<img src="./images/loop_in_B_field.png" align="center" style="width: 550px";/> The force on a segment of wire $L$ is $\mathbf{F} = I \mathbf{L} \times \mathbf{B}$ A current-carrying wire loop is in a constant magnetic field $\mathbf{B} = B \hat{z}$ as shown. What is the direction of the torque on the loop? 1. Zero 2. +x 3. +y 4. +z 5. None of these Note: * CORRECT ANSWER: B

## Announcements * Final Exam! * 12:45-2:45pm, Tues Dec. 10 * In this room (1415 BPS) * Details on Wednesday

The torque on a magnetic dipole in a B field is: $\mathbf{\tau} = \mathbf{m} \times \mathbf{B}$ How will a small current loop line up if the B field points uniformly up the page? <img src="./images/mag_loops.png" align="center" style="width: 800px";/>

Consider a paramagnetic material placed in a uniform external magnetic field, $\mathbf{B}_{ext}$. The paramagnetic magnetizes, so that the total magnetic field just outside the material is now... 1. smaller than 2. larger than 3. the same as it was before the material was placed. Note: * Correct Answer: B

A solid cylinder has uniform magnetization $\mathbf{M}$ throughout the volume in the $x$ direction as shown. What's the magnitude of the total magnetic dipole moment of the cylinder? <img src="./images/M_in_x_cylinder.png" align="right" style="width: 200px";/> 1. $\pi R^2 L M$ 2. $2\pi R L M$ 3. $2\pi R M$ 4. $\pi R^2M$ 5. Something else/it's complicated! Note: * CORRECT ANSWER: A

<img src="./images/M_in_z_cylinder.png" align="right" style="width: 200px";/> A solid cylinder has uniform magnetization $\mathbf{M}$ throughout the volume in the $z$ direction as shown. Where do bound currents show up? 1. Everywhere 2. Volume only, not surface 3. Top/bottom surface only 4. Side (rounded) surface only 5. All surfaces, but not volume Note: * CORRECT ANSWER: D

<img src="./images/M_in_x_cylinder.png" align="right" style="width: 200px";/> A solid cylinder has uniform magnetization $\mathbf{M}$ throughout the volume in the $x$ direction as shown. Where do bound currents show up? 1. Top/bottom surface only 2. Side (rounded) surface only 3. Everywhere 4. Top/bottom, and parts of (but not all of) side surface (but not in the volume) 5. Something different/other combination! Note: * CORRECT ANSWER: D

A sphere has uniform magnetization $\mathbf{M}$ in the $+z$ direction. Which formula is correct for this surface current? <img src="./images/sphere_uniform_M.png" align="right" style="width: 300px";/> 1. $M \sin \theta\,\hat{\theta}$ 2. $M \sin \theta\,\hat{\phi}$ 3. $M \cos \phi\,\hat{\theta}$ 4. $M \cos \phi\,\hat{\phi}$ 5. Something else Note: * CORRECT ANSWER: B