Correct Answer - Option 2 :

\(\frac{1}{ϵ_o}\)
__CONCEPT:__

Gauss's law:

- According to Gauss law, the total electric flux linked with a closed surface called Gaussian surface is \(\frac{1}{ϵ_o}\) the charge enclosed by the closed surface.

\(⇒ ϕ=\frac{Q}{ϵ_o}\)

Where ϕ = electric flux linked with a closed surface, Q = total charge enclosed in the surface, and ϵo = permittivity

Important points:

- Gauss’s law is true for any closed surface, no matter what its shape or size.
- The charges may be located anywhere inside the surface.

__EXPLANATION:__

Given Q = 6C

- By the Gauss law, if the total charge enclosed in a closed surface is Q, then the total electric flux associated with it will be given as,

\(⇒ ϕ=\frac{Q}{ϵ_o}\) -----(1)

By equation 1 the total flux linked with the cube is given as,

\(⇒ ϕ=\frac{Q}{ϵ_o}\)

\(⇒ ϕ=\frac{6}{ϵ_o}\)

So the flux linked with anyone face of the cube is given as,

\(⇒ ϕ'=\frac{\phi}{6}\)

\(⇒ ϕ'=\frac{1}{ϵ_o}\)

- Hence, option 2 is correct.