Answer :

Charge of particles A and B : q = Q
Separation between A and B : d

Here x is the displacement of particle C along AB.
Distance between A and C is :

Distance between B and C is :

Formula used:
For part (a), we will be using Coulomb’s Law,
Where F is the electrostatic force on B due to A, k is a constant .
k =
= 9× 109 Nm2C-2 and r is the distance between the two charges.
now, the net force acting on C is:

Fnet is the net electric force experience by particle C of charge q.
When x
Thus x2 can be neglected.
We get,

Fnet α x

Thus, when xd force is proportional to x

The condition for Simple harmonic Motion of a particle is:
Here, m is the mass of the particle C, ω is the angular frequency.
Let Fnet = F’
Thus comparing two equations of F’, we get
We know that Where t is the Time Period.

Hence time period when particle is displaced along AB is

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