When an uncharged conducting ball of radius `R` is placed in an external uniform electric field, a surface charge densityh `sigma = sigma_(0) cos theta` is induced on the ball's surface charge (here `sigma_(0)` is a constant, `theta` is a polar angle). Find the magnitude of the resultant electric force acting on an induced charge of the same sign.

Answer

`vecE=1//3vecksigma_(0)//epsi_(0)` where `veck` is the unit vector of the z-axis with respect to which the angle `theta` is read off. Clearly, the field inside the given
sphere is uniform.