Three concentric conducting spherical shells A, B and C have radii R, 2R and 3R respectively. The innermost shell A is given a charge Q and the outermost shell C is given a charge 2Q . If the middle shell B is earthed, the charge induced on shell B is :

Step-by-step solution

Let the charge induced on the middle shell B be q . Since shell B is earthed, its potential must be zero ( V_B = 0 ). The potential at shell B is the sum of potentials due to the charges on shells A, B and C . For the charge Q on shell A , shell B is outside, so the potential is k Q 2R . For the charge q on shell B , the potential is k q 2R . For the charge 2Q on shell C , shell B is inside, so the potential is uniform and equal to the surface potential of C , which is k 2Q 3R . Applying the superposition principle