Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole P as shown. In this case: (a) surface charge density on the inner surface is uniform and equal to (Q/2)4π a² (b) surface charge density on the inner surface of the shell is zero everywhere (c) surface charge density on the outer surface depends on |P| (d) electric field outside the shell is the same as that of a point charge at the centre of the shell

Answer: (d). The dipole has net charge zero, so the inner surface has total induced charge zero, but nonuniform (negative near + end, positive near - end). So (a), (b) are wrong. The outer surface carries the shell's charge Q, spread uniformly because the conductor shields the cavity; it does not depend on |P|. So (c) is wrong. A uniform charge Q on the outer sphere gives an outside field like a point charge Q at the centre. So the answer is (d).

Shown in the figure is a shell made of a conductor. It has inner… | JEE Main 2019 (12 Apr, Shift 1)

Q104JEE Main 2019 · 12 APR · SHIFT 1Medium

Electric Flux & Gauss's Law

Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole $\vec{P}$ as shown. In this case:

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Answer: (d)

The dipole has net charge zero, so the inner surface has total induced charge zero, but nonuniform (negative near $+$ end, positive near $-$ end). So (a), (b) are wrong.
The outer surface carries the shell's charge $Q$ , spread uniformly because the conductor shields the cavity; it does not depend on $|\vec{P}|$ . So (c) is wrong.
A uniform charge $Q$ on the outer sphere gives an outside field like a point charge $Q$ at the centre.
So the answer is (d).

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Electric Flux & Gauss's Law question from JEE Main 2019 (12 Apr, Shift 1)

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