A thin ring of radius `R` metre has charge `q` coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of `f` revolution/s. The value of magnetic induction in `Wb m^(-2)` at the centre of the ring is

Options

A. `(mu_0q)/(2fR)`
B. `(mu_0qf)/(2R)`
C. `(mu_0q)/(2pifR)`
D. `(mu_0qf)/(2piR)`

Answer

B

Explanation

The field at the center of a circular coil is given by `B=(mu_0)/(4pi)((2i)/r)` In this case r=R and the current is the rate of flow of charge `i=(dQ)/(dt)=q/T=qf (therefore 1/T=f)therefore B=(mu_0)/(4pi)((2qf)/R)=(mu_0qf)/(2R)`.