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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 center of the ring is
A
$\frac{\mu_0q}{2\pi fR}$
B
$\frac{\mu_0qf}{2\pi R}$
C
$\frac{\mu_0qf}{2R}$
D
$\frac{\mu_0q}{2fR}$
Detailed Solution
A rotating charged ring is equivalent to a circular current loop.
The charge q passes any point f times per second, so the current is $I = \frac{q}{T} = qf$
Magnetic field at the centre of a circular loop of radius R: $B = \frac{\mu_0I}{2R}$
$B = \frac{\mu_0qf}{2R}$
The charge q passes any point f times per second, so the current is $I = \frac{q}{T} = qf$
Magnetic field at the centre of a circular loop of radius R: $B = \frac{\mu_0I}{2R}$
$B = \frac{\mu_0qf}{2R}$