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Constant electric field in the sphere

  1. Mar 9, 2014 #1
    1. The problem statement, all variables and given/known data

    The region between two concentric spheres of radii a and b(>a) contains volume charge density ρ(r) = C / r where C is a constant and r is the radial distance, as shown in figure. A point charge q is placed at the origin, r= 0. Find the value of C for which the electric field in the region between the spheres is constant (i.e., r independent).

    A) q/πa2
    B) q/π(a2+b2)
    C) q/2πa2
    D) q/2πb2

    2. Relevant equations

    ε∫E.dS = qfree

    3. The attempt at a solution

    Let us consider a a gaussian surface, a concentric sphere at radius r .

    Applying Gauss law

    ε∫E.dS = q + 4πC(r2-a2)

    εE(4πr2) = q + 4πC(r2-a2)

    E = q/(4πr2ε) + C(r2-a2)/(εr2)

    Now for E to be constant ,

    q-4πca2 = 0 or C=q/(4πa2) .This is not given as one of the options .

    I would be grateful if somebody could help me with the problem.
     

    Attached Files:

  2. jcsd
  3. Mar 9, 2014 #2

    SammyS

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    You have not integrated the charge correctly.
     
  4. Mar 9, 2014 #3
    Hi SammyS...

    Yes.I missed a factor of 2 while integrating .

    Does that mean option C) i.e C=q/2πa2 is the correct answer ?
     
  5. Mar 9, 2014 #4

    SammyS

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    That's what I got .
     
  6. Mar 9, 2014 #5
    Thank you very much :smile:
     
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