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.