In matter we have,
$$\nabla \cdot \mathbf{D} = \rho_f \qquad \nabla \cdot \mathbf{B} = 0$$
$$\nabla \times \mathbf{E} = -\dfrac{\partial \mathbf{B}}{\partial t} \qquad \nabla \times \mathbf{H} = \mathbf{J}_f + \dfrac{\partial \mathbf{D}}{\partial t}$$
with
$$\mathbf{D} = \varepsilon_0 \mathbf{E} + \mathbf{P} \qquad \mathbf{H} = \mathbf{B}/\mu_0 - \mathbf{M}$$
If there are no free charges or current, is $\nabla \cdot \mathbf{E} = 0$?
1. Yes, always
2. Yes, under certain conditions (what are they?)
3. No, in general this will not be true
4. ??
Note:
* Correct answer: B
In linear dielectrics, $\mathbf{D} = \varepsilon_0\mathbf{E} + \mathbf{P} = \varepsilon \mathbf{E}.$ In a linear dielectric is $\varepsilon > \varepsilon_0$?
1. Yes, always
2. No, never
3. Sometimes, it depends on the details of the dielectric.
Note:
* Correct answer: A
In a non-magnetic, linear dielectric,
$$v = \dfrac{1}{\sqrt{\mu \varepsilon}} = \dfrac{1}{\sqrt{\mu \varepsilon_r \varepsilon_0}} = \dfrac{c}{\sqrt{\varepsilon_r}}$$
How does $v$ compare to $c$?
1. $v>c$ always
2. $v<c$ always
3. It depends
Note:
* Correct Answer: B
A light rope (small $m/L$) is fused to a heavy rope (large $m/L$). If I wiggle the **light** rope,
1. most of the wiggles are reflected back; very few wiggles transmit through the heavy rope
2. some of the wiggles are reflected back; some of the wiggles transmit through the heavy rope
3. very few of the wiggles are reflected back; most of the wiggles transmit through the heavy rope
4. ???
Note:
* Correct answer: A
A light rope (small $m/L$) is fused to a heavy rope (large $m/L$). If I wiggle the **heavy** rope,
1. most of the wiggles are reflected back; very few wiggles transmit through the light rope
2. some of the wiggles are reflected back; some of the wiggles transmit through the light rope
3. very few of the wiggles are reflected back; most of the wiggles transmit through the light rope
4. ???
Note:
* Correct answer: B/C
How do the speed of the waves compare in the light rope ($v_l$) and heavy rope ($v_H$)?
1. $v_l < v_H$
2. $v_l = v_H$
3. $v_l > v_H$
Note:
* Correct Answer: C