A charge +10 \( \mu\mathrm{C} \) is placed at (0 mm, 0 mm) Another charge −5 \( \mu\mathrm{C} \) is moved from (3 mm, 0 mm) to (0 mm, 3 mm). Work done by the external agency is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0 J
The work done by an external agent in moving a charge \( q \) slowly from A to B in an electrostatic field is \( W = q\,(V_B - V_A) \). It depends only on the potentials at the two ends, not on the path.
The potential of the point charge \( Q = +10\,\mu\mathrm{C} \) at the origin depends only on the distance \( r \).
\( r_A = 3\,\mathrm{mm} \ \text{for } (3\,\mathrm{mm}, 0) \)
\( r_B = 3\,\mathrm{mm} \ \text{for } (0, 3\,\mathrm{mm}) \)
Both points lie on the same equipotential circle round the charge, so
\( \displaystyle V_A = V_B = \frac{kQ}{r} \;\Rightarrow\; W = q\,(V_B - V_A) = 0\,\mathrm{J} \)
NCERT (2026-27):
Equipotential Surfaces – “… Thus, equipotential surfaces of a single point charge are concentric spherical surfaces centred at the charge.”
Equipotential Surfaces – “… But this is in contradiction to the definition of an equipotential surface: there is no potential difference between any two points on the surface and no work is required to move a test charge on the surface.”