What is $\oint \mathbf{B}\cdot d\mathbf{l}$ around this purple (dashed) Amperian loop? <img src="./images/two_loops_ampere.png" align="left" style="width: 400px";/> 1. $\mu_0 (|I_2 | +|I_1 |)$ 2. $\mu_0 (|I_2|-|I_1|)$ 3. $\mu_0 (| I_2 | + | I_1 | \sin \theta)$ 4. $\mu_0 (| I_2 | - | I_1 | \sin \theta)$ 5. $\mu_0 (| I_2 | + | I_1 | \cos\theta)$ Note: * CORRECT ANSWER: A

I will be at next Wednesday's class. 1. Yes, I'll be there. 2. No, I'll be doing something more awesome!

<img src="./images/solenoid_2D.png" align="right" style="width: 100px";/> An infinite solenoid with surface current density $K$ is oriented along the $z$-axis. To use Ampere's Law, we need to argue what we think $\mathbf{B}(\mathbf{r})$ depends on and which way it points. For this solenoid, $\mathbf{B}(\mathbf{r})=$ 1. $B(z)\,\hat{z}$ 2. $B(z)\,\hat{\phi}$ 3. $B(s)\,\hat{z}$ 4. $B(s)\,\hat{\phi}$ 5. Something else?

<img src="./images/solenoid_loop_outside.png" align="right" style="width: 250px";/> An infinite solenoid with surface current density $K$ is oriented along the $z$-axis. Apply Ampere's Law to the rectangular imaginary loop in the $yz$ plane shown. What does this tell you about $B_z$, the $z$-component of the B-field outside the solenoid? 1. $B_z$ is constant outside 2. $B_z$ is zero outside 3. $B_z$ is not constant outside 4. It tells you nothing about $B_z$ Note: * CORRECT ANSWER: A

<img src="./images/solenoid_loop_outside.png" align="right" style="width: 250px";/> An infinite solenoid with surface current density $K$ is oriented along the $z$-axis. Apply Ampere's Law to the rectangular imaginary loop in the $yz$ plane shown. We can safely assume that $B(s\rightarrow\infty)=0$. What does this tell you about the B-field outside the solenoid? 1. $|\mathbf{B}|$ is a small non-zero constant outside 2. $|\mathbf{B}|$ is zero outside 3. $|\mathbf{B}|$ is not constant outside 4. We still don't know anything about $|\mathbf{B}|$ Note: * CORRECT ANSWER: B

What do we expect $\mathbf{B}(\mathbf{r})$ to look like for the infinite sheet of current shown below? <img src="./images/current_sheet_coords.png" align="right" style="width: 300px";/> 1. $B(x)\hat{x}$ 2. $B(z)\hat{x}$ 3. $B(x)\hat{z}$ 4. $B(z)\hat{z}$ 5. Something else Note: * CORRECT ANSWER: C

Which Amperian loop are useful to learn about $B(x,y,z)$ somewhere? <img src="./images/B_sheet_loops.png" align="center" style="width: 400px";/> E. More than 1 Note: * CORRECT ANSWER: E * Both B and A are useful!

Gauss' Law for magnetism, $\nabla \cdot \mathbf{B} = 0$ suggests we can generate a potential for $\mathbf{B}$. What form should the definition of this potential take ($\Phi$ and $\mathbf{A}$ are placeholder scalar and vector functions, respectively)? 1. $\mathbf{B} = \nabla \Phi$ 2. $\mathbf{B} = \nabla \times \Phi$ 3. $\mathbf{B} = \nabla \cdot \mathbf{A}$ 4. $\mathbf{B} = \nabla \times \mathbf{A}$ 5. Something else?! Note: * CORRECT ANSWER: D