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The flux passing through a closed three dimensional surface is equal to the electrostatic charge divided by ε (electric permittivity of the medium).

Application:

For a point charge Q, we want to find the electric field intensity at a distance d.

We imagine a spherical closed surface of radius d around the point charge Q (placed at the center). Then we apply Gauss' law of electrostatics. We find the surface integral. From symmetry of the sphere, electric field strength E is same all around on the surface. The angle between the surface and electric field is 0⁰ and same all over the surface. Both point along the radius.

Φ = E * 4π d² = Q / ε₀

=> E = 1/(4πε₀) * Q / d²

we know this formula already, which is derived from Coulomb's law.

Application:

For a point charge Q, we want to find the electric field intensity at a distance d.

We imagine a spherical closed surface of radius d around the point charge Q (placed at the center). Then we apply Gauss' law of electrostatics. We find the surface integral. From symmetry of the sphere, electric field strength E is same all around on the surface. The angle between the surface and electric field is 0⁰ and same all over the surface. Both point along the radius.

Φ = E * 4π d² = Q / ε₀

=> E = 1/(4πε₀) * Q / d²

we know this formula already, which is derived from Coulomb's law.