Question

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. $\frac{3 \rho R}{\varepsilon_{0}}$

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
$\varepsilon \,\phi\, E d s=\sigma,$
$ \varepsilon_{0} E 4 \pi r^{2}=\frac{4}{3} \pi r^{3} \rho $
$E=\frac{\rho r}{3 \varepsilon_{0}}$