In Coulomb’s law, \(F=k\,q_1q_2/r^{2}\), any positive value could have been chosen for the constant \(k\). The choice of the value of \(k\) decides
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → the size of the unit of charge
Once \( k \) is fixed, the law tells us how large a charge must be to give a known force at a known distance. That charge becomes the unit.
Option (1) the line along which the force acts — Incorrect. The force between two point charges always acts along the line joining them. A different value of \( k \) changes only the size of the force.
Option (2) the power of \( r \) in the force law — Incorrect. The \( 1/r^{2} \) dependence came from Coulomb’s experiments. It stays the same for any value given to \( k \).
Option (3) the size of the unit of charge — Correct. In SI units \( k \) is taken as about \( 9\times10^{9}\ \mathrm{N\,m^{2}\,C^{-2}} \). The unit of charge that follows from this choice is the coulomb. Two charges of 1 C placed 1 m apart in vacuum then repel with a force of about \( 9\times10^{9}\ \mathrm{N} \).
Option (4) whether like charges attract or repel — Incorrect. The value of \( k \) is always positive. Attraction or repulsion depends on the signs of \( q_1 \) and \( q_2 \).
NCERT (2026-27):
Coulomb’s Law – “Coulomb discovered his law without knowing the explicit magnitude of the charge. In fact, it is the other way round: Coulomb’s law can now be employed to furnish a definition for a unit of charge. … k is so far arbitrary. We can choose any positive value of k. The choice of k determines the size of the unit of charge.”