A point charge \(Q\) is placed at a point O. How many of the following statements about the electric potential due to this charge are correct?
(A) The potential at a point is the work done in bringing a unit positive charge, without acceleration, from infinity to that point.
(B) The work done in bringing a test charge from infinity to a point depends on the path followed.
(C) If \(Q\) is negative, the potential at every point near it is negative.
(D) The potential has the same value at all points that are at the same distance from O.
(E) The potential falls off with distance more slowly than the electric field.
(F) The potential is a vector quantity directed away from \(Q\).
(G) For \(Q=1\ \mathrm{nC}\), the potential at a distance of 3 m from O is 1 V.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Four
The potential of a point charge is \( V=Q/4\pi\varepsilon_0r \). It is a scalar and is taken as zero at infinity.
The statements that are correct:
(A) — correct; this is the definition of potential
(C) — correct; for \( Q\lt 0 \), \( V\lt 0 \)
(D) — correct; \( V \) depends only on \( r \)
(E) — correct; \( V\propto1/r \) while \( E\propto1/r^{2} \)
The statements that are not:
(B) — the electrostatic force is conservative, so the work does not depend on the path
(F) — potential is a scalar; it has no direction
(G) — the potential is \( 9\times10^{9}\times10^{-9}/3 \), that is, 3 V; the 1 V value comes from dividing by \( r^{2} \)
Number of correct statements = 4
NCERT (2026-27):
Electrostatic Potential – “In other words, the electrostatic potential (V ) at any point in a region with electrostatic field is the work done in bringing a unit positive charge (without acceleration) from infinity to that point.”
Introduction – “… It means that the work done by an electrostatic field in moving a charge from one point to another depends only on the initial and the final points and is independent of the path taken to go from one point to the other. …”
Potential Due to a Point Charge – “For Q < 0, V < 0, i.e., work done (by the external force) per unit positive test charge in bringing it from infinity to the point is negative. …”
Equipotential Surfaces – “This shows that V is a constant if r is constant. …”
Potential Due to a Point Charge – “… the electrostatic potential ( ∝ 1/r) and the electrostatic field ( ∝ 1/r2 ) varies with r.”