c12 A0

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 ${\displaystyle r<a}$ 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

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

a) 7.952E-03 T

b) 8.747E-03 T

c) 9.622E-03 T

d) 1.058E-02 T

e) 1.164E-02 T

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

a) 5.926E-11 N/m

b) 6.518E-11 N/m

c) 7.170E-11 N/m

d) 7.887E-11 N/m

e) 8.676E-11 N/m

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

a) 1.791E-05 T

b) 1.970E-05 T

c) 2.167E-05 T

d) 2.384E-05 T

e) 2.622E-05 T

c12 A1

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

a) 1.422E-11 N/m

b) 1.564E-11 N/m

c) 1.720E-11 N/m

d) 1.892E-11 N/m

e) 2.081E-11 N/m

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

a) 1.791E-05 T

b) 1.970E-05 T

c) 2.167E-05 T

d) 2.384E-05 T

e) 2.622E-05 T

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

a) 4.799E-02 T

b) 5.278E-02 T

c) 5.806E-02 T

d) 6.387E-02 T

e) 7.026E-02 T

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for ${\displaystyle r<a}$ 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 ${\displaystyle a=}$ 0.871 m and ${\displaystyle B_{max}=\,}$ 0.427 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.688 m that is centered on the axis with its plane perpendicular to the axis?

a) 1.404E+06 A

b) 1.544E+06 A

c) 1.699E+06 A

d) 1.869E+06 A

e) 2.056E+06 A

c12 A2

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

a) 1.208E-05 T

b) 1.329E-05 T

c) 1.462E-05 T

d) 1.608E-05 T

e) 1.769E-05 T

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

a) 2.977E-11 N/m

b) 3.274E-11 N/m

c) 3.602E-11 N/m

d) 3.962E-11 N/m

e) 4.358E-11 N/m

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

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

a) 4.162E-02 T

b) 4.578E-02 T

c) 5.036E-02 T

d) 5.540E-02 T

e) 6.094E-02 T

c12 B0

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 ${\displaystyle r<a}$ 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) 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

a) B_x= 6.545E-05 T

b) B_x= 7.200E-05 T

c) B_x= 7.919E-05 T

d) B_x= 8.711E-05 T

e) B_x= 9.583E-05 T

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

a) 3.416E-05 T

b) 3.758E-05 T

c) 4.133E-05 T

d) 4.547E-05 T

e) 5.001E-05 T

c12 B1

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

a) 1.935E-05 T

b) 2.128E-05 T

c) 2.341E-05 T

d) 2.575E-05 T

e) 2.832E-05 T

2) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for ${\displaystyle r<a}$ 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 ${\displaystyle a=}$ 0.52 m and ${\displaystyle B_{max}=\,}$ 0.657 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.295 m that is centered on the axis with its plane perpendicular to the axis?

