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