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  • A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when it rotated slightly about its diameter and released, it starts performing simple harmonic

A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when it rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period T. If the mass of the loop is m then :
Option: 1 T=\sqrt{\frac{\pi m}{IB}}      
Option: 2 T=\sqrt{\frac{\pi m}{2IB}}      
Option: 3   T=\sqrt{\frac{2m}{IB}}   
Option: 4 T=\sqrt{\frac{2\pi m}{IB}}
 

Answers (1)

best_answer

 

 

\tau =MB\sin \theta =I\alpha (using \; M=IA)

\Rightarrow \pi R^{2}IB\theta =\frac{mR^{2}}{2}\alpha \; (Using \ \alpha =-\omega ^{2}\theta )

\Rightarrow \omega =\sqrt{\frac{2\pi IB}{m}}=\frac{2\pi }{t}

\Rightarrow T =\sqrt{\frac{2\pi m}{IB}}

 

Hence the correct option is (4).

Posted by

avinash.dongre

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