Aring of radius 8 cm that lies in the ya plane carries positive charge of 2 μc uniformly distributed over its length. a particle of mass m that carries a charge of-2 oscillates about the center of the ring with an angular frequency of 22 rad/s find the angular frequency of oscillation of the mass if the radius of the ring is doubled

The angular frequency of oscillation of the mass is 11 rad/s.

Explanation:

Given that,

Charge = 2μC

Radius R₁= 8 cm

Radius R₂ = 16 cm

Angular frequency = 22 rad/s

We need to calculate the angular frequency of oscillation of the mass

The electric field produced along x axis

The force on the mass is

....(I)

For,x<<R

Now, using centripetal force

Put the value of F in equation (I)

We know that,

For, r<<R

Here,

The ratio of angular frequency

Put the value of

Hence, The angular frequency of oscillation of the mass is 11 rad/s.