Consider two spheres of the same radius R having uniformly distributed volume charge density of same magnitude but opposite sign `(+rho` and `-rho)` the spheres overlap such that the vector joining the centre of the negative sphere to that of the positive sphere is `vecd`. `(d lt lt R)`. Find magnitude of electric field at a point outside the spheres at a distance r in a direction making an angle `theta` with `vecd`. Distance r is measure with respect to the mid point of the line joining the centers of the two spheres.

Answer

`(rhoR^(3)d)/(3epsi_(0)r^(3))sqrt(3cos^(2)theta+1)`