Consider the following statements about the forces between several point charges:
(A) Electrostatic forces on a charge add by the parallelogram law, like forces of mechanical origin.
(B) In a system of \(n\) charges, the total force on \(q_1\) is the vector sum of \(n\) separate forces.
(C) A charge feels two forces, each of magnitude \(F\), at right angles to each other. The net force on it is \(\sqrt{2}\,F\).
(D) The force on \(q_1\) due to \(q_2\) changes when the other charges of the system are moved.
Which of the above statements are incorrect? Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (D) only
The force between any two charges is given by Coulomb’s law, whatever other charges are present. The total force on a charge is the vector sum of the forces due to all the other charges.
(A) Electrostatic forces on a charge add by the parallelogram law, like forces of mechanical origin. — True. Electrostatic forces are vectors. They are added by the parallelogram law, in the same way as mechanical forces.
(B) In a system of \(n\) charges, the total force on \(q_1\) is the vector sum of \(n\) separate forces. — False. The charge \( q_1 \) feels forces from the other \( n-1 \) charges only, \( \vec F_{12} \) to \( \vec F_{1n} \).
(C) A charge feels two forces, each of magnitude \(F\), at right angles to each other. The net force on it is \(\sqrt{2}\,F\). — True. The resultant of two equal forces at right angles is \( \sqrt{F^{2}+F^{2}}=\sqrt{2}\,F \).
(D) The force on \(q_1\) due to \(q_2\) changes when the other charges of the system are moved. — False. The force on \( q_1 \) due to \( q_2 \) depends only on \( q_1 \), \( q_2 \) and the distance between them. Moving the other charges does not change it.
NCERT (2026-27):
Forces Between Multiple Charges – “The vector sum is obtained as usual by the parallelogram law of addition of vectors.”
Forces Between Multiple Charges – “The principle of superposition says that in a system of charges q1, q2, ..., qn, the force on q1 due to q2 is the same as given by Coulomb’s law, i.e., it is unaffected by the presence of the other charges q3, q4, ..., qn. The total force F1 on the charge q1, due to all other charges, is then given by the vector sum of the forces F12, F13, ..., F1n”