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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.

    Thanks!
     

    Attached Files:

  2. jcsd
  3. Oct 15, 2013 #2

    mfb

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    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.

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

    mfb

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    Sure.

    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!
     
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