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Question

A uniformly charged ring of thickness t and surface charge density σ is rotated about its axis with angular velocity ω. The magnetic field at the centre is
1554161_2bb94f6efccd4e568747be338261edf0.png

A
μ0σtω
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B
μ0σtω2
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C
2μ0σtω
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D
None of these
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Solution

The correct option is B μ0σtω2
Given: Ring of thickness =t ; surface charge density =σ ; angular velocity =ω
Solution: A ring element of radius and thickness dt, then charge on the ring element., dq=σ2πtdt
and current, due to this element,
di=(σ2πrdt)ω2π=σωtdt
So, magnetic induction at the centre, due to this element : dB=μ02dit
and hence, from symmetry
B=dB=N0μ0σωtdtt=μ02σωt
So,the correct option:B

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