A non-conducting sphere of radius $R$ has a uniform charge density $\rho$. The difference in the electric…
- $\frac{-\rho R^{2}}{\epsilon_{0}}$
- $\frac{-2 \rho R^{2}}{\epsilon_{0}}$
- $\frac{\rho R^{2}}{3 \epsilon_{n}}$
- $\frac{-\rho R^{2}}{6 \epsilon_{0}}$
Solution
$V_{c}=\frac{3}{2} \frac{K Q}{R}$
$v_{0}=\frac{k Q}{R}$
Difference
$\begin{aligned}
\Delta V &=-\frac{k Q}{2 R} \\
&=\frac{-1}{4 \pi \varepsilon_{0}} \times \frac{1}{2 R}\left(\rho \times \frac{4}{3} \pi R^{3}\right) \\
&=\frac{-\rho R^{2}}{6 \varepsilon_{0}}
\end{aligned}$
.Asked in: JEE Mains - Electrostatics - Test 4