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Homework Help: Del(1/r) = -R/r^2

  1. Jan 5, 2010 #1
    1. The problem statement, all variables and given/known data
    let R be the separation vector from (a,b,c) to (x,y,z) and r be the magnitude of R.
    Show that: del(1/r) = -R/r^2

    2. Relevant equations
    del is the gradient operator

    3. The attempt at a solution
    The problem is that I keep getting a 3/2 power in the denominator when I calculate the left hand side.

    r = sqrt((x-a)^2 + (y-b)^2 + (z-c)^2)

    1/r = ((x-a)^2 + (y-b)^2 + (z-c)^2)^-0.5

    del(1/r) = -R/[(x-a)^2 + (y-b)^2 + (z-c)^2]^(3/2)
    Last edited: Jan 5, 2010
  2. jcsd
  3. Jan 5, 2010 #2
  4. Jan 5, 2010 #3
    I see, you're right. I missed the hat on R in my text. Thanks.
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