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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 centre of the ring is:
- μ₀qf / (2R)
- μ₀q / (2fR)
- μ₀q / (2πfR)
- μ₀qf / (2πR)
Correct answer: μ₀qf / (2πR)
Solution
The magnetic field at the center of the ring is due to the current created by the rotating charge. The current is given by I = qf, and the magnetic field at the center of a current loop is B = μ₀I / (2R). Substituting I = qf, we get B = μ₀qf / (2πR).
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