2 point charges with sphere inbetween

[Cairrd]

I am having a little trouble knowing how to approach the following question:

Twi point charges q and -q are placed 2d apart. Show that a conducting sphere of small radius r (where r << 2d) is placed midway between the charges, show the force on each is increased by a factor of approx (1 + 16 (r^3/a^3)).



Anyone want to help me here?

Thanks

 

[TMFKAN64]

Use the method of images on the conducting sphere, and then treat the two images as a dipole when you calculate the total force on one charge due to the other charge and the image charges.

Also, I assume you mean d, not a, in your factor.