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Electromagnetism, force between dipole and grounded plane

  • Thread starter Antti
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Homework Statement



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)

Homework 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]

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
 
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Answers and Replies

  • #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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