Question

If Particle is slightly along x axis displaced and released. proved its motion is shm. Also find Timeperiod.

Answer 1

T = 2π √(m a^3 / (4πε₀ Q q₀))

Answer 2

1. Calculate the net force on the particle at a small displacement $x$ from the origin along the x-axis due to the two fixed charges.

2. Show that for small $x$, the net force is a restoring force proportional to $x$ and opposite to the displacement, i.e., $F_{net} = -Kx$. This proves that the motion is SHM. This occurs when the fixed charges and the particle charge have the same sign.

3. Identify the force constant $K$.

4. Calculate the angular frequency $\omega = \sqrt{K/m}$.

5. Calculate the time period $T = 2\pi/\omega$.