Gauss Theorem

Description:

Gauss Theorem is taken as a first equation of MAXWELL. This theorem tell us that both electric charge and electric field is related to each other. A charge is the only responsible factor for electric field.

What is the relation between electric field and electric charge?

Maxwell used concept of electric flux in place of electric field. If any closed surface is placed in an  electric field, then there will be some flux linked with the surface. This flux may be zero or may have certain finite value depending on the charge placed within the closed surface.

Gauss Theorem states that − The electric flux linked to a closed surface kept in an electric field is (1/ε₀) times the total charge enclosed within the surface.

If a charge (q) is enclosed within a closed surface, then flux linked(Φ_E) with the surface will be −

Φ_E = q/ ε₀ ........(1)

we know that general formula of electric flux is −

Φ_E = ∮ E→ . dA→ = ∮ EdsCos θ

Putting the values in equation (1) we get −

∮ E→.dA→ = q/ ε₀

This equation can be used for all application.