The force between two electric charges is expressed by the equation: \( F = \displaystyle\frac{kq_1q_2}{r^2} \) Which of the following is a correct statement?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → The equation applies to point charges
The equation is Coulomb's law. It gives the force between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \), with \( k = 1/4\pi\varepsilon_0 = 9\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}} \).
Option (1) The equation applies to point charges — Correct. Coulomb's law holds for point charges, that is, charged bodies whose size is small compared with the distance between them.
Option (2) k is Boltzmann's constant — Incorrect. \( k \) is the electrostatic (Coulomb) constant \( 1/4\pi\varepsilon_0 \); the Boltzmann constant belongs to thermal physics.
Option (3) r is the radius of the spheres on which the two charges are placed — Incorrect. \( r \) is the distance between the two charges, not the radius of any sphere.
Option (4) The equation can only be applied to uniform electric fields — Incorrect. The law gives the force of one charge on another; it needs no external field, uniform or otherwise. The field of a point charge is itself non-uniform.
NCERT (2026-27):
Coulomb’s Law – “Coulomb’s law is a quantitative statement about the force between two point charges. When the linear size of charged bodies are much smaller than the distance separating them, the size may be ignored and the charged bodies are treated as point charges.”