There are two electric charges, \( Q_1 \) and \( Q_2 \), placed in vacuum. Identify the correct statements from the following
(A) There will be an electrostatic force between them.
(B) If these charges are placed in water, the force between them will increase.
(C) The electrostatic force between them is a conservative force.
(D) If both of the charges are doubled as \( 2Q_1 \) and \( 2Q_2 \), then the force between them will become 4 times.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (C) and (D) only
By Coulomb's law the force between two point charges in a medium of dielectric constant \( K \) is
\( \displaystyle F = \frac{1}{4\pi\epsilon_0 K}\,\frac{Q_1 Q_2}{r^{2}} \)
(A) There will be an electrostatic force between them. — Correct. Any two charges exert a force on each other.
(B) If these charges are placed in water, the force between them will increase. — Incorrect. Water has a large dielectric constant (\( K \approx 80 \)), so the force falls to \( 1/K \) of its value in vacuum.
(C) The electrostatic force between them is a conservative force. — Correct. The work done by the force depends only on the end points, not on the path.
(D) If both of the charges are doubled as \( 2Q_1 \) and \( 2Q_2 \), then the force between them will become 4 times. — Correct. \( F \propto Q_1 Q_2 \), so doubling both gives \( 2\times2 = 4 \) times the force.
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.”
Introduction – “… Coulomb force between two (stationary) charges is also a conservative force.”