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Electric potential

  1. Feb 24, 2005 #1
    A rod of length L lies along the x axis with its left end at the origin and has a nonuniform charge density @ = &x. What is the electic potential a distance d from the origin?

    V = k int dQ/x where:

    dQ = &x dx so:

    V = k& int (x/x+d)dx from (0 to L)
    I let u = x+d and x = u-d
    so:
    V = k& int (1 - d/u)du = (x+d) - dln(x+d) (0 to L)
    and I get: V = k&[L + dln(1 + d/L)]

    in the book the answer is: k&[L - dln(1 + L/d)]

    what am I doing wrong?
     
  2. jcsd
  3. Feb 24, 2005 #2
    look very carefully:

    + dln(1 + d/L) [your solution] = - dln(1 + L/d) [book's solution]

    by the properties of logarithms.
     
  4. Feb 24, 2005 #3
    I know the properties of logarithms, but look:

    (x+d) - dln(x+d) from (0 to L)

    [(L+d) - dln(L+d)] - [d - dln(d)] = [L - dln(L+d) + dln(d)] = L + dln(d/L+d): so somewhere I must be making a mistake with the signs, but where?
     
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