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✨Q.What is Gauss theorem ? Derive also.
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Answers
Gauss's law states that the enclosed electric charge in a closed surface is proportional to the net flux of an electric field through the surface.Gauss law is also defined as the total charge Q enclosed within a surface divided by dielectric constant.
Hence Gauss law can be mathematically written as,
ϕϕ = Qϵ0Qϵ0Where,
ϕϕ = Electric flux through a given surface,
Q = total charge within a given surface,
ϵ0ϵ0 = Electric constant.
From the equation (1) we can also state that the electric flux flowing outwards to the surface is proportional to the total electric charge enclosed by it.
The Gauss law can also be mathematically defined as surface integral of the electric field through the given surface,
ϕϕ = ∮x=sx=0∮x=0x=s E.dA ................(2)where,
E = electric field,
dA = infinitesimal element of area of the enclosed surface.
The above equation (2) can also be written by the divergence theorem as,
▽▽ .E = ρϵ0ρϵ0 ..............(3)where,
▽▽ .E = electric field divergence,
ρρ = Total electric charge density.
ϕϕ = ∮x=sx=0∮x=0x=s E.dA.ϕϕ = ∮v=Vv=0∮v=0v=V ρϵ0ρϵ0 dvϕϕ = 1ϵ01ϵ0∮v=Vv
HOPE IT WILL HELPFUL.
Hey !
In electrostatics Gauss Law's is a powerful tool which is useful in simplying electric field calculations where there is symmetry in charge distribution. This law can be used to find total flux associated with a closed surface. It also gives us insight into how electric charge distributed itself over conducting bodies. The statement of Gasses's law is given below.
"The total electric flux through a closed surface is equal to the net charge enclosed by the surface divided by €o".
Here €o is permittivity of free space.
Good luck!
