1. Not finding help here? Sign up for a free 30min 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!

Problem on Potential of Sphere

  1. Sep 15, 2005 #1

    Could somebody please help me on a problem regarding Potential?

    Calculate the potential inside and outside a sphere of radius R and charge Q,in which the charge is distributed uniformly throughout. [Hine: The additive constant for the potential inside the charged sphere must be chose so that the two potentials inside and outside, agree at r=R]

    So far, I know that V(outside)=Q/(4*PI*e0*r) when r>R.

    How would I find the V(outside) when r<R?
    The answer given in the back of the book is V=[Q/(8*PI*e0*R)][3-(r/R)^2]
    I have no idea how to obtain it.

    Also how would I go about finding the V(inside) for when r>R, and r<R?

    Any help would be greatly appreciated!
  2. jcsd
  3. Sep 15, 2005 #2

    Physics Monkey

    User Avatar
    Science Advisor
    Homework Helper

    You seem to be a bit confused. The potential "outside" refers to r>R while the potential "inside" refers to r<R. Your outside potential looks good. In order to find the inside potential perhaps you should begin by calculating the electric field inside (r<R) ...
  4. Sep 15, 2005 #3


    User Avatar
    Homework Helper

    The potential due to a thin spherical shell inside the shell is same as that on the surface.

    Consider a point P at distance r (< R) from the center of the sphere. The sphere can be considered as a solid sphere of radius r, and a hollow sphere of inner radius r and outer radius R. Potential at point P is due to both.
    1 Due to inner sphere and
    2 due to outer part.

    For first calculate charge and solve as on sphere of radius r.
    For second consider a thin shell of radius x and thickness dx (R > x > r) calculate charge dq on the shell, potential at P due to this charge is dq/4*pi*e0*x
    Integrate this for x = r to x = R
    add the two potentials.

    Hope this much is sufficient.
  5. Sep 15, 2005 #4
    okay so the Electric Field inside is = (Q/4*PI*e0)(r/R^3). to find Potential, what would i do?

    After i find this potential, i add it to the potential outside to get the total?

    Thanks for all the input guys!
  6. Sep 15, 2005 #5
    ah! nevermind. i got it!

    first i had to find the electric field inside and integrate it, since dV=-E ds

    I just integrate it from the interval [R,r] and that gives me the answer!

    Thanks for all the help!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Problem on Potential of Sphere
  1. Sphere problem (Replies: 14)