Maximum potential (coaxial cable)

  1. 1. The problem statement, all variables and given/known data
    Given a coaxial cable with outer conductor of radius b, and inner conductor of radius a. Prove that maximum potential is obtained when a = b /e, e is base of natural log.

    2. Relevant equations
    gauss law, ...


    3. The attempt at a solution
    By using Gauss Law,
    for a < r < b,
    i have E = 2*k*[tex]\lambda[/tex] / r, where [tex]\lambda[/tex] = Q/L

    then the potential difference, V= [tex]\int[/tex] E dr
    V = 2*k*[tex]\lambda[/tex] ln (b/a),

    but i am not sure how to continue by differentiating V wrt a.
    Help me pls...
    Thank you.
     
    Last edited: Mar 23, 2011
  2. jcsd
  3. Anyone pls help ......
     
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