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• Homework 2 solutions posted
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For me, the second homework was ...

1. fairly straight-forward; lower difficulty than I expected.
2. challenging, but at the level of difficulty I expected
3. a bit more difficult than I expected, but still manageable
4. much more difficult than I expected.

I spent ... hours on the second homework.

1. 1-4
2. 5-6
3. 7-8
4. 9-10
5. More than 10

Electric Potential

Which of the following two fields has zero curl?

I	II

1. Both do.
2. Only I is zero
3. Only II is zero
4. Neither is zero
5. ???

What is the curl of the vector field, $\mathbf{v}= c\hat{\phi}$, in the region shown below?

1. non-zero everywhere
2. zero at some points, non-zero at others
3. zero curl everywhere

What is the curl of this vector field, in the red region shown below?

1. non-zero everywhere in the box
2. non-zero at a limited set of points
3. zero curl everywhere shown
4. we need a formula to decide

What is the curl of this vector field, $\mathbf{v} = \dfrac{c}{s}\hat{\phi}$, in the red region shown below?

1. non-zero everywhere in the box
2. non-zero at a limited set of points
3. zero curl everywhere shown

Is it mathematically ok to do this?

$$\mathbf{E} = \dfrac{1}{4\pi\varepsilon_0}\int_V\rho(\mathbf{r}')d\tau'\left(-\nabla\dfrac{1}{\mathfrak{R}}\right)$$

$$\longrightarrow \mathbf{E} =-\nabla\left( \dfrac{1}{4\pi\varepsilon_0}\int_V\rho(\mathbf{r}')d\tau'\dfrac{1}{\mathfrak{R}}\right)$$

1. Yes
2. No
3. ???

If $\nabla \times \mathbf{E} = 0$, then $\oint_C \mathbf{E} \cdot d\mathbf{l} =$

1. 0
2. something finite
3. $\infty$
4. Can't tell without knowing $C$

Can superposition be applied to electric potential, $V$?

$$V_{tot} \stackrel{?}{=} \sum_i V_i = V_1 +V_2 + V_3 + \dots$$

1. Yes
2. No
3. Sometimes