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Two concentric thin conducting shells of radii a and 2a carry charges Q and -Q respectively. A point charge Q is placed at distance a/2 from the common centre. Which of the following statement(s) is/are correct?

1. The electric field energy stored between r = a and r = 2a is Q² / (4*pi*epsilon0*a), where r is the radial distance from the common centre.
2. The electric potential of the inner shell is 3Q / (8*pi*epsilon0*a) (taking potential at infinity as zero).
3. If switch S is closed connecting the outer shell to earth, the charge flowing to earth through the switch is 5Q/2.
4. On closing switch S, the electric field at the common centre remains unchanged.

Correct answer: The electric field energy stored between r = a and r = 2a is Q² / (4*pi*epsilon0*a), where r is the radial distance from the common centre.

Solution

The net charge enclosed within radius r in the gap (a < r < 2a) is Q (point) + Q (inner shell) = 2Q, giving E = 2Q/(4*pi*epsilon0*r²). Energy in gap = Q²/(4*pi*epsilon0*a). Potential of inner shell by superposition equals 3Q/(8*pi*epsilon0*a). When outer shell is grounded only Q flows to earth, and the field at centre (due to symmetric shells) is zero before and after. Options A, B, D are correct; option C gives an incorrect charge value of 5Q/2.

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