A point charge causes an electric flux of $ -200 \mathrm{~N} \mathrm{~m}^{2} \mathrm{C}^{-1} $ to pass through spherical Gaussian surface of $ 10 \mathrm{~cm} $ radius centered on the charge. If the radius of the Gaussian surface is doubled, the total electric flux passing through the surface is

Question

A point charge causes an electric flux of $ -200 \mathrm{~N} \mathrm{~m}^{2} \mathrm{C}^{-1} $ to pass through spherical Gaussian surface of $ 10 \mathrm{~cm} $ radius centered on the charge. If the radius of the Gaussian surface is doubled, the total electric flux passing through the surface is, $ -200 \mathrm{Nm}^{2} \mathrm{C}^{-1} $, $ -100 \mathrm{Nm}^{-2} \mathrm{C}^{-1} $, $ +200 \mathrm{Nm}^{2} \mathrm{C}^{-1} $, $ -50 \mathrm{Nm}^{2} \mathrm{C}^{-1} $

MARKS App · Accepted Answer

According to Gauss's theorem, electric flux through a closed surface is given by, ∅ = q ε 0 , where, q is charge enclosed, ε 0 is constant. Here even if the radius is doubled, the charge enclosed is the same, so the flux through the surface is also the same. Hence, flux is - 200 Nm 2 C - 1 .

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