a) 7.876E+05 A

b) 8.664E+05 A

c) 9.530E+05 A

d) 1.048E+06 A

e) 1.153E+06 A

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

a) 2.015E-10 N/m

b) 2.216E-10 N/m

c) 2.438E-10 N/m

d) 2.682E-10 N/m

e) 2.950E-10 N/m

a) B_x= 9.053E-05 T

b) B_x= 9.959E-05 T

c) B_x= 1.095E-04 T

d) B_x= 1.205E-04 T

e) B_x= 1.325E-04 T

c12 B2

a) B_x= 1.335E-04 T

b) B_x= 1.468E-04 T

c) B_x= 1.615E-04 T

d) B_x= 1.777E-04 T

e) B_x= 1.954E-04 T

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

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

a) 6.484E-11 N/m

b) 7.133E-11 N/m

c) 7.846E-11 N/m

d) 8.631E-11 N/m

e) 9.494E-11 N/m

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

a) 1.935E-05 T

b) 2.128E-05 T

c) 2.341E-05 T

d) 2.575E-05 T

e) 2.832E-05 T

c12 C0

a) B_y= 5.611E-05 T

b) B_y= 6.172E-05 T

c) B_y= 6.789E-05 T

d) B_y= 7.468E-05 T

e) B_y= 8.215E-05 T

a) B_x= 1.335E-04 T

b) B_x= 1.468E-04 T

c) B_x= 1.615E-04 T

d) B_x= 1.777E-04 T

e) B_x= 1.954E-04 T

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

a) 5.034E+00 Tesla

b) 5.538E+00 Tesla

c) 6.091E+00 Tesla

d) 6.701E+00 Tesla

e) 7.371E+00 Tesla

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

a) 2.072E-05 T

b) 2.279E-05 T

c) 2.507E-05 T

d) 2.758E-05 T

e) 3.034E-05 T

c12 C1

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

a) B_y= 7.518E-05 T

b) B_y= 8.270E-05 T

c) B_y= 9.097E-05 T

d) B_y= 1.001E-04 T

e) B_y= 1.101E-04 T

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

a) 3.324E-05 T

b) 3.657E-05 T

c) 4.022E-05 T

d) 4.424E-05 T

e) 4.867E-05 T

a) B_x= 6.545E-05 T

b) B_x= 7.200E-05 T

c) B_x= 7.919E-05 T

d) B_x= 8.711E-05 T

e) B_x= 9.583E-05 T

c12 C2

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

a) B_x= 3.394E-05 T

b) B_x= 3.733E-05 T

c) B_x= 4.106E-05 T

d) B_x= 4.517E-05 T

e) B_x= 4.969E-05 T

a) B_y= 7.576E-05 T

b) B_y= 8.333E-05 T

c) B_y= 9.167E-05 T

d) B_y= 1.008E-04 T

e) B_y= 1.109E-04 T

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

a) 3.498E+00 Tesla

b) 3.848E+00 Tesla

c) 4.233E+00 Tesla

d) 4.656E+00 Tesla

e) 5.122E+00 Tesla

c12 D0

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

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

a) 1.559E-02 T

b) 1.715E-02 T

c) 1.886E-02 T

d) 2.075E-02 T

e) 2.283E-02 T

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

a) 1.589E+00 Tesla

b) 1.748E+00 Tesla

c) 1.923E+00 Tesla

d) 2.116E+00 Tesla

e) 2.327E+00 Tesla

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

c12 D1

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

a) 5.711E+00 Tesla

b) 6.283E+00 Tesla

c) 6.911E+00 Tesla

d) 7.602E+00 Tesla

e) 8.362E+00 Tesla

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

a) 1.127E-02 T

b) 1.240E-02 T

c) 1.364E-02 T

d) 1.500E-02 T

e) 1.650E-02 T

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

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 ${\displaystyle r<a}$ 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 D2

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

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

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

a) 3.774E+00 Tesla

b) 4.151E+00 Tesla

c) 4.566E+00 Tesla

d) 5.023E+00 Tesla

e) 5.525E+00 Tesla

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

c12 E0

a) B_y= 4.688E-05 T

b) B_y= 5.156E-05 T

c) B_y= 5.672E-05 T

d) B_y= 6.239E-05 T

e) B_y= 6.863E-05 T

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

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

a) 1.720E-05 T

b) 1.892E-05 T

c) 2.081E-05 T

d) 2.289E-05 T

e) 2.518E-05 T

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

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 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

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

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

a) B_y= 1.205E-04 T

b) B_y= 1.325E-04 T

c) B_y= 1.458E-04 T

d) B_y= 1.604E-04 T

e) B_y= 1.764E-04 T

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

a) 1.488E-05 T

b) 1.637E-05 T

c) 1.800E-05 T

d) 1.981E-05 T

e) 2.179E-05 T

c12 E2

a) B_y= 4.028E-05 T

b) B_y= 4.431E-05 T

c) B_y= 4.874E-05 T

d) B_y= 5.361E-05 T

e) B_y= 5.897E-05 T

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

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

a) 1.944E-05 T

b) 2.138E-05 T

c) 2.352E-05 T

d) 2.587E-05 T

e) 2.846E-05 T

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

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 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

c12 F0

1) A solenoid has 4.380E+04 turns wound around a cylinder of diameter 1.77 cm and length 16 m. The current through the coils is 0.916 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

