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Deriving Electric Field from Voltage

  1. Feb 29, 2008 #1
    This is probably more Calculus than it is physics. The voltage at a point X produced by a uniformly charged rod is V = (Ke*Q/l)*[ln(l+sqr(l^2+a^2))-ln(a)], in which point X is right above the left end of the rod by a distance a, l is the rod's length, Q is the charge of the rod, and Ke as the constant (sqr( ) refers to square root and ln is natural log).

    X(point X a distance a from the left end of the rod, in which a is constant)

    __________________ (uniformly charged rod)

    I'm supposed to find the y-component of the Electric Field at X, in which I would just find the negative partial derivative of V in respect to y. Would that imply that I derive in respect to a? I've actually tried quite a number of derivations, but they always end up in something lengthy. The answer is Ey = Ke*Q/[a*sqr(l^2+a^2)].
  2. jcsd
  3. Mar 1, 2008 #2

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    You are correct and so is the final answer. Try it once more. Remember, you have to differentiate wrt 'a' only. (There's a factor (l + sqrt(l^2+a^2) which cancels out.)
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