 1.285E+00 Tesla
b) 1.413E+00 Tesla
c) 1.554E+00 Tesla
d) 1.710E+00 Tesla
e) 1.881E+00 Tesla
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.78 kA, I2=2.61 kA, and I3=3.76 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
9)
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 (I1, I2, I2) are (2.45 A, 2.44 A, 1.61 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 9.388E-05 T
b) By= 1.033E-04 T
c) By= 1.136E-04 T
d) By= 1.250E-04 T
e) By= 1.375E-04 T

10) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

11) 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

#### c12 B2

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 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

2) 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

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

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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.549 m and ${\displaystyle B_{max}=\,}$ 0.599 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
5)
Three wires sit at the corners of a square of length 0.739 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.93 A, 2.48 A, 1.36 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.397E-05 T
b) Bx= 7.037E-05 T
c) Bx= 7.740E-05 T
d) Bx= 8.514E-05 T
e) Bx= 9.366E-05 T

6) 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

7) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.57 kA, I2=0.708 kA, and I3=1.48 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

9) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 19 turns per centimeter and the current applied to the solenoid is 421 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.302E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.432E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.576E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.733E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.907E+03
10)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.44 kA, I2=1.1 kA, and I3=1.99 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
11)
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 (I1, I2, I2) are (2.01 A, 1.09 A, 1.56 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 4.688E-05 T
b) By= 5.156E-05 T
c) By= 5.672E-05 T
d) By= 6.239E-05 T
e) By= 6.863E-05 T

### c12 C0

1) 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
2)
Three wires sit at the corners of a square of length 0.51 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.16 A, 2.46 A, 2.15 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 9.053E-05 T
b) Bx= 9.959E-05 T
c) Bx= 1.095E-04 T
d) Bx= 1.205E-04 T
e) Bx= 1.325E-04 T
3)
Three wires sit at the corners of a square of length 0.865 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.62 A, 2.13 A, 2.2 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 5.131E-05 T
b) By= 5.644E-05 T
c) By= 6.208E-05 T
d) By= 6.829E-05 T
e) By= 7.512E-05 T

4) 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

5) 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

6) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.14 mm from the center of a wire of radius 3 mm if the current is 1A?

a) 2.533E-05 T
b) 2.787E-05 T
c) 3.065E-05 T
d) 3.372E-05 T
e) 3.709E-05 T

7) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.571 m and ${\displaystyle B_{max}=\,}$ 0.331 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.61 kA, I2=2.2 kA, and I3=5.1 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
9)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.78 kA, I2=2.61 kA, and I3=3.76 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

10) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

11) 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 525 mA, the net magnetic field is measured to be 1.45 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.249E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.074E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.981E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.098E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.208E+03

#### c12 C1

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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.253 m and ${\displaystyle B_{max}=\,}$ 0.489 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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

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) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.804E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.685E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.065E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.172E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.289E+03
3)
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 (I1, I2, I2) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 4.028E-05 T
b) By= 4.431E-05 T
c) By= 4.874E-05 T
d) By= 5.361E-05 T
e) By= 5.897E-05 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
5)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.33 kA, I2=0.741 kA, and I3=2.21 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
6)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.61 kA, I2=2.2 kA, and I3=5.1 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

7) 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
8)
Three wires sit at the corners of a square of length 0.688 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.73 A, 1.37 A, 1.65 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.171E-05 T
b) Bx= 6.788E-05 T
c) Bx= 7.467E-05 T
d) Bx= 8.213E-05 T
e) Bx= 9.035E-05 T

9) 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

10) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.04 mm from the center of a wire of radius 5 mm if the current is 1A?

a) 1.115E-05 T
b) 1.226E-05 T
c) 1.349E-05 T
d) 1.484E-05 T
e) 1.632E-05 T

11) A solenoid has 8.890E+04 turns wound around a cylinder of diameter 1.32 cm and length 15 m. The current through the coils is 0.297 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−1.41 cm to z=+2.56 cm

a) 7.257E-05 T-m
b) 7.983E-05 T-m
c) 8.781E-05 T-m
d) 9.660E-05 T-m
e) 1.063E-04 T-m

#### c12 C2

1) 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
2)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.39 kA, I2=0.414 kA, and I3=1.3 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 2.812E-03 T-m
b) 3.093E-03 T-m
c) 3.402E-03 T-m
d) 3.742E-03 T-m
e) 4.117E-03 T-m

3) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

4) 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
5)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.43 kA, I2=1.64 kA, and I3=4.81 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
6)
Three wires sit at the corners of a square of length 0.547 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.78 A, 1.34 A, 1.64 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 6.118E-05 T
b) By= 6.730E-05 T
c) By= 7.403E-05 T
d) By= 8.144E-05 T
e) By= 8.958E-05 T

7) 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

8) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.571 m and ${\displaystyle B_{max}=\,}$ 0.331 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
9)
Three wires sit at the corners of a square of length 0.688 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.73 A, 1.37 A, 1.65 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.171E-05 T
b) Bx= 6.788E-05 T
c) Bx= 7.467E-05 T
d) Bx= 8.213E-05 T
e) Bx= 9.035E-05 T

10) 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 525 mA, the net magnetic field is measured to be 1.44 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 5.515E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 6.066E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 6.673E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.340E+02
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.074E+02

11) 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 D0

1) 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
2)
Three wires sit at the corners of a square of length 0.739 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.93 A, 2.48 A, 1.36 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.397E-05 T
b) Bx= 7.037E-05 T
c) Bx= 7.740E-05 T
d) Bx= 8.514E-05 T
e) Bx= 9.366E-05 T
3)
Three wires sit at the corners of a square of length 0.787 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.68 A, 2.44 A, 2.47 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 6.091E-05 T
b) By= 6.700E-05 T
c) By= 7.370E-05 T
d) By= 8.107E-05 T
e) By= 8.917E-05 T

4) 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

5) 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

6) 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

7) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.619 m and ${\displaystyle B_{max}=\,}$ 0.215 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.4 kA, I2=2.64 kA, and I3=3.96 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
9)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.42 kA, I2=0.904 kA, and I3=1.34 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

10) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

11) 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) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.211E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.932E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.726E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.598E+02
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.056E+03

#### c12 D1

1)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.42 kA, I2=0.904 kA, and I3=1.34 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

2) A solenoid has 7.170E+04 turns wound around a cylinder of diameter 1.56 cm and length 9 m. The current through the coils is 0.391 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−2.73 cm to z=+2.56 cm

a) 1.414E-04 T-m
b) 1.556E-04 T-m
c) 1.711E-04 T-m
d) 1.882E-04 T-m
e) 2.071E-04 T-m

3) 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 265 mA, the net magnetic field is measured to be 1.11 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.376E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.514E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.666E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.832E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 2.015E+03

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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.568 m and ${\displaystyle B_{max}=\,}$ 0.214 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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

5) 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

6) 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
7)
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 (I1, I2, I2) are (1.57 A, 2.03 A, 2.08 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 7.270E-05 T
b) Bx= 7.997E-05 T
c) Bx= 8.797E-05 T
d) Bx= 9.677E-05 T
e) Bx= 1.064E-04 T
8)
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 (I1, I2, I2) are (2.18 A, 1.82 A, 1.35 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 7.035E-05 T
b) By= 7.739E-05 T
c) By= 8.512E-05 T
d) By= 9.364E-05 T
e) By= 1.030E-04 T
9)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.43 kA, I2=1.64 kA, and I3=4.81 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

10) 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

11) 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

#### c12 D2

1) Two parallel wires each carry a 9.68 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.55 cm, 1.79 cm), while the other is located at (3.16 cm, 4.78 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) 5.684E-10 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

3) 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) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.185E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.303E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.433E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.577E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.734E+03
4)
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 (I1, I2, I2) are (1.57 A, 2.03 A, 2.08 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 7.270E-05 T
b) Bx= 7.997E-05 T
c) Bx= 8.797E-05 T
d) Bx= 9.677E-05 T
e) Bx= 1.064E-04 T
5)
Three wires sit at the corners of a square of length 0.865 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.62 A, 2.13 A, 2.2 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 5.131E-05 T
b) By= 5.644E-05 T
c) By= 6.208E-05 T
d) By= 6.829E-05 T
e) By= 7.512E-05 T

6) 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
7)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.43 kA, I2=1.81 kA, and I3=3.23 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

8) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.547 m and ${\displaystyle B_{max}=\,}$ 0.597 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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

9) 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
10)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.5 kA, I2=1.28 kA, and I3=3.4 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

