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

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?

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

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?

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. ???

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?

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

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?

1. $\mathbf{K}_B$ points parallel to $I$
2. $\mathbf{K}_B$ points anti-parallel to $I$
3. Other/not sure