1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Potential difference inside a spherical shell

  1. Oct 4, 2011 #1
    1. The problem statement, all variables and given/known data

    A top half of a spherical shell has radius R and uniform charge density sigma. Find the potential difference V(b)-V(a) between point b at the north pole, and point a at the center of the sphere.

    2. Relevant equations

    3. The attempt at a solution

    [itex]\oint E ds = \frac{\int \sigma ds}{\epsilon_{0}}[/itex]

    I integrated sigma ds from 0 to 2pi and 0 to pi/2, and got the total surface area as 2pi r^2. Now I want to solve for E, and then use [itex]-\int E dl[/itex] to give me the potential difference, but what does the left hand side of my original equation equal?

    E is uniform along the surface, so I can pull it out of the integral and be left with the integral of ds. But wouldnt that be 2pir^2 as well? I'd be left with E=sigma/epsilon0
  2. jcsd
  3. Oct 5, 2011 #2
    Would it be easier to integrate the potential directly?

    V(r) = C * ∫ σ(r')*da'/[r - r']
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook