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?

<img src="./images/wamps_gre_2.png" align="center" style="width: 800px";/>

$$V(r,\theta) = \sum_{l=0}^{\infty} \left(A_l r^l + \dfrac{B_l}{r^{l+1}}\right)P_l(\cos \theta)$$ Suppose V on a spherical shell is: $$V(R,\theta) = V_0 \left(1+\cos^2\theta\right)$$ Which terms do you expect to appear when finding **V(inside)**? 1. Many $A_l$ terms (but no $B_l$'s) 2. Many $B_l$ terms (but no $A_l$'s) 3. Just $A_0$ and $A_2$ 4. Just $B_0$ and $B_2$ 5. Something else! Note: * CORRECT ANSWER: C * Avoid blowup and match cosine

$$V(r,\theta) = \sum_{l=0}^{\infty} \left(A_l r^l + \dfrac{B_l}{r^{l+1}}\right)P_l(\cos \theta)$$ Suppose V on a spherical shell is: $$V(R,\theta) = V_0 \left(1+\cos^2\theta\right)$$ Which terms do you expect to appear when finding **V(outside)**? 1. Many $A_l$ terms (but no $B_l$'s) 2. Many $B_l$ terms (but no $A_l$'s) 3. Just $A_0$ and $A_2$ 4. Just $B_0$ and $B_2$ 5. Something else! Note: * CORRECT ANSWER: D * Avoid blowup and match cosine