Question

Charge $q$ is uniformly spread on a thin ring of radius $R$. The ring rotates about its axis with a uniform frequency $f$ $Hz$. The magnitude of magnetic induction at the centre of the ring is

• A. $\frac{{\mu }_{0}qf}{2R}$
• B. $\frac{{\mu }_{0}q}{2fR}$
• C. $\frac{{\mu }_{0}q}{2\pi fR}$
• D. $\frac{{\mu }_{0}qf}{2\pi R}$

Answer 1

Answer: (A)

$\frac{{\mu }_{0}qf}{2R}$

We know magnetic field
$\beta =\frac{{\mu }_{0}i}{2R}$
$q=it\Rightarrow i=\frac{q}{t}=qf$
$\therefore \beta =\frac{{\mu }_{0}qf}{2R}$