Question

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

• 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}} $

Answer 1

Answer: (C)

Charge which is enclosed in the surface is given by
$\sigma=\frac{4}{3} \pi r^{3} \rho$
Now, according to Gaussian law
$\varepsilon \oint E d s=\sigma$
$\varepsilon_{0} E 4 \pi r^{2}=\frac{4}{3} \pi r^{3} \rho$
$E=\frac{\rho r}{3 \varepsilon_{0}}$