A non-conducting sphere of radius $R$ has a uniform charge density $\rho$. The difference in the electric…

A non-conducting sphere of radius $R$ has a uniform charge density $\rho$. The difference in the electric potential at $r=R$ and $r=0$ from the centre is
  1. $\frac{-\rho R^{2}}{\epsilon_{0}}$
  2. $\frac{-2 \rho R^{2}}{\epsilon_{0}}$
  3. $\frac{\rho R^{2}}{3 \epsilon_{n}}$
  4. $\frac{-\rho R^{2}}{6 \epsilon_{0}}$

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

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