Recall the machined copper from last class, with steady current flowing left to right through it
<img src="./images/machined_copper_2.png" align="center" style="width: 600px";/>
In steady state, do you expect there will be any surface charge accumulated anywhere on the walls of the conductor?
1. Yes
2. No
Note:
* Correct Answer: A
$\mathcal{E} = \oint \mathbf{E} \cdot d\mathbf{l}$
EMF ($\mathcal{E}$) is the line integral of the total force per unit charge around a closed loop.
The units of EMF are:
1. Farads
2. Joules
3. Amps, (that’s why current flows.)
4. Newtons, (that’s why it’s called emf)
5. Something else
Note:
* Correct Answer: E; J/C = V
Imagine a charge $q$ able to move around a tube which makes a closed loop. If we want to drive the charge around the loop, we **cannot** do this with E-field from a single stationary charge.
<img src="./images/loop_with_charge.png" align="right" style="width: 400px";/>
Can we drive the charge around the loop with some combination of stationary + and – charges?
1. Yes
2. No
Note:
* Correct Answer: B
Consider a pure electrostatic electric field $\mathbf{E}_{es}$; in this case, the curl of the field vanishes (as we have seen before).
$$\nabla \times \mathbf{E}_{es} = 0$$
What is the $EMF$ associated with such a field over a closed loop?
$$\oint \mathbf{E}_{es} \cdot d\mathbf{l} = ??$$
1. Non-zero
2. Zero
2. Positive
4. Negative
Note:
* Correct Answer: B
A circuit with a battery with voltage difference $\Delta V$ is attached to a resistor. The force per charge due to the charges is $\mathbf{E}$. The force per charge inside the battery is $\mathbf{f} = \mathbf{f}_{bat} + \mathbf{E}$.
How many of the following statements are true?
<img src="./images/latex-image-1.png" align="center" style="width: 600px";/>
<img src="./images/latex-image-2.png" align="center" style="width: 600px";/>
A. 0 B. 1 C. 2 D. 3 E. 4
Note:
* Correct Answer: D