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Question: A conductor A is given a charge of amount +Q and then placed inside an uncharged deep metal can B, w...

A conductor A is given a charge of amount +Q and then placed inside an uncharged deep metal can B, without touching it.

A

The potential of A does not change when it is placed inside B.

B

if B is earthed, +Q amount of charge flows from it into the earth.

C

if B is earthed, the potential of A is reduced.

D

if B is earthed, the potential of A and B both becomes zero.

Answer

Options (B) and (C) are correct.

Explanation

Solution

  1. Analysis without Earthing:

    When the charged conductor A (+Q) is placed inside the uncharged metal can B, it induces a charge of -Q on the inner surface of B and +Q on its outer surface. Thus, the potential of A will be affected by the induced charges on B. So, statement (A) is false.

  2. Analysis with Earthing:

    When B is earthed, its potential is fixed at 0. The induced +Q on the outer surface will be neutralized by flowing into the earth (net +Q flows out from B to earth), leaving B with a net charge of –Q (due to its inner surface charge). Hence, statement (B) is correct.

    Also, because B is now at 0 potential, the shielding effect of the earthing reduces the potential of A relative to its value when isolated. Therefore, statement (C) is correct.

    However, statement (D) claims that both A and B become zero potential; A remains at a nonzero potential because it is not directly earthed. So, (D) is false.

Minimal Explanation:

  • A induces -Q inside B and +Q on the outer surface, altering A's potential.

  • When B is earthed, +Q leaves B (option B) and the shielding lowers A's potential (option C).

  • A’s potential remains nonzero since it is not grounded.