Question

A solid sphere of radius $R$ carries a uniform volume charge density $p$. The magnitude of electric field inside the sphere at a distance $r$ from the centre is :

• A. $\frac{rp}{3{\epsilon }_0}$
• B. $\frac{R\rho }{3{\epsilon }_0}$
• C. $\frac{R^{2}p}{r{\epsilon }_0}$
• D. $\frac{R^{3}p}{r^2{\epsilon }_0}$

Answer 1

Answer: (A)

Given, solid sphere,
Radius $=R$
Volume charge density $=p$
charge $=q$
distance from centre $=r$
To find Electric Field, $E$.
We know,
Electric field ( $E$ ),
$E=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{qr}{R^3}...(1)$
(above is formula for $E$ inside the sphere)
$\therefore E=\frac{q}{\frac{4}{3}\pi R^3}\times \frac{r}{3{\epsilon }_0}$
$[$ Reurranging $e{q}^n(1)]$
We know, volume $\Rightarrow V=\frac{4}{3}\pi R^3...(2)$
charge density $\Rightarrow p=\frac{q}{V}...(3)$
$\therefore P=\frac{q}{\frac{4}{3}\pi R^3}[$ from (2) $f(3)]$
$\therefore E=\frac{pr}{3{\epsilon }_0}$