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";/>
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
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
<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 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