Two point charges, \( 4\,\mu\mathrm{C} \) and \( -3\,\mu\mathrm{C} \) (with no external field) are placed at \( (-6\,\mathrm{cm}, 0, 0) \) and \( (6\,\mathrm{cm}, 0, 0) \), respectively. The amount of work required to separate the two charges infinitely away from each other will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 0.9\,\mathrm{J} \)
The electrostatic potential energy of two point charges is \( U = kq_1q_2/r \). The work needed to take them infinitely far apart equals the negative of this energy, because the energy at infinite separation is zero.
\( \displaystyle r = 6 - (-6) = 12\,\mathrm{cm} = 0.12\,\mathrm{m} \)
\( \displaystyle U = \frac{9\times10^{9} \times (4\times10^{-6}) \times (-3\times10^{-6})}{0.12} = -0.9\,\mathrm{J} \)
\( \displaystyle W = U_{\mathrm{final}} - U_{\mathrm{initial}} = 0 - (-0.9) = +0.9\,\mathrm{J} \)
The charges attract each other, so work has to be done against the attraction.
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 Single Charge – …
