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Electric potential at the center of a insulating sphere

  1. Mar 24, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider a uniformly charged insulating sphere with radius R and total charge Q in- side the sphere.

    If Q = 2.9 × 10−6 C, what is the magnitude of the electric field at r=R/2 K=columbs constant. The answer to this question is E=(K)(Q) / (2)*(R)^(2)

    The second part of the question which I am having trouble with is...

    If the sphere has a radius of 3.3 m, find the potential at r = 0. The Coulomb constant is 8.98764 × 109 N · m2/C2 . Follow the convention that the electric potential at r = ∞ is zero. answer in units of V

    2. Relevant equations
    Q=2.9E-6 C
    r=3.3m
    k=8.98764E9 N*m^2 / C^2


    3. The attempt at a solution

    So I have set up the problem as two integrals

    that are shown in the picture. I thought that this would give me the electric potential at r=0 however i am still getting it incorrect. Im not sure what I am doing wrong any help would be appreciated.
    Thank you,
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Mar 24, 2013 #2
    Have you tried using the fact that the potential inside a spherical shell is constant and is equal to the potential on its surface?
     
  4. Mar 24, 2013 #3

    I understood that concept but i guess because this was a two part problem i was trying to incorporate an integral that would relate to the first part of the problem, so no i really didnt...

    ..in that case the electric potential on the surface would be = (K)*(Q) / (R) Correct?

    where R is the radius of the sphere and R=3.3 m
     
  5. Mar 24, 2013 #4
    no this is incorrect, so looking back at my integral, i am more sure that my set up was correct, in the orignal post w/ picture. the question now i believe is the sign (-) or (+)???
     
  6. Mar 24, 2013 #5
    The second part can be solved by assuming the sphere to be made of thin concentric spherical shell of uniform charge densities. Every shell contributes a potential equal to that on it's surface. The solution is simply obtained by integrating the potentials. Note that Q is evenly distributed throughout the sphere and hence it helps to assign a constant as charge density and then use it.
     
    Last edited: Mar 24, 2013
  7. Mar 24, 2013 #6
    okay, thank you for the reply i greatly appreciate it.

    using the integrals i set up, after simplifying the two i obtain -((3)*(k)*(Q) / (2)*(R)) which is a similar formula i just found a min ago however there formula did not have a negative sign. so why when my method is correct, do i come up with a negative sign assuming that the integral sums up the shells.
     
  8. Mar 24, 2013 #7
    I'm a bit confused about how you got your limits of integration. Would you mind explaining? What is the final answer to this problem, by the way?
     
  9. Mar 24, 2013 #8

    well i set them up incorrectly that is why i kept coming up with a negative answer. see picture for how i switched them. the worked integral is in the first attached picture however the answer should be positive.
     
    Last edited: Mar 24, 2013
  10. Mar 24, 2013 #9
    Is the answer 3Q/8πεR? If correct I'll explain my method, else I'll check what I've done wrong and later suggest a solution.
     
  11. Mar 24, 2013 #10
    sorry i forgot the picture.
     

    Attached Files:

  12. Mar 24, 2013 #11
    yes, i get the same answer from your (simplified) solution and the same from the two integrals i set up however my problem was i did not set up the limits of integration correctly hence the negative sign.

    thank you for your help
     
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