A spherical metal shell A of radius RA and a solid metal sphere B of radius RB (< RA) are kept far apart and each is given '+Q'. Now they are connected by thin metal wire. Then?

The potential for both the objects is the same, so KQA/RA = KQB/RB or QA/QB = RA/RB. As RB < RA, we get QA > QB. The above equation represents that option B is correct. From Gauss's law, the electric field inside a spherical shell is zero, so option C is correct. Now σA = QA/4πRA² and σB = QB/4πRB². Thus σA/σB = (QA/QB) × (RB/RA)² = (RA/RB) × (RB/RA)² = RB/RA. Thus option D is also correct. Electric fields on the surface of the shell and sphere are EA = σA/εo and EB = σB/εo. Thus EA/EB = σA/σB < 1 or EA < EB. So option A is also correct.