question_answer

A conducting loop is placed in a magnetic field of strength B perpendicular to its plane. Radius of the loop is r, current in the loop is; and linear mass density of the wire of loop is m. Speed of any transverse wave in the loop will be

A) \[\sqrt{\frac{Bir}{m}}\]

B) \[\sqrt{\frac{Bir}{2m}}\]

C) \[\sqrt{\frac{2Bir}{m}}\]

D) \[2\sqrt{\frac{Bir}{m}}\]

Correct Answer: A

Solution :

[a] \[F\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\,Bi\ell \] \[2T\,\sin \frac{\theta }{2}=F\]                or  \[2T\left( \frac{\theta }{2} \right)=Bi(r\theta )\] \[\therefore \,\,\,\,\,\,\,\,T=Bir\] Now speed, \[v=\sqrt{\frac{T}{m}}\] \[=\sqrt{\frac{Bir}{m}}\]