# Gauss law Formula

Gauss's Law is a general law applying to any closed surface that permits to calculate of the field of an enclosed charge by mapping the field on a surface outside the charge distribution. It simplifies the calculation of the electric field if the geometries of sufficient symmetric. The typical case, is a charge particle with spherical symmetry.

Electric flux = enclosed charge / permittivity

The equation is:

Φ =Q/ϵ

Where:

Φ: Electric flux

Q: Enclosed charge by the surface

ϵ: Permittivity

Gauss Law Formula Questions:

1) If the electric flux throughout a sphere is E 4 π r^{2}. What is the electric field due to this flux?

Answer:

From the formula of the Gauss law,

Φ = E 4 π r^{2} = Q/ϵ

This implies that

E = Q/(4 π r^{2})ϵ which is the electric field due to a particle with charge Q.

2) An electric flux of 2 V-m goes through a sphere in vacuum space. What is the charge that origins that flux?

Answer:

From the formula of the Gauss law,

Φ = Q/ϵ

Q = Φ ϵ = 2 V m * 8.85*10^{(-12)} F/m = 17.7*10^{(-12)} V*F

17.7*10^{(-12)} C

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