11) 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

### c12 E0

1) 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
2)
Three wires sit at the corners of a square of length 0.64 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.76 A, 1.02 A, 1.08 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 3.394E-05 T
b) Bx= 3.733E-05 T
c) Bx= 4.106E-05 T
d) Bx= 4.517E-05 T
e) Bx= 4.969E-05 T
3)
Three wires sit at the corners of a square of length 0.865 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.62 A, 2.13 A, 2.2 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 5.131E-05 T
b) By= 5.644E-05 T
c) By= 6.208E-05 T
d) By= 6.829E-05 T
e) By= 7.512E-05 T

4) 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

5) 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

6) 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

7) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.547 m and ${\displaystyle B_{max}=\,}$ 0.597 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.32 kA, I2=2.0 kA, and I3=3.66 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
9)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.58 kA, I2=1.11 kA, and I3=2.47 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 4.092E-03 T-m
b) 4.501E-03 T-m
c) 4.951E-03 T-m
d) 5.446E-03 T-m
e) 5.991E-03 T-m

10) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

11) 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) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.310E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.024E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.126E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.239E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.363E+03

#### c12 E1

1) 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

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 numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.39 kA, I2=0.414 kA, and I3=1.3 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 2.812E-03 T-m
b) 3.093E-03 T-m
c) 3.402E-03 T-m
d) 3.742E-03 T-m
e) 4.117E-03 T-m

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
5)
Three wires sit at the corners of a square of length 0.51 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.16 A, 2.46 A, 2.15 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 9.053E-05 T
b) Bx= 9.959E-05 T
c) Bx= 1.095E-04 T
d) Bx= 1.205E-04 T
e) Bx= 1.325E-04 T

6) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

7) A wire carries a current of 193 A in a circular arc with radius 3.13 cm swept through 40 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) 1.285E+00 Tesla
b) 1.413E+00 Tesla
c) 1.554E+00 Tesla
d) 1.710E+00 Tesla
e) 1.881E+00 Tesla
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.49 kA, I2=0.996 kA, and I3=2.61 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
9)
Three wires sit at the corners of a square of length 0.532 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.11 A, 1.25 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 5.930E-05 T
b) By= 6.523E-05 T
c) By= 7.175E-05 T
d) By= 7.892E-05 T
e) By= 8.682E-05 T

10) 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) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.211E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.932E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.726E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.598E+02
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.056E+03

11) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.571 m and ${\displaystyle B_{max}=\,}$ 0.331 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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

#### c12 E2

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 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
3)
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 (I1, I2, I2) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 4.028E-05 T
b) By= 4.431E-05 T
c) By= 4.874E-05 T
d) By= 5.361E-05 T
e) By= 5.897E-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 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
5)
Three wires sit at the corners of a square of length 0.688 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.73 A, 1.37 A, 1.65 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.171E-05 T
b) Bx= 6.788E-05 T
c) Bx= 7.467E-05 T
d) Bx= 8.213E-05 T
e) Bx= 9.035E-05 T

6) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.51 m and ${\displaystyle B_{max}=\,}$ 0.649 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
7)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.84 kA, I2=2.02 kA, and I3=4.24 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.5 kA, I2=1.53 kA, and I3=2.34 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

9) A solenoid has 8.890E+04 turns wound around a cylinder of diameter 1.32 cm and length 15 m. The current through the coils is 0.297 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−1.41 cm to z=+2.56 cm

a) 7.257E-05 T-m
b) 7.983E-05 T-m
c) 8.781E-05 T-m
d) 9.660E-05 T-m
e) 1.063E-04 T-m

10) 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 265 mA, the net magnetic field is measured to be 1.11 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.376E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.514E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.666E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.832E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 2.015E+03

11) 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 F0

1) A wire carries a current of 193 A in a circular arc with radius 3.13 cm swept through 40 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) 1.285E+00 Tesla
b) 1.413E+00 Tesla
c) 1.554E+00 Tesla
d) 1.710E+00 Tesla
e) 1.881E+00 Tesla
2)
Three wires sit at the corners of a square of length 0.533 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.17 A, 2.25 A, 2.22 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 1.037E-04 T
b) Bx= 1.141E-04 T
c) Bx= 1.255E-04 T
d) Bx= 1.381E-04 T
e) Bx= 1.519E-04 T
3)
Three wires sit at the corners of a square of length 0.532 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.11 A, 1.25 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 5.930E-05 T
b) By= 6.523E-05 T
c) By= 7.175E-05 T
d) By= 7.892E-05 T
e) By= 8.682E-05 T

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

5) 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

6) 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

7) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.259 m and ${\displaystyle B_{max}=\,}$ 0.575 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.4 kA, I2=2.64 kA, and I3=3.96 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
9)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.38 kA, I2=0.839 kA, and I3=2.27 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

