Two point charges \(q_1\) and \(q_2\) are held fixed, and the force on \(q_1\) due to \(q_2\) is \(\vec F\). A third point charge \(q_3\) is now fixed near them. Which of the following is found in experiments?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → The force on \(q_1\) due to \(q_2\) is still \(\vec F\), and the total force on \(q_1\) is the vector sum of \(\vec F\) and the force due to \(q_3\).
Experiments show that the force between two charges is not changed by other charges nearby. This is the principle of superposition. The total force on a charge is found by adding the separate forces as vectors.
Option (1) The force on \(q_1\) due to \(q_2\) becomes larger if \(q_3\) has the same sign as \(q_2\). — Incorrect. The force of \( q_2 \) on \( q_1 \) depends only on \( q_1 \), \( q_2 \) and the distance between them. The sign of \( q_3 \) does not change it.
Option (2) The force on \(q_1\) due to \(q_2\) becomes zero if \(q_3\) is placed between them. — Incorrect. A charge placed in between does not block the force. The force of \( q_2 \) on \( q_1 \) is still given by Coulomb’s law.
Option (3) The force on \(q_1\) due to \(q_2\) is still \(\vec F\), and the total force on \(q_1\) is the vector sum of \(\vec F\) and the force due to \(q_3\). — Correct. The force \( \vec F \) stays the same, and \( q_3 \) adds its own force on \( q_1 \). The two forces are added by the parallelogram law.
Option (4) The total force on \(q_1\) is the sum of the magnitudes of \(\vec F\) and the force due to \(q_3\). — Incorrect. Forces are vectors. Adding magnitudes is correct only when both forces act in the same direction.
NCERT (2026-27):
Forces Between Multiple Charges – “Experimentally, it is verified that force on any charge due to a number of other charges is the vector sum of all the forces on that charge due to the other charges, taken one at a time. The individual forces are unaffected due to the presence of other charges. This is termed as the principle of superposition.”