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A thin ring of radius R meter has charge q coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of f revolutions/s. The value of magnetic induction in Wb/$m^2$ at the centre of the ring is
A
$\frac{\mu_0qf}{2R}$
B
$\frac{\mu_0qf}{2\pi R}$
C
$\frac{\mu_0q}{2\pi fR}$
D
$\frac{\mu_0q}{2fR}$
Detailed Solution
A rotating charged ring is equivalent to a circular current.
The charge q crosses any point f times each second, so the current is $I = qf$
Field at the centre of a circular loop of radius R: $B = \frac{\mu_0I}{2R}$
$B = \frac{\mu_0qf}{2R}$
The charge q crosses any point f times each second, so the current is $I = qf$
Field at the centre of a circular loop of radius R: $B = \frac{\mu_0I}{2R}$
$B = \frac{\mu_0qf}{2R}$