Question

Three particles, each having a charge of $10\mu C$ are placed at the corners of an equilateral triangle of side $10cm$. The electrostatic potential energy of the system is (Given $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^{9}N{m}^2/C^2)$

• A. Zero
• B. Infinite
• C. $27J$
• D. $100J$

Answer 1

The correct option is C $27J$

Potential energy of system of charges $U=\sum \frac{1}{4\pi {\epsilon }_0}.\frac{q_1{q}_2}{r}$


$U_{\text{system}}=\frac{1}{4\pi {\epsilon }_0}.\frac{Q\left(Q\right)}{r}+\frac{1}{4\pi {\epsilon }_0}.\frac{Q\left(Q\right)}{r}+\frac{1}{4\pi {\epsilon }_0}.\frac{Q\left(Q\right)}{r}$

$U_{\text{system}}=\frac{3}{4\pi {\epsilon }_0}.\frac{Q\left(Q\right)}{r}$

$U_{\text{system}}=\frac{3}{4\pi {\epsilon }_0}\left[\frac{10\times {10}^{-6}\times 10\times {10}^{-6}}{10/100}\right]$
$U_{system}=3\times 9\times {10}^9\times \frac{100\times {10}^{-12}\times 100}{10}=27J$