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

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

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 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

a) B_x= 6.545E-05 T

b) B_x= 7.200E-05 T

c) B_x= 7.919E-05 T

d) B_x= 8.711E-05 T

e) B_x= 9.583E-05 T

c12 F1

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

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.205E+02

b) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.026E+02

c) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.928E+02

d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.092E+03

e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.201E+03

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

a) B_x= 7.270E-05 T

b) B_x= 7.997E-05 T

c) B_x= 8.797E-05 T

d) B_x= 9.677E-05 T

e) B_x= 1.064E-04 T

4) A solenoid has 3.950E+04 turns wound around a cylinder of diameter 1.64 cm and length 16 m. The current through the coils is 0.441 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

c12 F2

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 ${\displaystyle r<a}$ 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

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

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.188E+03

b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.307E+03

c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.438E+03

d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.582E+03

e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.740E+03

a) B_x= 6.545E-05 T

b) B_x= 7.200E-05 T

c) B_x= 7.919E-05 T

d) B_x= 8.711E-05 T

e) B_x= 9.583E-05 T

4) A solenoid has 5.980E+04 turns wound around a cylinder of diameter 1.8 cm and length 17 m. The current through the coils is 0.933 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

c12 G0

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

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

a) 2.733E-02 T

b) 3.007E-02 T

c) 3.307E-02 T

d) 3.638E-02 T

e) 4.002E-02 T

3) A solenoid has 3.950E+04 turns wound around a cylinder of diameter 1.64 cm and length 16 m. The current through the coils is 0.441 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

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

a) 1.902E+00 Tesla

b) 2.092E+00 Tesla

c) 2.301E+00 Tesla

d) 2.532E+00 Tesla

e) 2.785E+00 Tesla

c12 G1

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

a) 5.302E-02 T

b) 5.832E-02 T

c) 6.415E-02 T

d) 7.056E-02 T

e) 7.762E-02 T

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

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

a) 4.652E+00 Tesla

b) 5.117E+00 Tesla

c) 5.629E+00 Tesla

d) 6.192E+00 Tesla

e) 6.811E+00 Tesla

4) A solenoid has 7.610E+04 turns wound around a cylinder of diameter 1.21 cm and length 9 m. The current through the coils is 0.696 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

c12 G2

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

2) A solenoid has 7.610E+04 turns wound around a cylinder of diameter 1.21 cm and length 9 m. The current through the coils is 0.696 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

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

a) 7.952E-03 T

b) 8.747E-03 T

c) 9.622E-03 T

d) 1.058E-02 T

e) 1.164E-02 T

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

a) 5.034E+00 Tesla

b) 5.538E+00 Tesla

c) 6.091E+00 Tesla

d) 6.701E+00 Tesla

e) 7.371E+00 Tesla

c12 H0

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 ${\displaystyle r<a}$ 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

a) B_x= 7.270E-05 T

b) B_x= 7.997E-05 T

c) B_x= 8.797E-05 T

d) B_x= 9.677E-05 T

e) B_x= 1.064E-04 T

a) B_y= 3.480E-05 T

b) B_y= 3.828E-05 T

c) B_y= 4.210E-05 T

d) B_y= 4.631E-05 T

e) B_y= 5.095E-05 T

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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 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 ${\displaystyle r<a}$ 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 ${\displaystyle a=}$ 0.52 m and ${\displaystyle B_{max}=\,}$ 0.657 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.295 m that is centered on the axis with its plane perpendicular to the axis?