10) A solenoid has 8.890E+04 turns wound around a cylinder of diameter 1.32 cm and length 15 m. The current through the coils is 0.297 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−1.41 cm to z=+2.56 cm

a) 7.257E-05 T-m
b) 7.983E-05 T-m
c) 8.781E-05 T-m
d) 9.660E-05 T-m
e) 1.063E-04 T-m

11) 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) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.804E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.685E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.065E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.172E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.289E+03

#### c12 F1

1)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.5 kA, I2=1.28 kA, and I3=3.4 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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) 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

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 424 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.092E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.201E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.321E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.454E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.599E+03

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
5)
Three wires sit at the corners of a square of length 0.686 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.28 A, 1.27 A, 1.61 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 5.409E-05 T
b) Bx= 5.950E-05 T
c) Bx= 6.545E-05 T
d) Bx= 7.200E-05 T
e) Bx= 7.920E-05 T
6)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.4 kA, I2=2.64 kA, and I3=3.96 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
7)
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 (I1, I2, I2) are (2.45 A, 2.44 A, 1.61 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 9.388E-05 T
b) By= 1.033E-04 T
c) By= 1.136E-04 T
d) By= 1.250E-04 T
e) By= 1.375E-04 T

8) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.37 m and ${\displaystyle B_{max}=\,}$ 0.556 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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

9) 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

10) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

11) 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 F2

1)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.44 kA, I2=1.1 kA, and I3=1.99 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

2) 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 424 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.092E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.201E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.321E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.454E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.599E+03
3)
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 (I1, I2, I2) are (2.47 A, 2.1 A, 2.24 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 1.191E-04 T
b) By= 1.310E-04 T
c) By= 1.441E-04 T
d) By= 1.585E-04 T
e) By= 1.744E-04 T
4)
Three wires sit at the corners of a square of length 0.75 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.1 A, 1.11 A, 2.26 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 7.507E-05 T
b) Bx= 8.257E-05 T
c) Bx= 9.083E-05 T
d) Bx= 9.991E-05 T
e) Bx= 1.099E-04 T

5) 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

6) 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

7) 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

8) Two parallel wires each carry a 9.68 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.55 cm, 1.79 cm), while the other is located at (3.16 cm, 4.78 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) 5.684E-10 N/m

9) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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
10)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.81 kA, I2=1.2 kA, and I3=1.84 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

11) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.547 m and ${\displaystyle B_{max}=\,}$ 0.597 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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 G0

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
2)
Three wires sit at the corners of a square of length 0.784 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.19 A, 1.51 A, 2.18 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 7.487E-05 T
b) Bx= 8.236E-05 T
c) Bx= 9.060E-05 T
d) Bx= 9.966E-05 T
e) Bx= 1.096E-04 T
3)
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 (I1, I2, I2) are (2.41 A, 1.87 A, 2.21 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 6.718E-05 T
b) By= 7.390E-05 T
c) By= 8.129E-05 T
d) By= 8.942E-05 T
e) By= 9.836E-05 T

4) 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

5) 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

6) 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

7) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.547 m and ${\displaystyle B_{max}=\,}$ 0.597 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.45 kA, I2=2.68 kA, and I3=5.5 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
9)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.84 kA, I2=3.3 kA, and I3=5.85 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

10) A solenoid has 5.640E+04 turns wound around a cylinder of diameter 1.35 cm and length 16 m. The current through the coils is 0.912 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−1.11 cm to z=+2.76 cm

a) 1.068E-04 T-m
b) 1.175E-04 T-m
c) 1.292E-04 T-m
d) 1.421E-04 T-m
e) 1.563E-04 T-m

11) 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 344 mA, the net magnetic field is measured to be 1.12 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.922E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.714E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.586E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.054E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.160E+03

#### c12 G1

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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.571 m and ${\displaystyle B_{max}=\,}$ 0.331 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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) 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

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
4)
Three wires sit at the corners of a square of length 0.687 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.38 A, 1.87 A, 2.03 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 7.134E-05 T
b) Bx= 7.847E-05 T
c) Bx= 8.632E-05 T
d) Bx= 9.495E-05 T
e) Bx= 1.044E-04 T

5) 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 424 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.092E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.201E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.321E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.454E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.599E+03

6) Two parallel wires each carry a 9.68 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.55 cm, 1.79 cm), while the other is located at (3.16 cm, 4.78 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) 5.684E-10 N/m

7) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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
8)
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 (I1, I2, I2) are (2.41 A, 1.87 A, 2.21 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 6.718E-05 T
b) By= 7.390E-05 T
c) By= 8.129E-05 T
d) By= 8.942E-05 T
e) By= 9.836E-05 T
9)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.84 kA, I2=2.02 kA, and I3=4.24 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
10)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.84 kA, I2=0.476 kA, and I3=1.57 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

11) 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 G2

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
2)
Three wires sit at the corners of a square of length 0.787 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.68 A, 2.44 A, 2.47 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 6.091E-05 T
b) By= 6.700E-05 T
c) By= 7.370E-05 T
d) By= 8.107E-05 T
e) By= 8.917E-05 T

3) 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) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.804E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.685E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.065E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.172E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.289E+03
4)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.48 kA, I2=1.47 kA, and I3=2.6 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
5)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.38 kA, I2=0.839 kA, and I3=2.27 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

6) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

7) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.353 m and ${\displaystyle B_{max}=\,}$ 0.697 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
8)
Three wires sit at the corners of a square of length 0.705 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.92 A, 1.14 A, 1.11 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 4.333E-05 T
b) Bx= 4.766E-05 T
c) Bx= 5.243E-05 T
d) Bx= 5.767E-05 T
e) Bx= 6.343E-05 T

9) 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

10) 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

11) A wire carries a current of 193 A in a circular arc with radius 3.13 cm swept through 40 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) 1.285E+00 Tesla
b) 1.413E+00 Tesla
c) 1.554E+00 Tesla
d) 1.710E+00 Tesla
e) 1.881E+00 Tesla

### c12 H0

1) A wire carries a current of 306 A in a circular arc with radius 2.04 cm swept through 55 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) 3.551E+00 Tesla
b) 3.907E+00 Tesla
c) 4.297E+00 Tesla
d) 4.727E+00 Tesla
e) 5.200E+00 Tesla
2)
Three wires sit at the corners of a square of length 0.64 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.76 A, 1.02 A, 1.08 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 3.394E-05 T
b) Bx= 3.733E-05 T
c) Bx= 4.106E-05 T
d) Bx= 4.517E-05 T
e) Bx= 4.969E-05 T
3)
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 (I1, I2, I2) are (2.47 A, 2.1 A, 2.24 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 1.191E-04 T
b) By= 1.310E-04 T
c) By= 1.441E-04 T
d) By= 1.585E-04 T
e) By= 1.744E-04 T

4) 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

5) 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

6) 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

7) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.852 m and ${\displaystyle B_{max}=\,}$ 0.476 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.48 kA, I2=1.47 kA, and I3=2.6 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
9)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.78 kA, I2=2.61 kA, and I3=3.76 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

10) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

11) 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) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.310E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.024E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.126E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.239E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.363E+03

#### c12 H1

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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.549 m and ${\displaystyle B_{max}=\,}$ 0.599 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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

2) A wire carries a current of 332 A in a circular arc with radius 2.47 cm swept through 44 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) 3.389E+00 Tesla
b) 3.727E+00 Tesla
c) 4.100E+00 Tesla
d) 4.510E+00 Tesla
e) 4.961E+00 Tesla

3) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 3.07 mm from the center of a wire of radius 5 mm if the current is 1A?

a) 1.677E-05 T
b) 1.845E-05 T
c) 2.030E-05 T
d) 2.233E-05 T
e) 2.456E-05 T
4)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.32 kA, I2=2.0 kA, and I3=3.66 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

5) 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

6) 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) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.185E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.303E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.433E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.577E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.734E+03

7) A solenoid has 5.640E+04 turns wound around a cylinder of diameter 1.35 cm and length 16 m. The current through the coils is 0.912 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−1.11 cm to z=+2.76 cm

a) 1.068E-04 T-m
b) 1.175E-04 T-m
c) 1.292E-04 T-m
d) 1.421E-04 T-m
e) 1.563E-04 T-m
8)
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 (I1, I2, I2) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 4.028E-05 T
b) By= 4.431E-05 T
c) By= 4.874E-05 T
d) By= 5.361E-05 T
e) By= 5.897E-05 T

