Deduce Coulomb's law from Gauss's theorem in electrostatics.
Answers
Answer:
In order to derive Coulomb's Law from Gauss's Law, we must first choose our Gaussian surface that encloses a stationary point charge. We choose our surface to be a sphere with a radius r in which the charge is located at the center.
Gauss's Theorem: According to Gauss's theorem total number of electric lines of force passing normally through a closed surface of ray shape in an electric field(i.e., total electric flux) is equal to 1/εo
times the total charge present within that surface.
i.e., Φe=q/e0
where, ε0 = permitivity if free space, q in vaccum.
Derivation of Gauss's Theorem: Let +q charge is placed at a point O and a point P lies at distance r from the point O. Imagine a sphere of radius r and centre O. Thus, point P lies on the surface of the sphere. Now, the surface of the sphere will be have as Gaussian surface. Therefore, the intensity of electric field on the surface at all the points will be equal in magnitude and will be directed radially outward.
∴ The electric flux passing through the spherical surface.
Φ=E.S.cos0 degree
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