The electrostatic potential energy of a system consisting of two charges, \( 5\ \mu\mathrm{C} \) and \( -2\ \mu\mathrm{C} \) located at \( (-9\ \mathrm{cm}, 0, 0) \) and \( (9\ \mathrm{cm}, 0, 0) \) from the origin of Cartesian co-ordinate system, respectively, is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( -5\times10^{-1}\ \mathrm{J} \)
The potential energy of two point charges is the work needed to assemble them from infinity; the charges are put in with their signs.
\( \displaystyle U = \frac{1}{4\pi\varepsilon_{0}}\,\frac{q_{1}q_{2}}{r} \)
The charges sit at x = −9 cm and x = +9 cm on the x-axis, so the separation is
\( r = 9\ \mathrm{cm} - (-9\ \mathrm{cm}) = 18\ \mathrm{cm} = 0.18\ \mathrm{m} \)
\( \displaystyle U = \frac{(9\times10^{9}\ \mathrm{N\,m^{2}\,C^{-2}}) \times (5\times10^{-6}\ \mathrm{C}) \times (-2\times10^{-6}\ \mathrm{C})}{0.18\ \mathrm{m}} \)
\( \displaystyle U = \frac{-0.09}{0.18}\ \mathrm{J} = -0.5\ \mathrm{J} = -5\times10^{-1}\ \mathrm{J} \)
The negative sign shows that the unlike charges attract: work would have to be done 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 – …
