# Positive charge Q

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× 109 Nm2C-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, x2 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 Rate this question :

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