The work done in moving a unit charge from one point to another point by an electric field is known as:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → line integral of electric field.
The work done by the field in moving a charge through a small displacement \( d\vec{l} \) is \( q\,\vec{E}\cdot d\vec{l} \). For a unit charge moved from A to B, adding these up gives the line integral of the electric field along the path, which also equals the potential difference between the points.
\( \displaystyle W = \int_{A}^{B} \vec{E}\cdot d\vec{l} \)
\( W = V_A - V_B \)
Why the other options are incorrect
Option (1) electric flux. — Incorrect. Electric flux measures the field passing through a surface, \( \oint \vec{E}\cdot d\vec{S} \); it is not work.
Option (2) surface integral of electric field. — Incorrect. A surface integral of the electric field is the electric flux, again not work.
Option (4) potential gradient. — Incorrect. The potential gradient \( dV/dr \) is the rate of change of potential with distance; it gives the field (\( E = -dV/dr \)), not the work done.