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A conducting spherical shell has inner radius a and outer radius b and carries a net charge Q. A point electric dipole p is placed at the centre of the cavity. Which statement is correct?

1. The electric field outside the shell is the same as that of a point charge Q located at the centre of the shell.
2. The surface charge density on the inner surface of the shell is zero everywhere.
3. The surface charge density on the inner surface is uniform and equal to (Q/2)/(4*pi*a²).
4. The surface charge density on the outer surface depends on the magnitude of p.

Correct answer: The electric field outside the shell is the same as that of a point charge Q located at the centre of the shell.

Solution

The dipole at the centre induces equal and opposite charges on the inner surface arranged in a dipolar (non-uniform) pattern, so the inner-surface density is not zero and not uniform - eliminating options 2 and 3. The net induced charge on the inner surface is zero (dipole has zero net charge), so the outer surface carries the full net charge Q distributed uniformly; the external field is exactly that of a point charge Q at the centre and is independent of p. Hence option 1 is correct and option 4 is wrong.

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