Question

In finding the electric field using Gauss law the formula `|vec"E"| = "q"_"enc"/(epsilon_0|"A"|)` is applicable. In the formula ε₀ is permittivity of free space, A is the area of Gaussian surface and q_enc is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?

Options

• Only when the Gaussian surface is an equipotential surface.

• Only when the Gaussian surface is an equipotential surface and `|vec"E"|` is constant on the surface.

• Only when `|vec"E"|` = constant on the surface.

• For any choice of Gaussian surface.

Answer 1

Only when the Gaussian surface is an equipotential surface and `|vec"E"|` is constant on the surface.

Explanation:

By Gauss law

`oint vec"E".vec"da" = "q"_"in"/epsilon_0`

If E = cons. and `vec"E"` ||_r `vec"A"`, then |E| |A| =`"q"_"in"/epsilon_0`

⇒ |E| = `"q"_"in"/(epsilon_0"A")` And `vec"E"` is always ⊥ r to equipotential surface 

Since, the Gaussian surface is equipotential.