A non-conducting thin disc of radius R has uniform surface charge density σ and rotates with angular speed ω. Which option correctly gives both the magnetic field at its centre and the magnetic moment?
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Question

A non-conducting thin disc of radius R has uniform surface charge density σ and rotates with angular speed ω. Which option correctly gives both the magnetic field at its centre and the magnetic moment?

Options

G1 Physics · Accepted Answer

Treat a ring of radius r and width dr: dq=σ2πrdr, current dI=ωdq/(2π)=σωrdr. Its centre field is dB=μ₀dI/(2r)=μ₀σωdr/2; integrate 0→R to get B=μ₀σωR/2. Magnetic moment dμ=dI·πr²=σωπr³dr, giving μ=σωπR⁴/4. Hence A.