Correct Answer - B::D
Figure shows that the magnetic field ` vec(B)` is present on the right hand side of `AB` . The electron `(e)` and protton `(p)` moving on straight parallel paths with the same velocity enter the region of uniform magnetic field.
The entry and exit of electron & proton in the magnetic field makes the same angle with `AB` as shown .
Therefore both will come out travelling in parallel paths.
The time taken by proton
` t_(p) = (distance)/(speed) = (arc)/( speed) = (a n gl e xx radius)/( speed) = (2 theta xx R_(p))/(v)`
` = ( 2 theta)/(v) xx(( m_(p)v)/(eB)) = ( 2 theta m_(p))/( eB)`
The time taken by electron is
` t_(e) = 2pi - 2 theta)R_(e))/(v) = ((2 pi - theta))/(v) ((m_(e)v)/(eB)) = (( 2 pi - 2 theta )m_(e))/( eB)`
Clearly ` t_(e)` is not equal to `t_(p)` as `m_(p) gtgt m_(e)`
:. (b) ,(d) are correct options