question_answer

If a charged particle of charge to mass ratio \[\frac{q}{m}=\alpha \] is entering in a magnetic field of strength B at a speed \[v=(2\,\alpha \,d)\,\,(B),\] then which of the following is correct:

A) angle subtended by charged particle at the centre of circular path is \[2\pi .\]

B) the charge will move on a circular path and will come out from magnetic field at a distance 4d from the point of insertion.

C) the time for which particle will be in the magnetic field is \[\frac{2\pi }{\alpha B}.\]

D) the charged particle will subtend an angle of  \[90{}^\circ \] at the centre of circular path

Correct Answer: B

Solution :

Electromagnetic force will provide the necessary centripetal force.

\[eqv=\frac{m{{v}^{2}}}{r}\]

\[\Rightarrow \]   \[r=\frac{mv}{qB}=\frac{v}{B\,\alpha }=\frac{(2\,\alpha \,d)\,\,(B)}{(B\,\alpha )}=2\,d\]

i.e. the electron will move out after travelling on a semicircular path of radius \[r=2d.\]

Hence [B]