If an insulated non-conducting sphere of radius R has charge density ρ. The electric field at a distance r from the centre of sphere (r > R) will be

$\frac{ρ R}{3 ε_{o}}$

$\frac{ρ r}{ε_{o}}$

$\frac{ρ r}{3 ε_{o}}$

$\frac{3 ρ R}{ε_{o}}$

Solution

$\frac{ρ r}{3 ε_{o}}$

Gauss law allows us to determine the electric field at a point when there is sufficient symmetry.

Charge which is enclosed in the surface is given by

$σ = \frac{4}{3} π r^{3} ρ Now according ro Gaussian law ε ϕ E ds = σ ε_{o} E 4 π r^{2} = \frac{4}{3} π r^{3} ρ E = \frac{ρ r}{3 ε_{o}}$

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