What is the work done in moving a \( \delta q \) charge from A to B?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0
The work done in moving a charge between two points in an electric field depends only on the potential difference between them.
\( \displaystyle W = \delta q\,(V_B - V_A) \)
The potential of the point charge \( q \) at a distance \( r \) is \( V = kq/r \). A and B both lie on the circle of radius \( r \) around \( q \), which is an equipotential surface.
\( \displaystyle V_A = V_B = \frac{kq}{r} \)
\( \displaystyle W = \delta q \times 0 = 0 \)
The path from A to B does not matter; the work done is zero.
NCERT (2026-27):
Equipotential Surfaces – “… This shows that V is a constant if r is constant. 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.”