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Question

A thin ring of radius r carries a uniformly distributed charge. The ring rotates at a constant angular speed of n revolutions per second about an axis passing through centre and perpendicular to its plane. If B is the magnitude of magnetic field at the centre of ring, then the charge carried by the ring is

A
2rBμ0n
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B
μ0n2rB
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C
μ0nr
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D
2rBq
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Solution

The correct option is A 2rBμ0n
Magnitude of magnetic field at the centre of circular current carrying wire is given by,
B=μ0I2r ...(i)
Frequency of revolution (n rev/sec) of charge (q) (uniformly distributed on ring) is:
f=1T=n ...(ii)
current in wire due to revolving charge
I=qT=qf ...(iii)
I=qn
From Eq. (i),
B=μ0(qn)2r

q=2rBμ0n

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