Electrostatics

JEE Main level, single correct, medium

300 of 311

Question 300 of 311

In finding the electric field using Gauss law the formula ∣E⃗∣=qencϵ0∣A∣\left|\vec{E}\right|=\dfrac{{q}_{enc}}{{\epsilon }_{0}\left|A\right|} is applicable. In the formula ϵ0{\epsilon }_{0} is permittivity of free space, AA is the area of Gaussian surface and qenc{q}_{enc} is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?

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Answer: (B) Only when the Gaussian surface is an equipotential surface and ∣E⃗∣\left|\vec{E}\right| is constant on the surface.

According to Gauss law of electrostatics, the electric flux through an enclosed surface is given by ϕE=qencϵ0{\phi }_{E}=\dfrac{{q}_{enc}}{{\epsilon }_{0}}
From the formula of electric flux, ϕ=E⃗⋅ds⃗\phi =\vec{E}\cdot d\vec{s}
Also, the relation between electric field and electric potential is given by V=E⃗⋅dr⃗V=\vec{E}\cdot d\vec{r}
So, the formula ∣E⃗∣=qencϵ0∣A∣\left|\vec{E}\right|=\dfrac{{q}_{enc}}{{\epsilon }_{0}\left|A\right|} is only applicable when the Gaussian surface is an equipotential surface and ∣E⃗∣\left|\vec{E}\right| is constant on the surface.

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