According to gauss theorem, the electric flux on a closed surface depends on?

CONCEPT

• Electric Flux: It is defined as the number of electric field lines passing through the perpendicular unit area.

• Electric Flux = (Φ) = EA_⊥ [E = electric field, A = perpendicular area]
• Electric flux (Φ) = EA cos θ [where θ is the angle between area plane and electric field]

• The flux is maximum when the angle is 0°
• Gauss Law: According to gauss’s law, total electric flux through a closed surface enclosing a charge is 1/ϵ₀ times the magnitude of charge enclosed.

\(i.e.~{{\mathbf{\Phi }}_{net}}=\frac{\left( {{Q}_{in}} \right)}{{{\epsilon }_{0}}}\)

\(i.e.~\oint \vec{E}\cdot d\vec{S}=\frac{{{Q}_{in}}}{{{\epsilon }_{0}}}\)

Where, Φ = electric flux, Q_in = charge enclosed the sphere, ϵ₀ = permittivity of space (8.85 × 10^-12 C²/Nm²), dS = surface area

EXPLANATION

According to gauss’s law,

The flux of the net electric field through a closed surface equals the net charge enclosed by the surface divided by ϵ₀.

\(\oint \vec{E}\cdot d\vec{S}=\frac{{{Q}_{in}}}{{{\epsilon }_{0}}}\)

Electric flux on a closed surface only depends on the enclosed charge.