Problem 3.70

When an uncharged conducting ball of radius \(R\) is placed in an external uniform electric field, a surface charge density \(\sigma\) \(=\sigma_{0} \cos \theta\) is induced on the ball's surface (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.