Question

Using Gauss Law, derive the expression for the electric field intensity at any point inside and outside of a sphere of radius ‘a’ due to a uniform spherical charge distribution of volume charge density of ‘ρ’.

Answer 1

Let
the uniform surface charge density of a thin spherical shell of radius R .Let us find out electric field intensity at a point P outside or inside the shell.
1. Field outside the shell-
Let us find out electric field intensity at a point P outside the spherical shell, such that OP=r. Here we take Gaussian surface as a sphere of radius r. the electric field intensity,

Answer 2

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