The electrostatic potential energy of a system consisting of two charges 7 mC and −2 mC placed at (−9 cm, 0, 0) and (9 cm, 0, 0), respectively, is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → −7 × 105 J
The potential energy of a pair of point charges is the work needed to bring them from infinity to their separation r. The charges lie on the x-axis, and \( 1/4\pi\varepsilon_0 = 9\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}} \).
\( r = 9\,\mathrm{cm} - (-9\,\mathrm{cm}) = 18\,\mathrm{cm} = 0.18\,\mathrm{m} \)
\( q_1 = 7\,\mathrm{mC} = 7\times10^{-3}\,\mathrm{C} \)
\( q_2 = -2\,\mathrm{mC} = -2\times10^{-3}\,\mathrm{C} \)
\( \displaystyle U = \frac{1}{4\pi\varepsilon_0}\,\frac{q_1 q_2}{r} \)
\( \displaystyle U = \frac{9\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}} \times (7\times10^{-3}\,\mathrm{C}) \times (-2\times10^{-3}\,\mathrm{C})}{0.18\,\mathrm{m}} \)
\( \displaystyle U = \frac{-1.26\times10^{5}}{0.18}\,\mathrm{J} \)
\( U = -7\times10^{5}\,\mathrm{J} \)
The energy is negative because the charges are of opposite sign and attract: work must be done on the system to separate them.
Note: NTA picked this question from an NCERT (2026-27) example and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27):
Potential Energy of a System of Two Charges in an External Field – …
