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  4. A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of 40 π rad s-1 about its axis, perpendicular to its plane. If the magnetic field at its centre is 3.8 × 10-9 T, then the charge carried by the ring is close to (μ0 = 4 π × 10-7 N/A2) :

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Q. A thin ring of $10\, cm$ radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $40 \; \pi \; rad \; s^{-1}$ about its axis, perpendicular to its plane. If the magnetic field at its centre is $3.8 \times 10^{-9}\, T$, then the charge carried by the ring is close to ($\mu_0 = 4 \pi \times 10^{-7} \; N/A^2$) :

JEE MainJEE Main 2019Moving Charges and Magnetism

Solution:

$B =\frac{\mu_{0} i}{2R} = \frac{\mu_{0}q\omega}{2R 2\pi} $
$ \Rightarrow q=3 \times10^{-5} C$