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Energy stored by a point charge

  1. Mar 5, 2013 #1
    1. The problem statement, all variables and given/known data
    9uC charge at origin. How much energy does its electric field store outside a sphere centered about the origin with a radius of 5mm?


    2. Relevant equations
    C(sphere)=ab/(k(b-a)) V=kq/r U(cap)=(1/2)CV^2 E=kq/(r^2)
    a=inner radius b=outer radius

    3. The attempt at a solution
    let the outer radius -> infinity, then C=a/k. V is 0 at infinity.
    U=(1/2)CV^2=(1/2)(a/k)(kr/r)^2=(1/2)aqE= 72.9J which is the answer given in the book
    This solution is something I dimly remember seeing but my reasoning is very shaky.
    Why doesn't integrating ((1/2)εE^2)4∏r^2dr from r to infinity work? I get integral=-(1/2)ε(kq)^2(4∏/r) which is not at all the same
     
    Last edited: Mar 5, 2013
  2. jcsd
  3. Mar 5, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    E is the electric field at a radius of a? So ##E=\frac{k q}{ a^2}## and therefore
    $$U=\frac{1}{2}aq \frac{k q}{ a^2} = \frac{1}{2} \frac{k q^2}{a}$$
    Using ##k=\frac{1}{4\pi\epsilon}## in your equation gives the same formula.
     
  4. Mar 5, 2013 #3

    rude man

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    Homework Helper
    Gold Member



    It does! Did you run the numbers & not get the advertised answer?
     
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