9) Two parallel wires each carry a 9.68 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.55 cm, 1.79 cm), while the other is located at (3.16 cm, 4.78 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) 5.684E-10 N/m
10)
Three wires sit at the corners of a square of length 0.64 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.76 A, 1.02 A, 1.08 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 3.394E-05 T
b) Bx= 3.733E-05 T
c) Bx= 4.106E-05 T
d) Bx= 4.517E-05 T
e) Bx= 4.969E-05 T
11)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.89 kA, I2=1.19 kA, and I3=3.5 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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 H2

1) 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

2) A wire carries a current of 306 A in a circular arc with radius 2.04 cm swept through 55 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) 3.551E+00 Tesla
b) 3.907E+00 Tesla
c) 4.297E+00 Tesla
d) 4.727E+00 Tesla
e) 5.200E+00 Tesla
3)
Three wires sit at the corners of a square of length 0.702 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.24 A, 1.37 A, 2.3 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 7.576E-05 T
b) By= 8.333E-05 T
c) By= 9.167E-05 T
d) By= 1.008E-04 T
e) By= 1.109E-04 T

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 19 turns per centimeter and the current applied to the solenoid is 421 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.302E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.432E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.576E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.733E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.907E+03
5)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.72 kA, I2=2.17 kA, and I3=3.21 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

6) A solenoid has 9.350E+04 turns wound around a cylinder of diameter 1.85 cm and length 18 m. The current through the coils is 0.872 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−4.55 cm to z=+1.58 cm

a) 2.383E-04 T-m
b) 2.621E-04 T-m
c) 2.884E-04 T-m
d) 3.172E-04 T-m
e) 3.489E-04 T-m

7) 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

8) 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
9)
Three wires sit at the corners of a square of length 0.739 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.93 A, 2.48 A, 1.36 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.397E-05 T
b) Bx= 7.037E-05 T
c) Bx= 7.740E-05 T
d) Bx= 8.514E-05 T
e) Bx= 9.366E-05 T

10) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.645 m and ${\displaystyle B_{max}=\,}$ 0.469 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
11)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.31 kA, I2=1.08 kA, and I3=1.77 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

### c12 I0

1) A wire carries a current of 148 A in a circular arc with radius 1.44 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) 4.299E+00 Tesla
b) 4.729E+00 Tesla
c) 5.202E+00 Tesla
d) 5.722E+00 Tesla
e) 6.294E+00 Tesla
2)
Three wires sit at the corners of a square of length 0.687 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.38 A, 1.87 A, 2.03 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 7.134E-05 T
b) Bx= 7.847E-05 T
c) Bx= 8.632E-05 T
d) Bx= 9.495E-05 T
e) Bx= 1.044E-04 T
3)
Three wires sit at the corners of a square of length 0.865 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.62 A, 2.13 A, 2.2 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 5.131E-05 T
b) By= 5.644E-05 T
c) By= 6.208E-05 T
d) By= 6.829E-05 T
e) By= 7.512E-05 T

4) 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

5) 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

6) 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

7) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.736 m and ${\displaystyle B_{max}=\,}$ 0.204 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.532 m that is centered on the axis with its plane perpendicular to the axis?

a) 3.764E+05 A
b) 4.140E+05 A
c) 4.554E+05 A
d) 5.010E+05 A
e) 5.510E+05 A
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.84 kA, I2=0.476 kA, and I3=1.57 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
9)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.38 kA, I2=0.839 kA, and I3=2.27 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

10) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

11) 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 344 mA, the net magnetic field is measured to be 1.12 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.922E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.714E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.586E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.054E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.160E+03

#### c12 I1

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

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
3)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.58 kA, I2=1.27 kA, and I3=1.99 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
4)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.32 kA, I2=2.0 kA, and I3=3.66 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

5) 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) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.310E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.024E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.126E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.239E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.363E+03
6)
Three wires sit at the corners of a square of length 0.705 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.92 A, 1.14 A, 1.11 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 4.333E-05 T
b) Bx= 4.766E-05 T
c) Bx= 5.243E-05 T
d) Bx= 5.767E-05 T
e) Bx= 6.343E-05 T

7) 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

8) A solenoid has 5.640E+04 turns wound around a cylinder of diameter 1.35 cm and length 16 m. The current through the coils is 0.912 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−1.11 cm to z=+2.76 cm

a) 1.068E-04 T-m
b) 1.175E-04 T-m
c) 1.292E-04 T-m
d) 1.421E-04 T-m
e) 1.563E-04 T-m

9) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.432 m and ${\displaystyle B_{max}=\,}$ 0.402 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
10)
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 (I1, I2, I2) are (2.41 A, 1.87 A, 2.21 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 6.718E-05 T
b) By= 7.390E-05 T
c) By= 8.129E-05 T
d) By= 8.942E-05 T
e) By= 9.836E-05 T

11) Two loops of wire carry the same current of 43 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.516 m while the other has a radius of 1.22 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 0.565 m from the first (smaller) loopif the disance between the loops is 1.78 m?

a) 1.798E-02 T
b) 1.978E-02 T
c) 2.176E-02 T
d) 2.394E-02 T
e) 2.633E-02 T

#### c12 I2

1)
Three wires sit at the corners of a square of length 0.518 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.31 A, 1.32 A, 1.62 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.013E-05 T
b) Bx= 6.614E-05 T
c) Bx= 7.275E-05 T
d) Bx= 8.003E-05 T
e) Bx= 8.803E-05 T

2) 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
3)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.31 kA, I2=1.08 kA, and I3=1.77 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

4) A solenoid has 7.540E+04 turns wound around a cylinder of diameter 1.36 cm and length 14 m. The current through the coils is 0.807 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−2.75 cm to z=+3.28 cm

a) 2.722E-04 T-m
b) 2.994E-04 T-m
c) 3.293E-04 T-m
d) 3.623E-04 T-m
e) 3.985E-04 T-m

5) 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
6)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.38 kA, I2=1.58 kA, and I3=4.31 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
7)
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 (I1, I2, I2) are (2.47 A, 2.1 A, 2.24 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 1.191E-04 T
b) By= 1.310E-04 T
c) By= 1.441E-04 T
d) By= 1.585E-04 T
e) By= 1.744E-04 T

8) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.37 m and ${\displaystyle B_{max}=\,}$ 0.556 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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

9) A wire carries a current of 306 A in a circular arc with radius 2.04 cm swept through 55 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) 3.551E+00 Tesla
b) 3.907E+00 Tesla
c) 4.297E+00 Tesla
d) 4.727E+00 Tesla
e) 5.200E+00 Tesla

10) 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) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.211E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.932E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.726E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.598E+02
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.056E+03

11) 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

### c12 J0

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
2)
Three wires sit at the corners of a square of length 0.518 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.31 A, 1.32 A, 1.62 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.013E-05 T
b) Bx= 6.614E-05 T
c) Bx= 7.275E-05 T
d) Bx= 8.003E-05 T
e) Bx= 8.803E-05 T
3)
Three wires sit at the corners of a square of length 0.532 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.11 A, 1.25 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 5.930E-05 T
b) By= 6.523E-05 T
c) By= 7.175E-05 T
d) By= 7.892E-05 T
e) By= 8.682E-05 T

4) 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

5) 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

6) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.9 mm from the center of a wire of radius 4 mm if the current is 1A?

a) 1.784E-05 T
b) 1.963E-05 T
c) 2.159E-05 T
d) 2.375E-05 T
e) 2.613E-05 T

7) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.568 m and ${\displaystyle B_{max}=\,}$ 0.214 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.84 kA, I2=0.476 kA, and I3=1.57 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
9)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.31 kA, I2=1.16 kA, and I3=2.13 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

10) A solenoid has 8.890E+04 turns wound around a cylinder of diameter 1.32 cm and length 15 m. The current through the coils is 0.297 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−1.41 cm to z=+2.56 cm

a) 7.257E-05 T-m
b) 7.983E-05 T-m
c) 8.781E-05 T-m
d) 9.660E-05 T-m
e) 1.063E-04 T-m

11) 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 525 mA, the net magnetic field is measured to be 1.45 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.249E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.074E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.981E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.098E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.208E+03

#### c12 J1

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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.619 m and ${\displaystyle B_{max}=\,}$ 0.215 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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) 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 4 mm if the current is 1A?

a) 3.325E-05 T
b) 3.658E-05 T
c) 4.023E-05 T
d) 4.426E-05 T
e) 4.868E-05 T
3)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.84 kA, I2=2.02 kA, and I3=4.24 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

4) 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
5)
Three wires sit at the corners of a square of length 0.796 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.48 A, 1.4 A, 1.47 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 4.506E-05 T
b) Bx= 4.957E-05 T
c) Bx= 5.452E-05 T
d) Bx= 5.997E-05 T
e) Bx= 6.597E-05 T

6) 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

7) 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

8) 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 525 mA, the net magnetic field is measured to be 1.44 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 5.515E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 6.066E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 6.673E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.340E+02
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.074E+02