a) 7.876E+05 A

b) 8.664E+05 A

c) 9.530E+05 A

d) 1.048E+06 A

e) 1.153E+06 A

a) B_y= 3.480E-05 T

b) B_y= 3.828E-05 T

c) B_y= 4.210E-05 T

d) B_y= 4.631E-05 T

e) B_y= 5.095E-05 T

a) B_x= 4.559E-05 T

b) B_x= 5.015E-05 T

c) B_x= 5.517E-05 T

d) B_x= 6.068E-05 T

e) B_x= 6.675E-05 T

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

c12 H2

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

a) B_y= 6.999E-05 T

b) B_y= 7.699E-05 T

c) B_y= 8.469E-05 T

d) B_y= 9.316E-05 T

e) B_y= 1.025E-04 T

a) B_x= 1.037E-04 T

b) B_x= 1.141E-04 T

c) B_x= 1.255E-04 T

d) B_x= 1.381E-04 T

e) B_x= 1.519E-04 T

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

c12 I0

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

a) 4.799E-02 T

b) 5.278E-02 T

c) 5.806E-02 T

d) 6.387E-02 T

e) 7.026E-02 T

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

a) 1.973E-10 N/m

b) 2.170E-10 N/m

c) 2.387E-10 N/m

d) 2.625E-10 N/m

e) 2.888E-10 N/m

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \beta }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

a) B_x= 7.134E-05 T

b) B_x= 7.847E-05 T

c) B_x= 8.632E-05 T

d) B_x= 9.495E-05 T

e) B_x= 1.044E-04 T

c12 I1

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

a) 2.634E-11 N/m

b) 2.897E-11 N/m

c) 3.187E-11 N/m

d) 3.506E-11 N/m

e) 3.856E-11 N/m

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \beta }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

a) B_x= 8.371E-05 T

b) B_x= 9.208E-05 T

c) B_x= 1.013E-04 T

d) B_x= 1.114E-04 T

e) B_x= 1.226E-04 T

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

a) 4.253E-02 T

b) 4.678E-02 T

c) 5.146E-02 T

d) 5.661E-02 T

e) 6.227E-02 T

c12 I2

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \beta }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

a) 1.547E-03 T-m

b) 1.702E-03 T-m

c) 1.872E-03 T-m

d) 2.060E-03 T-m

e) 2.266E-03 T-m

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

a) 4.253E-02 T

b) 4.678E-02 T

c) 5.146E-02 T

d) 5.661E-02 T

e) 6.227E-02 T

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

a) 1.434E-10 N/m

b) 1.578E-10 N/m

c) 1.736E-10 N/m

d) 1.909E-10 N/m

e) 2.100E-10 N/m

a) B_x= 6.171E-05 T

b) B_x= 6.788E-05 T

c) B_x= 7.467E-05 T

d) B_x= 8.213E-05 T

e) B_x= 9.035E-05 T

c12 J0

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

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \beta }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

a) B_y= 4.028E-05 T

b) B_y= 4.431E-05 T

c) B_y= 4.874E-05 T

d) B_y= 5.361E-05 T

e) B_y= 5.897E-05 T

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

a) 2.015E-10 N/m

b) 2.216E-10 N/m

c) 2.438E-10 N/m

d) 2.682E-10 N/m

e) 2.950E-10 N/m

c12 J1

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \beta }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

a) 1.331E-03 T-m

b) 1.464E-03 T-m

c) 1.611E-03 T-m

d) 1.772E-03 T-m

e) 1.949E-03 T-m

a) B_y= 5.611E-05 T

b) B_y= 6.172E-05 T

c) B_y= 6.789E-05 T

d) B_y= 7.468E-05 T

e) B_y= 8.215E-05 T

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

a) 1.840E-10 N/m

b) 2.024E-10 N/m

c) 2.227E-10 N/m

d) 2.449E-10 N/m

e) 2.694E-10 N/m

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

a) 7.836E-03 T

b) 8.620E-03 T

c) 9.482E-03 T

d) 1.043E-02 T

e) 1.147E-02 T

c12 J2

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

a) 1.127E-02 T

b) 1.240E-02 T

c) 1.364E-02 T

d) 1.500E-02 T

e) 1.650E-02 T

a) B_y= 7.576E-05 T

b) B_y= 8.333E-05 T

c) B_y= 9.167E-05 T

d) B_y= 1.008E-04 T

e) B_y= 1.109E-04 T

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \beta }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

a) 8.204E-04 T-m

b) 9.025E-04 T-m

c) 9.927E-04 T-m

d) 1.092E-03 T-m

e) 1.201E-03 T-m

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

a) 2.449E-10 N/m

b) 2.694E-10 N/m

c) 2.963E-10 N/m

d) 3.260E-10 N/m

e) 3.586E-10 N/m

c12 K0

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \beta }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

