An alpha particle of mass m moves on a circular path of radius r in a plane inside and normal to uniform magnetic field B. The time taken by this particle to complete one revolution is ________

Options

A. `(4pieB)/m`
B. `(8pie^(2)B)/m`
C. `(4pime)/B`
D. `(pim)/(Be)`

Answer

D

Explanation

When `alpha`-particle of charge q = 2e enters perpendicularly to magnetic field, magnetic force provides the centripetal force.
`(mv^(2))/r=Bqv`
`(mv)/r=Bq`
`(mxromega)/r=B(2e)`
`(2pi)/T=(2Be)/m" "thereforeT=(2pim)/(2Be)=(pim)/(Be)`