If a charge q is placed at the centre of the line joining to equal like charges Q. The system of the

Question

If a charge q is placed at the centre of the line joining to equal like charges Q. The system of the three will be in equilibrium if q is

Professor PC Thomas Classes · Answer

For equilibrium, the force on charge q must be zero. This means the forces from the two Q charges must balance. Since q is at the center of the line, it experiences equal forces from both Q charges. The only way for these forces to balance is if q is negative (to experience attraction), and its magnitude must be $\frac{Q}{4}$ to create the right amount of force.