Identify the correct statements among the following.
A. The electrostatic field at a distance \(r\) from a point charge is proportional to \(1/r^{2}\).
B. The electrostatic force between two point charges separated by distance \(r\) is proportional to \(1/r^{2}\).
C. The electric potential at a distance \(r\) from a point charge is proportional to \(1/r^{2}\).
D. The electric potential at a distance \(r\) from a point charge is proportional to \(1/r\).
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A, B and D only
For a point charge q, Coulomb’s law gives the force and field as inverse-square laws, while the potential falls off only as 1/r.
\( \displaystyle F = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r^{2}} \)
\( \displaystyle E = \frac{1}{4\pi\varepsilon_0}\frac{q}{r^{2}} \)
(A) The electrostatic field at a distance \( r \) from a point charge is proportional to \( 1/r^{2} \). — Correct. \( E = q/(4\pi\varepsilon_0 r^{2}) \).
(B) The electrostatic force between two point charges separated by distance \( r \) is proportional to \( 1/r^{2} \). — Correct. This is Coulomb’s law.
(C) The electric potential at a distance \( r \) from a point charge is proportional to \( 1/r^{2} \). — Incorrect. The potential is \( V = q/(4\pi\varepsilon_0 r) \), which varies as 1/r.
(D) The electric potential at a distance \( r \) from a point charge is proportional to \( 1/r \). — Correct. This is the result used in (C) above.
NCERT (2026-27):
Summary – “… 5. Coulomb’s Law: The mutual electrostatic force between two point charges q1 and q2 is proportional to the product q1q2 and inversely proportional to the square of the distance r21 separating them.”
Potential Due to a Point Charge – “… Figure (2.4) shows how the electrostatic potential (\( \propto \) 1/r) and the electrostatic field (\( \propto \) 1/r2) varies with r.”