A uniform mangetic field of strength B exists in a region of width d. A particle of charge q and mass m is shot perpendicularly (as shown in Fig. ) into the magnetic field. Find the time spent by the particle in the magnetic field if
(a) `dgt (m u)/(qB)`
(b) `dlt (m u)/(qB)`

Explanation

(a) `dgt(m u)/(qB)` means `dgtR`, the particle will complete semicircle in the field.
`:.` Time spent `t=T/2=(pim)/(qB)`

(b) `d lt ("mu")/(qB) rArr q lt R`, the particle will not be able to complete semicircle and it will come out from other side of the field.
`sin theta=d/R`
`implies t=m/(qB)sin^-1(d/R)`
.