<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

For linearly magnetizable materials, the relationship between the magnetization and the H-field is, $\mathbf{M} = \chi_m \mathbf{H}$ What do you expect the sign of $X_m$ to be for a paramagnetic/diamagnetic material? 1. para: $\chi_m<0 \;$ dia: $\chi_m>0$ 2. para: $\chi_m>0 \;$ dia: $\chi_m<0$ 3. Both positive 4. Both negative Note: Correct answer: B