An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi infinite region of uniform magnetic field perpendicular to the velocity.
Which of the following statement(s) is /are true?

Options

A. They will never come out of the magnetic field region.
B. They will come out travelling along parallel paths.
C. They will come out at the same time.
D. They will come out at different times.

Answer

B, D

Explanation

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