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Two concentric conducting spherical shells A (inner) and B (outer) are such that A carries charge Q and B is uncharged. B is then connected to earth (grounded). Which of the following statements are correct?

1. The charge appearing on the inner surface of B is -Q.
2. The electric field inside and outside A is zero.
3. The electric field in the region between A and B is not zero.
4. The charge on the outer surface of B is zero.

Correct answer: The charge appearing on the inner surface of B is -Q.

Solution

Inner surface of B: Gauss's law on a surface inside the conductor of B requires charge = -Q. So statement A is TRUE. Field inside shell A: by Gauss's law the field inside the conducting material of A is zero, but the region inside A (the hollow) does not have zero field if A has charge Q — wait, A is a solid or shell? Assuming A is a shell, the field inside A (the cavity) is zero by Gauss's law (no enclosed charge in cavity). But the statement says 'inside AND outside A' — outside A but between A and B, field = Q/(4*pi*eps*r²) ≠ 0. So statement B is FALSE. Statement C: field between A and B = kQ/r² ≠ 0, TRUE. Statement D: outer surface of B = 0 after grounding, TRUE. Correct: A, C, D.

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