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

What is the magnitude of $\dfrac{d\mathbf{l}\times\hat{\mathfrak{R}}}{\mathfrak{R}^2}$?

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!

What is $d\mathbf{B}_z$ (the contribution to the vertical component of $\mathbf{B}$ from this $d\mathbf{l}$ segment?)

1. $\frac{dl}{z^2+a^2}\frac{a}{\sqrt{z^2+a^2}}$
2. $\frac{dl}{z^2+a^2}$
3. $\frac{dl}{z^2+a^2}\frac{z}{\sqrt{z^2+a^2}}$
4. $\frac{dl \cos \phi}{\sqrt{z^2+a^2}}$
5. Something else!

What is $\oint \mathbf{B}\cdot d\mathbf{l}$ around this purple (dashed) Amperian loop?

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. $\mu_0 (| I_2 | + | I_1 | \cos\theta)$

Stoke's Theorem says that for a surface $S$ bounded by a perimeter $L$, any vector field $\mathbf{B}$ obeys:

$$\int_S (\nabla \times \mathbf{B}) \cdot dA = \oint_L \mathbf{B} \cdot d\mathbf{l}$$

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

Rank order $\int \mathbf{J} \cdot d\mathbf{A}$ (over blue surfaces) where $\mathbf{J}$ is uniform, going left to right:

1. iii > iv > ii > i
2. iii > i > ii > iv
3. i > ii > iii > iv
4. Something else!!
5. Not enough info given!!

Much like Gauss's Law, Ampere's Law is always true (for magnetostatics), but only useful when there's sufficient symmetry to "pull B out" of the integral.

So we need to build an argument for what $\mathbf{B}$ looks like and what it can depend on.

For the case of an infinitely long wire, can $\mathbf{B}$ point radially (i.e., in the $\hat{s}$ direction)?

1. Yes
2. No
3. ???

Continuing to build an argument for what $\mathbf{B}$ looks like and what it can depend on.

For the case of an infinitely long wire, can $\mathbf{B}$ depend on $z$ or $\phi$?

1. Yes
2. No
3. ???

Finalizing the argument for what $\mathbf{B}$ looks like and what it can depend on.

For the case of an infinitely long wire, can $\mathbf{B}$ have a $\hat{z}$ component?

1. Yes
2. No
3. ???

For the infinite wire, we argued that $\mathbf{B}(\mathbf{r}) = B(s)\hat{\phi}$. For the case of an infinitely long thick wire of radius $a$, is this functional form still correct? Inside and outside the wire?

1. Yes
2. Only inside the wire ($s<a$)
3. Only outside the wire ($s>a$)
4. No