Given below are two statements:
Statement I: The force on a charge due to a number of other charges is the vector sum of the forces due to each of them, taken one at a time.
Statement II: Three equal charges \(q\) are fixed at the corners of an equilateral triangle. A charge \(Q\) is placed at its centroid. If one corner charge is removed, the net force on \(Q\) is twice the force due to one corner charge.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Statement I is correct but Statement II is incorrect
Statement I The force on a charge due to a number of other charges is the vector sum of the forces due to each of them, taken one at a time. — True. This is the principle of superposition. Each force is found from Coulomb’s law as if the other charges were not there. The separate forces are then added as vectors.
Statement II Three equal charges \( q \) are fixed at the corners of an equilateral triangle. A charge \( Q \) is placed at its centroid. If one corner charge is removed, the net force on \( Q \) is twice the force due to one corner charge. — False. The centroid is at the same distance from all three corners, so each corner charge exerts a force of the same size \( F \) on \( Q \). With all three charges present, these forces add to zero. When one charge is removed, the two forces left must add up to a force equal and opposite to the removed one. So the net force on \( Q \) is \( F \). Taking it as \( 2F \) adds the two sizes and ignores their directions.
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. …”
Example 1.5 – “… It is clear also by symmetry that the three forces will sum to zero. …”