<img src="./images/long_wire_A.png" align="right" style="width: 200px";/>
The vector potential A due to a long straight wire with current I along the z-axis is in the direction parallel to:
1. $\hat{z}$
2. $\hat{\phi}$ (azimuthal)
3. $\hat{s}$ (radial)
*Assume the Coulomb Gauge*
Note:
* CORRECT ANSWER: A
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Consider a fat wire with radius $a$ with uniform current $I_0$ that runs along the $+z$-axis. We can compute the vector potential due to this wire directly. What is $\mathbf{J}$?
1. $I_0/(2 \pi)$
2. $I_0/(\pi a^2)$
1. $I_0/(2 \pi a) \hat{z}$
4. $I_0/(\pi a^2) \hat{z}$
5. Something else!?
Note:
* CORRECT ANSWER: D
Consider a fat wire with radius $a$ with uniform current $I_0$ that runs along the $+z$-axis.
Given $\mathbf{A}(\mathbf{r}) = \dfrac{\mu_0}{4\pi}\int \dfrac{\mathbf{J}(\mathbf{r}')}{\mathfrak{R}}d\tau'$, which components of $\mathbf{A}$ need to be computed?
1. All of them
2. Just $A_x$
3. Just $A_y$
4. Just $A_z$
5. Some combination
Note:
* CORRECT ANSWER: D
Consider line of charge with uniform charge density, $\lambda = \rho \pi a^2$. What is the magnitude of the electric field outside of the line charge (at a distance $s>a$)?
1. $E = \lambda/(4 \pi \varepsilon_0 s^2)$
2. $E = \lambda/(2 \pi \varepsilon_0 s^2)$
3. $E = \lambda/(4 \pi \varepsilon_0 s)$
4. $E = \lambda/(2 \pi \varepsilon_0 s)$
5. Something else?!
*Use Gauss' Law*
Note:
* CORRECT ANSWER: D
Consider a shell of charge with surface charge $\sigma$ that is rotating at angular frequency of $\mathbf{\omega}$. Which of the expressions below describe the surface current, $\mathbf{K}$, that is observed in the fixed frame.
1. $\sigma\,\mathbf{\omega}$
2. $\sigma\,\mathbf{\dot{r}}$
3. $\sigma\,\mathbf{r} \times \mathbf{\mathbf{\omega}}$
4. $\sigma\,\mathbf{\mathbf{\omega}} \times \mathbf{r}$
5. Something else?
Note:
* CORRECT ANSWER: D