Two non-conducting solid spheres of radii R and 2 R , having uniform volume charge densities ρ 1 and ρ 2 , respectively, touch each other. The net electric field at a distance 2 R from the centre of the smaller sphere, along the line joining the centres of the spheres, is zero. The ratio ρ 1 ρ 2 can be

Step-by-step solution

Field due to small sphere = K ρ 1 4 3 π R 3 2 R 2 Field due to bigger sphere = K ρ 2 4 3 π 2 R 3 × R 2 R 3 The net electric field at point P will be E → net = 0 Equating above two, we get ρ 1 ρ 2 = 4 [Charges cannot be of an opposite sign otherwise field will not zero] Similarly, the net electric field at point Q becomes zero. Then ρ 1 ρ 2 = - 3 2 2 5 here both spheres should have opposite polarity.