A ring of radius R carries a linear charge density `lambda`. It is rotating with angular speed `omega`. The magnetic field at its center is

Problem: A ring of radius R carries a linear charge density `lambda`. It is rotating with angular speed `omega`. The magnetic field at its center is

(A)`(3mu_0 lambda omega)/2`   ✅(B) `(mu_0 lambda omega)/2`    (C) `(mu_0 lambda omega)/pi`    (D)`mu_0 lambda omega`

Answer:

The magnetic field at the center is 

`B=(mu_0I)/(2R)`

The current I is given by 

`I=lambda v`

Where `v` is the velocity. 

We know that,

`vecv=vecomega xx vecR`

or, `v=omega R`

The magnetic field is becomes,

`B=(mu_0)/(2R)lambda omega R`

or, `B=(mu_0 lambda omega)/2`

Option B is correct.