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If an insulated non-conducting sphere of radius fi has charge density $ρ$ , the electric field at a distance r from the centre of sphere (r< R) will be

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$\frac{ρR}{3 ε_{0}}$

$\frac{ρR}{ε_{0}}$

$\frac{ρr}{3 ε_{0}}$

$\frac{ρr}{ε_{0}}$

answer is A.

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Detailed Solution

Charge enclosed within the surface $= \frac{4}{3} {πr}^{3} ρ$
Applying Gauss's law, we have $ε_{0} ∮ E \cdot dS = \frac{4}{3} {πr}^{3} ρ$
or $ε_{0} E 4 {πr}^{2} = \frac{4}{3} {πr}^{3} ρ$
$E = \frac{ρr}{3 ε_{0}}$

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