Fall 2006 3 Em

A conducting sphere, of radius R, is in an external electric field $E_{ext}=E_{0} \hat{z}$

(a) Find the potential $\phi \left ( r, \theta \right )$ everywhere.

(b) Find the electric field E (in spherical coordinates) just outside the conductor, at r = R.

(c) Suppose that a cut is made at the equator of the conductor (at z = 0). How much force is required to hold the two hemispheres together?

***