Question

Three particles, each having a charge of $ 10\, \mu C $ are placed at the corners of an equilateral triangle of side $ 10\, cm $ . The electrostatic potential energy of the system is
$ \left(\text{Given}\, \frac{1}{4\pi\varepsilon_{0}} = 9 \times10^{9}\,N-m^{2}\,C^{2}\right) $

• A. Zero
• B. $ \infty $
• C. $ 27\,J $
• D. $ 100\,J $

Answer 1

Answer: (C)

For a pair of charges
$U=\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r}$
$U_{\text {system }}=\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{10 \times 10^{-6} \times 10 \times 10^{-6}}{10 / 100}\right.$
$+\frac{10 \times 10^{-6} \times 10 \times 10^{-6}}{10 / 100}$
$+ \left.\frac{10 \times 10^{-6} \times 10 \times 10^{-6}}{10 / 100}\right]$
$=3 \times 9 \times 10^{9} \times \frac{100 \times 10^{-12} \times 100}{10}$
$=27\, J$