Q. An insulated sphere of radius R has charge density$\rho$. The electric field at a distance r from the centre of the sphere (r < R)
A) $\frac{\rho r}{3\varepsilon_{0}}$
B) $\frac{\rho R}{3\varepsilon_{0}}$
C) $\frac{\rho r}{\varepsilon_{0}}$
D) $\frac{\rho R}{\varepsilon_{0}}$
Explanation
(a) Charge enclosed in the sphere of radius $r$
$q = \frac{4}{3}\pi r^{3}\rho\ $
$E = \frac{q}{4\pi\varepsilon_{0}r^{2}} = \frac{\frac{4}{3}\pi r^{3}\rho}{4\pi\varepsilon_{0}r^{2}} = \frac{r\rho}{3\varepsilon_{0}}\ \ $
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.