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Force and torque on a dipole placed near a grounded plane

1. A dipole p is placed at a distance x = a from the grounded conducting plane. The direction of p makes 30 degree with the plane. Find

a. The force.
b. The torque on the dipole.

Solution Preview

I assume that the dipole is pointing away from the plane at an angle of 30°. To solve this problem you introduce a fictitious "image" dipole. This dipole is at a distance a on the opposite side of the plane and has the same magnitude |p|. It points at 30° toward the plane such that the component of p along the plane is opposite to the component of the real dipole along the plane. The field of the fictitious image dipole is then the same as the field of the induced charges on the grounded plane.

The force can be calculated from the formula:

F = (p dot nabla) E

Here E is the field of image dipole. Let's introduce spherical coordinates such that the image ...

Solution Summary

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