Electromagnetism, force between dipole and grounded plane

[Antti]

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.

F = \frac{Q_{1}Q_{2}}{4 \pi \epsilon_{0} r^{2}}

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 each other. 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

 

[Roberto Bramb]

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