A VERY thin slab of thickness $d$ and area $A$ has volume charge density $\rho = Q / V$. Because it's so thin, we may think of it as a surface charge density $\sigma = Q / A$. <img src="./images/thin_slab_polarization.png" align="center" style="width: 400px";/> The relation between $\rho$ and $\sigma$ is: 1. $\sigma = \rho$ 2. $\sigma = \rho d$ 3. $\sigma = \rho/d$ 4. $\sigma = V \rho$ 5. $\sigma = \rho/V$ Note: * CORRECT ANSWER: B

Are $\rho_b$ and $\sigma_b$ due to real charges? 1. Of course not! They are as fictitious as it gets! 2. Of course they are! They are as real as it gets! 3. I have no idea Note: * CORRECT ANSWER: B

A dielectric slab (top area $A$, height $h$) has been polarized, with $\mathbf{P}=P_0$ in the $+z$ direction. What is the surface charge density, $\sigma_b$, on the bottom surface? <img src="./images/slab_p0_polarization.png" align="right" style="width: 400px";/> 1. 0 2. $-P_0$ 3. $P_0$ 4. $P_0 A h$ 5. $P_0 A$ Note: * CORRECT ANSWER: B

A dielectric sphere is uniformly polarized, $$\mathbf{P} = +P_0\hat{z}$$ What is the surface charge density? <img src="./images/sphere_p0_dielectric.png" align="right" style="width: 300px";/> 1. 0 2. Non-zero Constant 3. constant*$\sin \theta$ 4. constant*$\cos \theta$ 5. ?? Note: * CORRECT ANSWER: D

A dielectric sphere is uniformly polarized, $$\mathbf{P} = +P_0\hat{z}$$ What is the volume charge density? <img src="./images/sphere_p0_dielectric.png" align="right" style="width: 300px";/> 1. 0 2. Non-zero Constant 3. Depends on $r$, but not $\theta$ 4. Depends on $\theta$, but not $r$ 5. ? Note: * CORRECT ANSWER: A