# Gauss law and electrostatic induction. Concentric spheres

Imagine you have hollow concentric spheres A and B with radius a and b (b>a), respectively. If A is a conductor and B has a certain density charge, I´ve been taught that B will induce some net charge over A (appart from what it could have yet). But, if, according to Gauss law, the contribution to electric field inside sphere B from its surface charge distribution is zero, How can this interaccion ocurr? How can be any charge displacement inside B?

• Just my own thought: Your sphere is grounded which means it connects to something large far away. The E field of B push the charge from the ground to A? – velut luna Apr 25 '16 at 15:53
• This question come to me in an exercise where, as you say, A sphere was grounded, but I don´t know if it has much to do with my question. Anyway, any answer is welcome. – amejmar Apr 25 '16 at 15:59
• If it's not grounded but isolated, there won't be induced charge. – velut luna Apr 25 '16 at 16:01

• With the last two sentences I mean that the total charge must be zero. But you can have $Q$ on B and $-Q$ and A and that requirement would still be fulfilled. You do have a point with your second comment. Adding charge to B does not influence A in any way. If you however but charge $Q$ on A, then charge $-Q$ must be on the inside of B to shield the field; there must not be any field within B. Does that make sense now? – Martin Ueding Apr 25 '16 at 17:52