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Work required to move charge

  1. May 18, 2009 #1
    1. The problem statement, all variables and given/known data

    situation:
    there are two charges (+q) one at one corner of an equilateral triangle the other at another corner. the triangle has sides length a.

    what is the work required to bring another charge (+q) in from infinity to the other corner on the equilateral triangle.


    3. The attempt at a solution

    ok so i know dW = -dU = F.dl

    i thought that maybe finding (F) at the corner that we are bringing the charge to may help...this is:
    Fc [at corner] = q2 / 2*pi*epsilon*a2

    then i could just integrate this over the distance i am moving it with respect to a...however i know that the one limit will be [tex]\infty[/tex] however i dont know what the other will be

    thanks for any help
     
    Last edited: May 18, 2009
  2. jcsd
  3. May 18, 2009 #2

    LowlyPion

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    Consider the Voltage at the point from each of the 2 other charges.

    V = k*q / r

    Since work = q*ΔV

    and V = 0

    Then

    Work = q*ΣV
     
  4. May 18, 2009 #3
    ok so
    the E at the point is 2q / 4*pi*epsilon*a2
    the V at the point is 2q / 4*pi*epsilon*a

    so work to bring in point is = q(2q / 4*pi*epsilon*a) = q2 / 2*pi*epsilon*a
     
  5. May 18, 2009 #4

    LowlyPion

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    Looks like it.

    Though E is a vector, don't forget, and V is a scalar here. In your first equation then the E would need to be added as vectors. Whereas for V you are adding scalars.

    http://hyperphysics.phy-astr.gsu.edu/hbase/electric/mulpoi.html#c1
     
  6. May 18, 2009 #5
    ok thanks...:biggrin:
     
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