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!

Eletric potential inside charged sphere with hole inside

  1. Oct 15, 2013 #1
    1. The problem statement, all variables and given/known data
    Consider a charge density of ρ=k/r , k>0 , located between a sphere surface of r=a and another sphere surface of r=b, b>a.
    I'm supposed to find the electric field on all space, which I did. Now I have to find the electric potential in all space, which I also did for r>b, but I'm having problems finding it for a<r<b and for r<a.

    2. Relevant equations

    These are the electric field equations I came up with:
    r<a : E(r)=0
    r>b: E(r)=(k*(b2-a2))/(ε0*2*r2)
    a<r<b: E(r)=(k*(1-a2/r2))/(2*ε0)

    Electric potential for r>b: V(r)=(b2-a2)/(2ε0*r)

    3. The attempt at a solution

    For finding the EP at r>b I just had to integrate E(r) for r>b with limits between r and ∞ which is equal to V(r)-V(∞) with V(∞)=0, but I cant come up with any solution for the other Epotentials, if someone could give me a hint I would appreciate.


    Attached Files:

  2. jcsd
  3. Oct 15, 2013 #2


    User Avatar
    2017 Award

    Staff: Mentor

    Based on your solution for r>b, what is V(b)?
    Can you calculate the potential between a and b, if you know V(b)? The method is similar to the region r>b.
    r<a is easy once you have the region a<r<b, as there is no field inside.
  4. Oct 15, 2013 #3
    to find V(b) I can use the equation of the potential for r>b right?

    Then to find V(r) for a<r<b:

    V(r)=-∫rbE(r).dr + V(b)

    and then repeat the process to find V(r) for r<a, where there is no field, which means V(r) for r<a = V(r) for a<r<b.

    Last edited: Oct 15, 2013
  5. Oct 15, 2013 #4


    User Avatar
    2017 Award

    Staff: Mentor


    I guess that is a typo here.
  6. Oct 15, 2013 #5
    Ah yes! It should be V(r) = V(a) for r<a.

    That was the hint I needed, thanks!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted