[UPSC CSE 2008] Electrostatics and Magnetostatics (Q184, 20M)

State Gauss's Law of electrostatics both in integral form and differential forms. Two charged spheres of radius R each, have their centres a distance d apart such that d < 2R. One of the spheres has a uniform positive charge density \rho per unit volume while the other has opposite charge density -\rho. Show that the electric field in the region of overlap between two spheres is uniform.