Q. Let $p(r) = \frac{\mathcal{Q}r}{\pi R^{4}}$ be the charge density distribution for a solid sphere of radius $R$ and total charge $\mathcal{Q}.$ For a point $P$ inside the sphere at distance $r_{1}$ from the centre of the sphere, the magnitude of electric field is
A) Zero
B) $\frac{\mathcal{Q}}{4\pi\varepsilon_{0}r_{1}^{2}}$
C) $\frac{\mathcal{Q}r_{1}^{2}}{4\pi\varepsilon_{0}R^{4}}$
D) $\frac{\mathcal{Q}r_{1}^{2}}{3\pi\varepsilon_{0}R^{4}}$
Explanation
(c) $E \times 4\pi r_{1}^{2} = \frac{\int_{0}^{r_{1}}{\frac{\mathcal{Q}}{\pi R^{4}}r4\pi r^{2}dr}}{\varepsilon_{0}}$
$\Longrightarrow E = \frac{{\mathcal{Q}r}_{1}^{2}}{4\pi\varepsilon_{0}R^{4}}$
[image:1_image274.emf]
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.