What is the magnitude of electroctatic force acting on the dipole?

Question

A dipole P=q∆x has been placed inside a copper spherical shell or radius R at a distance a from the center of the shell (a < R). The dipole vector P points in radial direction.

Answer 1

You should be able to use method of images.

The charge-in-a-sphere is a common problem which you should be able to look up.

Hehe, even wiki has it:

http://en.wikipedia.org/wiki/Method_of_i...

The image will be in the same spot (R^2/a) as it would be for a point charge except it will be an inward-facing dipole. The ratio of the dipoles will be the same as the ratio of the charges, so the image dipole is (PR/a).

Then it&#039;s simple to calculate the dipole-dipole force, since they&#039;re all neatly lined up.

Original dipole: P facing out

Image dipole: PR/a facing in

Distance between them: (R^2 - a^2) / a

E (from inner dipole) =

2 k P / (distance between dipoles)^3

F = dE/dr * P

= 6 k P (PR/a) / ( (R^2 - a^2) / a)^4

= 6 k P^2 R a^3 / (R^2 - a^2)^4 (inward)