Read the following passage and answer the questions.
Coulomb used a torsion balance to study the force between two small charged metal spheres. A torsion balance is a very sensitive device for measuring small forces. The spheres were small compared with the distance between them, so they could be treated as point charges. At the start, Coulomb did not know the charge on either sphere.
To change a charge in a known way, he touched a charged sphere with an identical uncharged sphere. Then he took the second sphere away. He repeated this step to get smaller and smaller charges. In one set of readings, he kept the charges fixed and changed the distance between the spheres. In another set, he kept the distance fixed and changed the charges in pairs. By comparing all the readings, he arrived at a simple law for the force between two point charges.
In the set of readings with the distance kept fixed, a graph is plotted of the force \(F\) between the spheres against the product \(q_1q_2\) of their charges. The graph is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → a straight line passing through the origin
At a fixed distance, Coulomb’s law gives \( F=(k/r^{2})\,q_1q_2 \). Here \( k/r^{2} \) is a constant, so \( F \) is directly proportional to \( q_1q_2 \).
Option (1) a straight line passing through the origin — Correct. \( F\propto q_1q_2 \) has the form \( y=mx \). Its graph is a straight line through the origin with slope \( k/r^{2} \).
Option (2) a straight line parallel to the \(q_1q_2\)-axis — Incorrect. A line parallel to the axis would mean the force does not depend on the charges. A larger product gives a larger force.
Option (3) a curve whose slope keeps increasing — Incorrect. A steepening curve would need \( F \) to grow faster than \( q_1q_2 \), for example as its square. The force grows in direct proportion.
Option (4) a curve that falls as \(q_1q_2\) increases — Incorrect. A falling curve shows an inverse relation. The force falls in this way with distance, but it rises with the product of the charges.
NCERT (2026-27):
Coulomb’s Law – “Coulomb measured the force between two point charges and found that it varied inversely as the square of the distance between the charges and was directly proportional to the product of the magnitude of the two charges and acted along the line joining the two charges.”