How many boundary conditions (on the potential $V$) do you use to find $V$ inside the spherical plastic shell? <img src="./images/plastic_shell_vtheta.png" align="right" style="width: 350px";/> 1. 1 2. 2 3. 3 4. 4 5. It depends on $V_0(\theta)$ Note: * CORRECT ANSWER: B * Good for discussion; obviously you need the surface BC, but what about at r=0? Is that technically a BC?

## Announcements * Homework 8 has 2D relaxation problem - It is OK to post code on piazza and get help - Solution to HW7 problem 5 (1D relaxation) is linked (you may work from it) * DC out of town Monday; Norman Birge will cover

<img src="./images/dipole_moment.png" align="left" style="width: 300px";/> Two charges are positioned as shown to the left. The relative position vector between them is $\mathbf{d}$. What is the value of of the dipole moment? $\sum_i q_i \mathbf{r}_i$ 1. $+q\mathbf{d}$ 2. $-q\mathbf{d}$ 3. Zero 4. None of these Note: * CORRECT ANSWER: A

## Multipole Expansion <img src="./images/universe_multipole.jpg" align="center" style="width: 300px";/> Multipole Expansion of the Power Spectrum of CMBR Note: The radiation from cosmic microwave background can be described in terms of contributions using a basis of functions with increasing smaller contributions.