Shown in the figure are two point charges + Q and - Q inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If σ 1 is the surface charge on the inner surface and Q1 net charge on it and σ 2 the surface charge on the outer surface and Q2 net charge on it then: (a) σ 1 ≠ 0, Q1 ≠ 0 σ 2 ≠ 0, Q2 ≠ 0 (b) σ 1 ≠ 0, Q1 = 0 σ 2 ≠ 0, Q2 = 0 (c) σ 1 ≠ 0, Q1 = 0 σ 2 = 0, Q2 = 0 (d) σ 1 = 0, Q1 = 0 σ 2 = 0, Q2 = 0

Answer: (c). Inner surface: induced charges are opposite to the nearby charges, so σ₁ ≠ 0, but their total is -(+Q - Q) = 0, so Q₁ = 0. The shell is uncharged, so the outer surface has Q₂ = 0 - Q₁ = 0. With zero charge and shielding from the cavity, the outer surface density is σ₂ = 0. So the answer is (c).

Shown in the figure are two point charges + Q and - Q inside the… | JEE Main 2015 (10 Apr, Shift 1)

Q112JEE Main 2015 · 10 APR · SHIFT 1Medium

Electric Flux & Gauss's Law

Shown in the figure are two point charges + Q and $-$ Q inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If $\sigma$ 1 is the surface charge on the inner surface and Q1 net charge on it and $\sigma$ 2 the surface charge on the outer surface and Q2 net charge on it then:

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Answer: (c)

Inner surface: induced charges are opposite to the nearby charges, so $\sigma_1 \neq 0$ , but their total is $-(+Q - Q) = 0$ , so $Q_1 = 0$ .
The shell is uncharged, so the outer surface has $Q_2 = 0 - Q_1 = 0$ .
With zero charge and shielding from the cavity, the outer surface density is $\sigma_2 = 0$ .
So the answer is (c).

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Electric Flux & Gauss's Law question from JEE Main 2015 (10 Apr, Shift 1)

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