A small chunk of material (the “tan cube”) is placed above a solenoid. It magnetizes, weakly, as shown by small arrows inside.
What kind of material must the cube be?
<img src="./images/tan_cube_magnetization.png" align="right" style="width: 300px";/>
1. Dielectric
2. Conductor
3. Diamagnetic
4. Paramagnetic
5. Ferromagnetic
Note:
* CORRECT ANSWER: C
## Final Exam
* A few true/false questions conceptual questions
* Determine bound charge, $\mathbf{E}$, $\mathbf{D}$, $\mathbf{P}$ for some material with $\chi_e$, and explain where the bound charge is.
* Setup magnetic vector potential and field calculations. Compare the appraoches.
* Determine the $\mathbf{B}$ for some $\mathbf{J}$ using Ampere's Law.
* Determine bound currents, $\mathbf{B}$, and $\mathbf{H}$ for some material with a "simple" free current, and explain properties of the bound currents
<img src="./images/M_in_phi_cylinder.png" align="right" style="width: 200px";/>
A solid cylinder has uniform magnetization $\mathbf{M}$ throughout the volume in the $\phi$ direction as shown. In which direction does the bound surface current flow on the (curved) sides?
1. There is no bound surface current.
2. The current flows in the $\pm \phi$ direction.
3. The current flows in the $\pm s$ direction.
4. The current flows in the $\pm z$ direction.
5. The direction is more complicated.
A very long aluminum (paramagnetic!) rod carries a uniformly distributed current $I$ along the $+z$ direction.
What is the direction of the bound volume current?
<img src="./images/Al_rod_example_current_shown.png" align="right" style="width: 200px";/>
1. $\mathbf{J}_B$ points parallel to $I$
2. $\mathbf{J}_B$ points anti-parallel to $I$
3. It’s zero!
4. Other/not sure
Note:
* CORRECT ANSWER: A
A very long aluminum (paramagnetic!) rod carries a uniformly distributed current $I$ along the $+z$ direction. We know $\mathbf{B}$ will be CCW as viewed from above. (Right?) What about $\mathbf{H}$ and $\mathbf{M}$ inside the cylinder?
<img src="./images/Al_rod_example_B_shown.png" align="right" style="width: 200px";/>
1. Both are CCW
2. Both are CW
3. $\mathbf{H}$ is CCW, but $\mathbf{M}$ is CW
4. $\mathbf{H}$ is CW, $\mathbf{M}$ is CCW
5. ???
Note:
* CORRECT ANSWER: A
A very long aluminum (paramagnetic!) rod carries a uniformly distributed current $I$ along the $+z$ direction. What is the direction of the bound volume current?
<img src="./images/Al_rod_example_HBM_shown.png" align="right" style="width: 200px";/>
1. $\mathbf{J}_B$ points parallel to $I$
2. $\mathbf{J}_B$ points anti-parallel to $I$
3. It’s zero!
4. Other/not sure
Note:
* CORRECT ANSWER: A
A very long aluminum (paramagnetic!) rod carries a uniformly distributed current $I$ along the $+z$ direction. What is the direction of the bound surface current?
<img src="./images/Al_rod_example_current_shown.png" align="right" style="width: 200px";/>
1. $\mathbf{K}_B$ points parallel to $I$
2. $\mathbf{K}_B$ points anti-parallel to $I$
3. Other/not sure
Note:
* CORRECT ANSWER: B