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