A particle of charge q and mass m enters normally (at point P) in a region of magnetic field with speed v. It comes out noramally from Q after time T as shown in Fig. The magnetic field B is present only in the region of radius R and is uniform. Initial and final velocities are along radial direction and they are perpendicular to each other. For this to happen, which of the following expression (s) is are correct?

Options

A. `B=(mv)/(qR)`
B. `T=(piR)/(2v)`
C. `T=(pim)/(2qB)`
D. None of these

Answer

(a,b,c)

Explanation

The particle will move along an arc which
is part of a circle of radius: `r=(mv)/(Bq)`
From Fig. we can see that r=R
`:. R=(mv)/(Bq)`
`T=(pr//2)/v=(pir)/(2v)=(piR)/(2v) (because r=R=(mv)/(qB))`
`:. T=(pim)/(2Bq)`