Four closed surfaces and corresponding charge distributions are shown below [S₁ encloses a single charge 2q; S₂ encloses q, -q, q and q; S₃ encloses q₁ and q₂ with the charge 5q lying outside it; S₄ encloses 8q, -2q and -4q with the charge 3q lying outside it]. Let the respective electric fluxes th…

Question

Four closed surfaces and corresponding charge distributions are shown below [S₁ encloses a single charge 2q; S₂ encloses q, -q, q and q; S₃ encloses q₁ and q₂ with the charge 5q lying outside it; S₄ encloses 8q, -2q and -4q with the charge 3q lying outside it]. Let the respective electric fluxes through the surfaces be φ₁, φ₂, φ₃ and φ₄. Then

Accepted Answer

(1) φ₁=φ₂=φ₃=φ₄. Gauss's law says the flux through a closed surface depends only on the algebraic sum of the charges inside it. Charges outside contribute zero net flux, however close they sit. S₁: q_enc=2q. S₂: q_enc=q-q+q+q=2q. S₃: the labelled q₁ and q₂ add to 2q, and the external 5q is irrelevant. S₄: q_enc=8q-2q-4q=2q, and the external 3q is again irrelevant. Every surface encloses 2q, so φ₁=φ₂=φ₃=φ₄=(2q)/(ε₀).

Step-by-step solution

Why the other options are wrong