Question

Two identical positive point charges + Q each, are fixed at a distance of 2a apart. A point charge + q lies midways between the fixed charges. Show that for a small displacement along the line joining the fixed charges, the charge + q executes simple harmonic motion. Find the frequency of oscil-lations.

Answer 1

Let the charge + q be displaced through a distance x to the right (Fig. 1.27). Restoring force on charge + q is

where ∈₀ = 8.85 × 10^–12 C²/N.m². 

The equation of motion of the charge + q of mass m is

which represents SHM with frequency