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: Finding the potential outside a charge sphere

  1. Oct 26, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the potential outside a charged metal sphere(charge Q , radius R) placed in an otherwise uniform electric Field E0. Explain clearly where you are setting the zero of potential .

    2. Relevant equations

    3. The attempt at a solution

    At the boundaries of the sphere V=0. Since a sphere is a 3 dimensional object,





    wouldn't I be setting the potential to zero because the sphere might be an equipotential?

    Wait a minute , in the exterior region, wouldn't V(r,theta)=kR^3*cos(theta)/3epilison0*r^2
    Last edited: Oct 26, 2008
  2. jcsd
  3. Oct 26, 2008 #2


    User Avatar
    Homework Helper
    Gold Member

    The potential on the surface of the sphere certainly will be an epuipotential; and you could set it to zero if you choose to; however in this case the problem is much easier if you don't.

    Have you seen the solution for an uncharged metal sphere in a uniform electric field? What is the solution for that problem and where did they set the potential to zero?

    If you choose a clever spot to set the potential to zero in this problem, you can use the superposition principle with the solution for the uncharged sphere and a uniformly charged spherical shell of charge Q.
  4. Oct 26, 2008 #3
    Couldn't I set the potential to be zero at the boundary condition? Maybe at the edge of the sphere. Since the shape is the surface of a sphere, it wouldn't matter where I would set my boundary condition at the edge of the spheres?

    Outside a sphere V(r,theta)= (R^3/r^2)*cos(theta)

    Law of superposition principle :

    V=V(outside)+V(inside) ?

    I don't know the solution for a uniformly uncharged sphere. Why is the solution of a uncharged sphere relevant since I am asked to find the solution for a uniformily charged sphere?
  5. Oct 26, 2008 #4


    User Avatar
    Homework Helper
    Gold Member

    Start with the solution for the uncharged sphere in an uniform electric field... What is that solution? What are the boundary conditions for that problem?
  6. Oct 19, 2010 #5
    help anyone?

    I was wondering if we should simply add kQ/r to the potential given for the uncharged sphere or if there was a way to obtain this result more formally.
  7. Oct 20, 2010 #6


    User Avatar
    Homework Helper
    Gold Member

    Does your total potential satsify Laplace's equation then? Does it satsify the correct Boundary conditions? What does the uniqueness theorem tell you about that solution?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook