In the interior of a metal in static equilibrium the charge density $\rho$ is:
1. zero always.
2. never zero.
3. sometimes zero, sometime non-zero, depending on the conditions.
Note:
* Correct Answer: A
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* Last 20 minutes of class
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* Solve a Gauss' Law Problem with cylindrical symmetry
* Sketch a graph of the resulting electric field
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Which of the following is a correct statement of charge conservation?
1. $\frac{dQ_{enc}}{dt} = -\int \mathbf{J}\cdot d\mathbf{l}$
2. $\frac{dQ_{enc}}{dt} = -\int \mathbf{J}\cdot d\mathbf{A}$
3. $\frac{dQ_{enc}}{dt} = -\int \nabla \cdot \mathbf{J}\,d\tau$
4. $\frac{dQ_{enc}}{dt} = -\nabla \cdot \mathbf{J}$
5. None of these or *more* than one of these
Note:
* Correct Answer: E (it's B and C; connected by divergence theorem)
For everyday currents in home electronics and wires, which answer is the order of magnitude of the instantaneous speed of the electrons in the wire?
1. more than km/s
2. m/s
3. mm/s
4. $\mu$m/s
5. nm/s
Note:
* Correct Answer: A - using kT = 1/40 eV
An electric current $I$ flows along a copper wire (low resistivity) into a resistor made of carbon (high resistivity) then back into another copper wire. In which material is the electric field largest?
<img src="./images/simple_resistor.png" align="center" style="width: 600px";/>
1. In the copper wire
2. In the carbon resistor
3. It's the same in both copper and carbon
4. It depends on the sizes of the copper and carbon
Note:
* Correct Answer: D, normally B, but it will depend on the relative sizes (if the wire gets really small!)
**Activity**: A copper cylinder is machined to have the following shape. The ends are connected to a battery so that a current flows through the copper.
<img src="./images/machined_copper.png" align="center" style="width: 500px";/>
Rank order (from greatest to smallest, e.g. A=C>B)
Magnitude of E field, Conductivity, Current, & Current Density
Inside this resistor setup, (real world, finite sizes!) What does the E field look like inside ?
<img src="./images/simple_resistor_2.png" align="center" style="width: 600px";/>
1. Must be uniform and horizontal
2. Must have some nonuniformity, due to fringing effects!