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. $\frac{\rho R}{3{\epsilon }_0}$
• B. $\frac{\rho r}{{\epsilon }_0}$
• C. $\frac{\rho r}{3{\epsilon }_0}$
• D. $\frac{3\rho R}{{\epsilon }_0}$

Answer 1

The correct option is C $\frac{\rho r}{3{\epsilon }_0}$

Charge,

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

According to Gaussian law

$\epsilon \varphi Eds=\sigma$

${\epsilon }_{0}E4\pi r^2=\frac{4}{3}\pi r^3\rho$

$E=\frac{\rho r}{3{\epsilon }_0}$