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 r2. What is the electric field due to this flux?
Answer:
From the formula of the Gauss law,
Φ = E 4 π r2 = Q/ϵ
This implies that
E = Q/(4 π r2)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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