Force Superposition in Charge Interactions - Interactive Physics Problem

Force Superposition in Charge Interactions

A charge \( q_{1} \) exerts a force on a second charge \( q_{2} \) according to Coulomb's law. If a third charge \( q_{3} \) is brought near, what happens to:

(i) The force that \( q_{1} \) exerts on \( q_{2} \), and (ii) the net force on \( q_{2} \)?

Select the correct option:

• A) decreases, increases
• B) increases, increases
• C) remains unchanged, may increase or decrease
• D) remains unchanged, remains unchanged

Detailed Explanation

According to Coulomb’s law, the force between two charges is given by: \[ F = \frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}. \]

The key principle here is superposition: the force that \( q_{1} \) exerts on \( q_{2} \) depends only on these two charges and their distance. This force is unaffected by the presence of a third charge.

However, when a third charge \( q_{3} \) is brought near, it exerts its own force on \( q_{2} \). The net force on \( q_{2} \) becomes the vector sum of the force from \( q_{1} \) and the force from \( q_{3} \). Depending on the magnitude, direction, and sign of \( q_{3} \), the net force on \( q_{2} \) may increase or decrease, or even change direction.

Therefore, while the force from \( q_{1} \) on \( q_{2} \) remains unchanged, the net force on \( q_{2} \) may either increase or decrease. This corresponds to option (C).