If an insulated non-conducting sphere of radius R has charge density ρ . electric field at a distan

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1. Electric Charges and Fields

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

A

$\frac{{\rho \,R}}{{3{\varepsilon _0}}}$

B

$\frac{{\rho \,r}}{{{\varepsilon _0}}}$

C

$\frac{{\rho \,r}}{{3{\varepsilon _0}}}$

D

$\frac{{3\rho \,R}}{{{\varepsilon _0}}}$

Solution

Charge, $\sigma=\frac{4}{3} \pi r^{3} \rho$

According to Gaussian law

$\varepsilon \phi E d s=\sigma$

$\varepsilon_{0} E 4 \pi r^{2}=\frac{4}{3} \pi r^{3} \rho$

$E=\frac{\rho r}{3 \varepsilon_{0}}$

Standard 12

Physics

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