<img src="./images/parallel_currents.png" align="right" style="width: 250px";/> I have two very long, parallel wires each carrying a current $I_1$ and $I_2$, respectively. In which direction is the force on the wire with the current $I_2$? 1. Up 2. Down 3. Right 4. Left 5. Into or out of the page Note: * CORRECT ANSWER: D

What is the magnitude of $\dfrac{d\mathbf{l}\times\hat{\mathfrak{R}}}{\mathfrak{R}^2}$? <img src="./images/ringcurrent_R.png" align="right" style="width: 400px";/> 1. $\frac{dl \sin\phi}{z^2}$ 2. $\frac{dl}{z^2}$ 3. $\frac{dl \sin\phi}{z^2+a^2}$ 4. $\frac{dl}{z^2+a^2}$ 5. something else! Note: * CORRECT ANSWER: D

What is $d\mathbf{B}_z$ (the contribution to the vertical component of $\mathbf{B}$ from this $d\mathbf{l}$ segment?) <img src="./images/ringcurrent_R.png" align="right" style="width: 400px";/> 1. $\frac{dl}{z^2+a^2}\frac{a}{\sqrt{z^2+a^2}}$ 1. $\frac{dl}{z^2+a^2}$ 1. $\frac{dl}{z^2+a^2}\frac{z}{\sqrt{z^2+a^2}}$ 1. $\frac{dl \cos \phi}{\sqrt{z^2+a^2}}$ 5. Something else! Note: * CORRECT ANSWER: A

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

Stoke's Theorem says that for a surface $S$ bounded by a perimeter $L$, any vector field $\mathbf{B}$ obeys: <img src="./images/balloon_surface.png" align="right" style="width: 300px";/> $$\int_S (\nabla \times \mathbf{B}) \cdot dA = \oint_L \mathbf{B} \cdot d\mathbf{l}$$ Does Stoke's Theorem apply for any surface $S$ bounded by a perimeter $L$, even this balloon-shaped surface $S$? 1. Yes 2. No 3. Sometimes Note: * CORRECT ANSWER: A

Rank order $\int \mathbf{J} \cdot d\mathbf{A}$ (over blue surfaces) where $\mathbf{J}$ is uniform, going left to right: <img src="./images/current_surfaces.png" align="center" style="width: 600px";/> 1. iii > iv > ii > i 2. iii > i > ii > iv 3. i > ii > iii > iv 4. Something else!! 5. Not enough info given!! Note: * CORRECT ANSWER: D * They are all the same!