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

a) 7.952E-03 T

b) 8.747E-03 T

c) 9.622E-03 T

d) 1.058E-02 T

e) 1.164E-02 T

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

c12 K1

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

a) 7.836E-03 T

b) 8.620E-03 T

c) 9.482E-03 T

d) 1.043E-02 T

e) 1.147E-02 T

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

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \beta }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

c12 K2

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

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

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

a) 3.342E-02 T

b) 3.676E-02 T

c) 4.044E-02 T

d) 4.448E-02 T

e) 4.893E-02 T

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \beta }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

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

c12 L0

1) A solenoid has 7.610E+04 turns wound around a cylinder of diameter 1.21 cm and length 9 m. The current through the coils is 0.696 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

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

a) 1.208E-05 T

b) 1.329E-05 T

c) 1.462E-05 T

d) 1.608E-05 T

e) 1.769E-05 T

a) B_y= 5.930E-05 T

b) B_y= 6.523E-05 T

c) B_y= 7.175E-05 T

d) B_y= 7.892E-05 T

e) B_y= 8.682E-05 T

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

a) 4.412E-10 N/m

b) 4.853E-10 N/m

c) 5.338E-10 N/m

d) 5.872E-10 N/m

e) 6.459E-10 N/m

c12 L1

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

a) 2.977E-11 N/m

b) 3.274E-11 N/m

c) 3.602E-11 N/m

d) 3.962E-11 N/m

e) 4.358E-11 N/m

2) A solenoid has 7.690E+04 turns wound around a cylinder of diameter 1.63 cm and length 11 m. The current through the coils is 0.728 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

a) B_y= 7.576E-05 T

b) B_y= 8.333E-05 T

c) B_y= 9.167E-05 T

d) B_y= 1.008E-04 T

e) B_y= 1.109E-04 T

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

a) 1.098E-05 T

b) 1.208E-05 T

c) 1.329E-05 T

d) 1.462E-05 T

e) 1.608E-05 T

c12 L2

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

a) 1.920E-05 T

b) 2.112E-05 T

c) 2.323E-05 T

d) 2.556E-05 T

e) 2.811E-05 T

a) B_y= 6.118E-05 T

b) B_y= 6.730E-05 T

c) B_y= 7.403E-05 T

d) B_y= 8.144E-05 T

e) B_y= 8.958E-05 T

3) A solenoid has 5.500E+04 turns wound around a cylinder of diameter 1.45 cm and length 15 m. The current through the coils is 0.395 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ 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

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

a) 2.119E-11 N/m

b) 2.331E-11 N/m

c) 2.564E-11 N/m

d) 2.820E-11 N/m

e) 3.102E-11 N/m

c12 M0

a) B_y= 7.518E-05 T

b) B_y= 8.270E-05 T

c) B_y= 9.097E-05 T

d) B_y= 1.001E-04 T

e) B_y= 1.101E-04 T

${\displaystyle \beta }$

${\displaystyle \omega }$

${\displaystyle \omega }$

${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$

a) 4.031E-03 T-m

b) 4.434E-03 T-m

c) 4.877E-03 T-m

d) 5.365E-03 T-m

e) 5.901E-03 T-m

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

a) 1.564E-02 T

b) 1.720E-02 T

c) 1.892E-02 T

d) 2.081E-02 T

e) 2.289E-02 T

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

a) 3.882E-10 N/m

b) 4.270E-10 N/m

c) 4.697E-10 N/m

d) 5.167E-10 N/m

e) 5.683E-10 N/m

c12 M1

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

a) 1.564E-02 T

b) 1.720E-02 T

c) 1.892E-02 T

d) 2.081E-02 T

e) 2.289E-02 T

a) B_y= 7.035E-05 T

b) B_y= 7.739E-05 T

c) B_y= 8.512E-05 T

d) B_y= 9.364E-05 T

e) B_y= 1.030E-04 T

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

a) 2.977E-11 N/m

b) 3.274E-11 N/m

c) 3.602E-11 N/m

d) 3.962E-11 N/m

e) 4.358E-11 N/m