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Can we used gauss law to find out the electric field due to any charge distribution?Explain

Can we used gauss law to find out the electric field due to any charge distribution?Explain

Grade:12th pass

1 Answers

Arun
25757 Points
2 years ago
Gauss Law:
Gauss law states that electric flux through any closed surface is equal to the net charge enclosed inside the surface divided by the permittivity of vacuum.
Electric field due to a uniformly charged thin shell:
In the diagram, O is the centre of the spherical shell of radius R, and charge enclosed by the spherical shell is q.
Let a point A is outside the spherical shell, where we have to calculate the electric field.The distance between the centre of spherical shell and the point A.
ϕ=E.Scosθ
So, ϕ=E.4πr2−−−−−−−−−−−−−−(1)
As per gauss law,
ϕ=ϵo​q​−−−−−−−−−(2)
From equation (1) and (2)
E.4πr2=ϵo​q​
Now,
E=4πϵo​r2q​
This is the electric field at the distance r, outside from the shell.

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