9) A solenoid has 7.170E+04 turns wound around a cylinder of diameter 1.56 cm and length 9 m. The current through the coils is 0.391 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−2.73 cm to z=+2.56 cm

a) 1.414E-04 T-m
b) 1.556E-04 T-m
c) 1.711E-04 T-m
d) 1.882E-04 T-m
e) 2.071E-04 T-m
10)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.45 kA, I2=2.68 kA, and I3=5.5 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
11)
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 (I1, I2, I2) are (2.26 A, 1.75 A, 2.47 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 7.518E-05 T
b) By= 8.270E-05 T
c) By= 9.097E-05 T
d) By= 1.001E-04 T
e) By= 1.101E-04 T

#### c12 J2

1) 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
2)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.39 kA, I2=0.414 kA, and I3=1.3 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 2.812E-03 T-m
b) 3.093E-03 T-m
c) 3.402E-03 T-m
d) 3.742E-03 T-m
e) 4.117E-03 T-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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.353 m and ${\displaystyle B_{max}=\,}$ 0.697 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
4)
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 (I1, I2, I2) are (2.47 A, 2.1 A, 2.24 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 1.191E-04 T
b) By= 1.310E-04 T
c) By= 1.441E-04 T
d) By= 1.585E-04 T
e) By= 1.744E-04 T

5) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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
6)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.49 kA, I2=0.996 kA, and I3=2.61 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

7) 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 424 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.092E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.201E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.321E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.454E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.599E+03

8) 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

9) 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

10) 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
11)
Three wires sit at the corners of a square of length 0.796 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.48 A, 1.4 A, 1.47 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 4.506E-05 T
b) Bx= 4.957E-05 T
c) Bx= 5.452E-05 T
d) Bx= 5.997E-05 T
e) Bx= 6.597E-05 T

### c12 K0

1) A wire carries a current of 193 A in a circular arc with radius 3.13 cm swept through 40 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) 1.285E+00 Tesla
b) 1.413E+00 Tesla
c) 1.554E+00 Tesla
d) 1.710E+00 Tesla
e) 1.881E+00 Tesla
2)
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 (I1, I2, I2) are (1.4 A, 2.42 A, 1.9 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 1.335E-04 T
b) Bx= 1.468E-04 T
c) Bx= 1.615E-04 T
d) Bx= 1.777E-04 T
e) Bx= 1.954E-04 T
3)
Three wires sit at the corners of a square of length 0.547 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.78 A, 1.34 A, 1.64 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 6.118E-05 T
b) By= 6.730E-05 T
c) By= 7.403E-05 T
d) By= 8.144E-05 T
e) By= 8.958E-05 T

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

5) 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

6) 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

7) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.852 m and ${\displaystyle B_{max}=\,}$ 0.476 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.51 kA, I2=2.33 kA, and I3=5.35 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
9)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.81 kA, I2=1.2 kA, and I3=1.84 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

10) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

11) 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 331 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.593E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.753E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.928E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 2.121E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 2.333E+03

#### c12 K1

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 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

3) 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 331 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.593E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.753E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.928E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 2.121E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 2.333E+03

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
5)
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 (I1, I2, I2) are (2.47 A, 2.1 A, 2.24 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 1.191E-04 T
b) By= 1.310E-04 T
c) By= 1.441E-04 T
d) By= 1.585E-04 T
e) By= 1.744E-04 T

6) 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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

7) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.547 m and ${\displaystyle B_{max}=\,}$ 0.597 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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
8)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.4 kA, I2=2.64 kA, and I3=3.96 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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
9)
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 (I1, I2, I2) are (2.29 A, 1.77 A, 1.48 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 8.371E-05 T
b) Bx= 9.208E-05 T
c) Bx= 1.013E-04 T
d) Bx= 1.114E-04 T
e) Bx= 1.226E-04 T

10) 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
11)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.5 kA, I2=1.28 kA, and I3=3.4 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

#### c12 K2

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

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 ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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
3)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.51 kA, I2=2.33 kA, and I3=5.35 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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

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) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.718E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.890E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 2.079E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 2.287E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 2.515E+03
5)
Three wires sit at the corners of a square of length 0.739 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.93 A, 2.48 A, 1.36 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.397E-05 T
b) Bx= 7.037E-05 T
c) Bx= 7.740E-05 T
d) Bx= 8.514E-05 T
e) Bx= 9.366E-05 T

6) 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

7) 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.37 m and ${\displaystyle B_{max}=\,}$