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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 18

  • question_answer
    A particle of charge q and mass m moves in a circular orbit of radius r with angular speed co. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

    A) \[\omega \] and q        

    B) \[\omega q\] and m

    C) q and m        

    D)   \[\omega \] and m

    Correct Answer: C

    Solution :

    [c] : Magnetic moment, \[M=IA\] \[M=\frac{qv}{2\pi r}\times \pi {{r}^{2}}=\left( q\times \frac{\omega }{2\pi } \right)\pi {{r}^{2}}=\frac{1}{2}q\omega {{r}^{2}}\] Angular momentum, \[L=mvr=m(\omega r)r=m\omega {{r}^{2}}\] \[\therefore \]\[\frac{M}{L}=\frac{\frac{1}{2}q\omega {{r}^{2}}}{m\omega {{r}^{2}}}=\frac{1}{2}\frac{q}{m}\]


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