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

## Announcements * Exam 2 (Wednesday, November 6th 7-9pm) * Covers through Homework 9 (solutions posted after class) * "Comprehensive" exam (need to remember old stuff) * 1 sheet of your own notes; old exam and formula sheet will be posted

## What's on Exam 2? * Using Legendre polynomials and separation of variables in spherical coordinates, solve for the potential and distribution of charge in a boundary value problem * Using the multipole expansion, find the approximate form of the potential for a distribution of charge * Determine the bound charge in a material with a given polarization * Find the electric potential for a 1D Laplace problem * (BONUS) Solve a 3D Laplace problem

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

If you put a polarizable material (a dielectric) in an external field $\mathbf{E}_e$, it polarizes, adding a new field, $\mathbf{E}_p$ (from the bound charges). These superpose, making a total field, $\mathbf{E}_T$. What is the vector equation relating these three fields? 1. $\mathbf{E}_T + \mathbf{E}_e + \mathbf{E}_p = 0$ 2. $\mathbf{E}_T = \mathbf{E}_e - \mathbf{E}_p$ 3. $\mathbf{E}_T = \mathbf{E}_e + \mathbf{E}_p$ 4. $\mathbf{E}_T = -\mathbf{E}_e + \mathbf{E}_p$ 5. Something else Note: * CORRECT ANSWER: C