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Electric Potential Derivative

  1. Mar 7, 2012 #1
    1. The problem statement, all variables and given/known data The electrical potential can be described by the following equation:
    V= 200/(x2 + y2 )1/2 find dV when x=2 and y=1


    2. Relevant equations
    n/a


    3. The attempt at a solution
    dv/d(x,y) = ∂/∂x + ∂/∂y
    =200/(x2 + y2)(1/2) +200/(x2 + y2)(1/2)
    replace variables with C where necessary and rearrange for easy of deriving =200(x2 + C)(1/2) +200(C + y2)(1/2)
    Chain rule and exponent rule
    =200(-1/2)(2x)(x2 + C)(-3/2) +200(-1/2)(2y)(C + y2)(-3/2)
    =-200x(x2 + C)(-3/2) + -200y)(C + y2)(-3/2)
    =-200x(x2 + y2) )(-3/2) + -200y)(x2+ y2)(-3/2)
    Then I plug in the values x=2 and y=1 and dV=-53.7 V/m, I'm not very confident with multivariable calculus and just wanted to check to see if this is right.
     
    Last edited: Mar 7, 2012
  2. jcsd
  3. Mar 7, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    The result looks okay.
     
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