When Coulomb began his experiments, he did not know the charges on his metal spheres. How did he get charges in a known ratio, such as \(q\), \(q/2\) and \(q/4\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → He touched the charged sphere with an identical uncharged sphere.
Coulomb measured the force between two charged metal spheres with a torsion balance. He did not know their charges, so he needed a way to make charges in a fixed ratio.
Option (1) He measured the charge on each sphere with a gold-leaf electroscope. — Incorrect. An electroscope only shows the amount of charge by how far its leaves spread. It does not give charges in a known ratio.
Option (2) He touched the charged sphere with an identical uncharged sphere. — Correct. By symmetry the charge spreads equally over two identical spheres, so each gets \( q/2 \). Repeating the touch gives \( q/4 \), \( q/8 \) and so on.
Option (3) He rubbed each sphere for a measured length of time. — Incorrect. Rubbing for the same time does not give the same charge each time, so the ratio would still be unknown.
Option (4) He touched the charged sphere with a larger uncharged sphere. — Incorrect. Two spheres of different sizes do not share the charge equally. The halving needs two identical spheres.
NCERT (2026-27):
Coulomb’s Law – “… Coulomb thought of the following simple way: Suppose the charge on a metallic sphere is q. If the sphere is put in contact with an identical uncharged sphere, the charge will spread over the two spheres. By symmetry, the charge on each sphere will be q/2. Repeating this process, we can get charges q/2, q/4, etc. …”