(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have a question about an upper-division E&M HW

problem I'm stuck on. Any help would be GREATLY APPRECIATED!!!

Problem Statement:

An insulating spherical shell of radius R was set up to have a potential

on its surface of V=A*cos^2(theta), where A is a constant. The potential

at a distance very far away from the shell is defined to be zero.

(a) Find the potential V(r,theta) both inside and outside the shell.

2. Relevant equations

E=-(grad)V

3. The attempt at a solution

Since E=-(grad)V , I took the gradient in spherical coordinates of the V expression above

and got

E={[(2*A)/R]cos(theta)sin(theta)}theta-hat

for the E field on the surface of the shell. I then let R become the

variable r and tried to do the line integral from "infinity" to R

to get the potential outside the shell. But this involves a dot product with dr

which is orthogonal to theta-hat so I got ZERO!! which certainly

doesn't make sense...I would REALLY appreciate any advice someone might have on

this problem!!!

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# Homework Help: Insulating Spherical Shell Potential Problem question

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