Exams › JEE Advanced › Physics
Two thin concentric conducting shells of radii a and 2a carry charges Q and -Q respectively. A point charge Q is also placed at a distance a/2 from the common centre. Which of the following statements is/are correct? (A) The energy stored in the electric field in the region a <= r <= 2a equals Q²/(4*pi*epsilon0*a), where r is the radial distance from the common centre. (B) The electric potential of the inner shell is 3Q/(8*pi*epsilon0*a), taking potential at infinity as zero. (C) If a switch S connects the outer shell to earth and is closed, the charge that flows to earth through the switch is 5Q/2. (D) Closing switch S does not alter the electric field at the common centre.
- Energy stored in electric field from r = a to r = 2a is Q²/(4*pi*epsilon0*a), where r is radial distance from common center.
- Electric potential of inner shell is 3Q/(8*pi*epsilon0*a), (assuming potential at infinity is zero).
- If switch S is closed, then charge flow through the switch into the earth is 5Q/2.
- Electric field at common center remains unchanged on closing the switch S.
Correct answer: Electric field at common center remains unchanged on closing the switch S.
Solution
The electric field at the common centre is entirely due to the point charge Q (spherical shells produce zero field at centre by Gauss's law), so grounding the outer shell cannot change the field there. The energy stored in the shell-generated field between r = a and r = 2a is Q²/(8*pi*epsilon0*a), not Q²/(4*pi*epsilon0*a), making statement A false.
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