Consider a single point charge at the origin. It will have ONLY a monopole contribution to the potential at a location $\mathbf{r} = \langle x,y,z\rangle$. As we have seen, if we move the charge to another location (e.g., $\mathbf{r}' = \langle 0,0,d \rangle$), the distribution now has a dipole contribution to the potential at $\mathbf{r}$! What the hell is going on here? 1. It's just how the math works out. Nothing has changed physically at $\mathbf{r}$. 2. There is something different about the field at $\mathbf{r}$ and the potential is showing us that. 3. I'm not sure how to resolve this problem.

## Polarization <img src="./images/diel.gif" align="center" style="width: 400px";/>

<img src="./images/charge_near_block.png" align="right" style="width: 400px";/> A stationary point charge $+Q$ is near a block of polarization material (a linear dielectric). The net electrostatic force on the block due to the point charge is: 1. attractive (to the left) 2. repulsive (to the right) 3. zero Note: * CORRECT ANSWER: A

<img src="./images/sphere_p0_z.png" align="right" style="width: 300px";/> The sphere below (radius $a$) has uniform polarization $\mathbf{P}_0$, which points in the $+z$ direction. What is the total dipole moment of this sphere? 1. zero 2. $\mathbf{P}_0 a^3$ 3. $4\pi a^3 \mathbf{P}_0/3$ 4. $\mathbf{P}_0$ 5. None of these/must be more complicated Note: * CORRECT ANSWER: C

<img src="./images/cube_p0_z.png" align="right" style="width: 300px";/> The cube below (side $a$) has uniform polarization $\mathbf{P}_0$, which points in the $+z$ direction. What is the total dipole moment of this cube? 1. zero 2. $a^3 \mathbf{P}_0$ 3. $\mathbf{P}_0$ 4. $\mathbf{P}_0/a^3$ 5. $2 \mathbf{P}_0 a^2$ Note: * CORRECT ANSWER: B

In the following case, is the bound surface and volume charge zero or nonzero? <img src="./images/mini_dipoles_matter_1.png" align="center" style="width: 400px";/> 1. $\sigma_b = 0, \rho_b \neq 0$ 2. $\sigma_b \neq 0, \rho_b \neq 0$ 3. $\sigma_b = 0, \rho_b=0$ 4. $\sigma_b \neq 0, \rho_b=0$ Note: * CORRECT ANSWER: D

In the following case, is the bound surface and volume charge zero or nonzero? <img src="./images/mini_dipoles_matter_2.png" align="center" style="width: 400px";/> 1. $\sigma_b = 0, \rho_b \neq 0$ 2. $\sigma_b \neq 0, \rho_b \neq 0$ 3. $\sigma_b = 0, \rho_b=0$ 4. $\sigma_b \neq 0, \rho_b=0$ Note: * CORRECT ANSWER: B