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Homework Help: Electromagnetism, force between dipole and grounded plane

  1. Apr 8, 2008 #1
    1. The problem statement, all variables and given/known data

    An electric dipole is located at a certain distance from a grounded plane. What force does the dipole exert on the plane?

    (The answer is to be expressed as an equation. No data were given, only the above text)

    2. Relevant equations

    I am not sure about this, but the course is about "classical" electromagnetism. I would suspect that coulombs law should be used since the question is about the force between charged particles/objects.

    [tex]F = \frac{Q_{1}Q_{2}}{4 \pi \epsilon_{0} r^{2}}[/tex]

    3. The attempt at a solution

    At first I just thought that the grounded plane would have no net charge and thus the dipole and plane could not affect eachother. I now know that this is isn't true but I'm not sure why. A coursemate told me that the dipole should be treated as two point charges and that they would have equal but opposite charges (mirrored) in the grounded plane. Unfortunately I didn't get the chance to ask him further questions.

    Thankful for help
    Last edited: Apr 8, 2008
  2. jcsd
  3. Apr 8, 2008 #2
    If M1=Qd is the dipole moment (Q :charge, d:separation as a vector) the potential field is
    V(r)=1/(4*pi*e) M1.grad(1/r)
    Having a ground plane, this can be eliminated if you consider an image dipole (symmetrically placed under the ground plane). of moment M2=-M1.
    Then the interaction energy will be of the order
    W=M1*M2/(4 pi eps r^3)*(angle factor)
    where r is the distance between the two dipoles.
    The radial force will be
    F=-dW/dr=3m1m2/(4 pi eps r^4)*(angle factor)
    For the angle factor look at classic SMYTHE-Static&DynamicElectricity- McGraw 1968, p.7
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