MHT CET · Physics · Magnetic Effects of Current
A particle of charge ' \(\mathrm{q}\) ' and mass ' \(\mathrm{m}\) ' moves in a circular orbit of radius ' \(r\) ' with angular speed ' \(\omega\) '. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on
- A \(\omega\) and \(q\)
- B \(\omega\) and \(m\)
- C \(q\) and \(m\)
- D \(\omega, \mathrm{q}\) and \(\mathrm{m}\)
Answer & Solution
Correct Answer
(C) \(q\) and \(m\)
Step-by-step Solution
Detailed explanation
Angular momentum \((\mathrm{L})=\mathrm{I} \omega=\mathrm{mr}^2 \omega\)
Magnetic moment \((M)=\pi r^2 q f=\pi r^2 q \frac{\omega}{2 \pi}=\frac{1}{2} q \omega r^2\)
\(\therefore \frac{\mathrm{M}}{\mathrm{L}}=\frac{\mathrm{q}}{2 \mathrm{~m}}\)
Magnetic moment \((M)=\pi r^2 q f=\pi r^2 q \frac{\omega}{2 \pi}=\frac{1}{2} q \omega r^2\)
\(\therefore \frac{\mathrm{M}}{\mathrm{L}}=\frac{\mathrm{q}}{2 \mathrm{~m}}\)
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