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Electric Potential of three concentric spheres

  1. Mar 25, 2012 #1
    Hey, i have a conceptual doubt.

    Suppose there are three concentric conducting spheres A,B,C having radius a,b,c (a<b<c).

    We put charge q1, q2 and q3 on these three surfaces A,B,C respectively.

    Now using gauss law, we can prove that

    Charge on inner surface of A is 0

    Charge on outer surface of A is q1.

    Charge on inner surface of B is -q1

    Charge on outer surface of B is q2+q1

    Charge on inner surface of C is -q2-q1

    Charge on outer surface of C is q1+q2+q3.


    Now this is because electric field and therefore flux inside a conductor should be 0.

    Now my text book asks me to find the Potential at A and B (considering potential at infinity is 0)

    Now what I wanted to do is that since the field inside the conductor is 0 everywhere, the potential should be constant everywhere inside and therefore be equal to the potential at surface C
    which is
    k(q1+q2+q3)/c.
    So this should be potential at A and B

    However in the answer the potential at B is given as

    k[q1/b +q2/b+q3/c]

    And at A is given as k(q1/a+q2/b+q3/c).

    i.e they have now considered the three sphere alone in calculating potential.

    Is the text books solution right?

    Where am I going wrong?


    If the text book's solution is right, then isn't the potential not constant inside the sphere C, implying a non-zero electric field
     
  2. jcsd
  3. Mar 25, 2012 #2

    SammyS

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    The difficulty comes from what is meant by the word "inside". Inside refers to a location within the conducting material itself. It does not refer to every point interior to the outer surface of the sphere or spheres.

    I assume that these conducting spheres are spherical shells which have a very small thickness, a thickness so small that it may be ignored when compared to the radius of each spherical shell. However, to be a physically feasible problem, the spheres must truly have a finite thickness.
     
  4. Mar 25, 2012 #3
    No.The figure clearly shows these are three concentric solid conducting spheres.(not shells). That is all three are virtually in contact.

    I in fact fail to get why there would be any charge on sphere A and B.It should all move to the surface C and reside there.

    However, those are the exact lines stated in my book.

    I think it's wrong.
     
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