Q. 394.3( 7 Votes )

# Positive charge Q

Answer :

Given:Charge on the ring: Q

Radius of the ring : R

Charge of the particle at point P : q

Mass of the particle : m

Distance of P from the centre of the ring: x

Distance of P from the element A : l

**Formula used:**

Electric force is given as:

Where F is the electric force, q is the charge and E is the electric field.

Newton’s Law gives :

Time period is given as:

Where, l is the length. In this case OP=x and a is the acceleration.

Where F is the electric force, q is the charge and E is the electric field.Consider an element of charge dQ on the ring at A.

Electric field at P due to the element A is given as:

Here, dE is the electric field due to element A. k= =9× 10

^{9}Nm

^{2}C

^{-2}, dQ is the charge of the element A and l is the distance between A and P.

Now,

And

Ecosθ

Therefore, the net electric field at P due to the entire ring is:

Therefore substituting in equation (1) we get,

Here, F is the electric force on the particle due to entire charged ring.

**Now the condition given in the question is x≪R. Thus, x**

^{2}can be neglected.

Hence using equation (2) and (3) we get,

Putting the value of k:

Hence time period of oscillation of the particle is

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