What do y'all want to learn about after this week?
1. Potential theory and gauge (Ch. 10)
2. Accelerated charges and radiation (Ch. 11)
3. Special relativity (Ch. 12)
An EM wave passes from air to metal, what does **your intution** say happens to the wave in the metal?
1. It will be amplified because of free electrons
2. It will die out over some distance
3. It will be blocked right at the interface because there's no E field in a metal
4. Not sure
An EM wave passes from air to metal, which do you think is **most likely** the physics will give us?
1. It will be amplified because of free electrons
2. It will die out over some distance
3. It will be blocked right at the interface because there's no E field in a metal
4. Not sure
Suppose I stick some charge $\rho_f$ down somewhere in a metal (with conductivity $\sigma$). What does $\rho(t)$ look like if we can invoke Ohm's law ($\mathbf{J} = \sigma \mathbf{E}$)? *Hint: Think about charge conservation.*
1. $\rho(t) = \rho_f \sin(\sigma t/\varepsilon_0)$
2. $\rho(t) = \rho_f \cos(\sigma t/\varepsilon_0)$
3. $\rho(t) = \rho_f e^{-\sigma t/\varepsilon_0}$
4. $\rho(t) = \rho_f e^{-\varepsilon_0 t/\sigma}$
5. Something else
Note:
* Correct Answer: C
Consider a good conductor ($\sigma \sim 10^8$ S/m), how long roughly does it take for free charge to dissipate ($t \sim \varepsilon_0/\sigma$)?
1. 10$^{-19}$s
2. 10$^{-12}$s
3. 10$^{-8}$s
4. 10$^{12}$s
5. Something else
Note:
* Correct Answer: A
Given our estimates of collision times (10$^{-14}$s), for what kinds of light is our analysis not so great for?
1. X-Rays ($\sim 10^{18}$ Hz)
2. Visible light ($\sim 10^{15}$ Hz)
3. IR ($\sim 10^{13}$ Hz)
4. Radio ($\sim 10^{8}$ Hz)
5. More than one of these
Note:
* Correct Answer: E (it's A and B)
What does this ansatz attempt (i.e., using $\sim e^{(kz-i\omega t)}$) remind you for this?
1. Solving the simple harmonic oscillator
2. Solving the damped harmonic oscillator
3. Solving the driven harmonic oscillator
4. Some other set up
Note:
* Correct Answer: is likely B
With the proposed solution, $\widetilde{\mathbf{E}} = \widetilde{\mathbf{E}}_0 e^{i(kz-\omega t)}$, what equation does $k$ satisfy?
Think about the wave equation: $\nabla^2 \mathbf{E} = \mu \sigma \dfrac{\partial \mathbf{E}}{\partial t}+\mu \varepsilon \dfrac{\partial^2 \mathbf{E}}{\partial t^2}$
1. $k^2 = i \omega \mu \sigma + \omega^2 \sigma \varepsilon$
2. $k^2 = \omega \mu \sigma + i \omega^2 \sigma \varepsilon$
3. $k = \omega \mu \sigma + i \omega^2 \sigma \varepsilon$
4. $k = i \omega \mu \sigma + \omega^2 \sigma \varepsilon$
5. Something else
Note:
* Correct Answer: A
What is the $\sqrt{i}$?
1. -$i$
2. $\frac{1+i}{\sqrt{2}}$
3. -1
4. $e^{i\pi/4}$
5. None or more than one of these
Note:
* Correct Answer: E (B and D)