A beam of charged particles having kinetic energy `10^3eV` and containing masses `8xx10^(-27)kg` and `1*6xx10^(-26)kg`, emerges from the end of an accelerated tube. There is a plate at a distance `10^-2m` from the end of the tube and placed perpendicular to the beam. Calculate the magnitude of the smallest magnetic field which can prevent the beam from striking the plate.

Explanation

The motion of a charged particle is a transverse field is a circle of radius r given by
`r=(mv)/(Bq)=(sqrt(2mE_k))/(Bq)`
The particle will not hit the plate if `rled`
or `(sqrt(2mE_k))/(Bq)led` or `Bge(sqrt(2mE_k))/(qd)`
Now `(sqrt(2mE_k))/(qd)` will be maximum if m is maximum so,
`Bge(sqrt(2m_(max.)E_k))/(qd)`
or `Bge(sqrt(2xx1*6xx10^(-26)xx(10^3xx1*6xx10^(-19))))/(qxx10^-2)`
`=sqrt2/9xx1*6xx10^(-19)`
Since the charge on the particle is not given, we can assume, q=ne where `n=1, 2, 3..........`
so `Bge(sqrt2xx1*6xx10^(-19))/("ne")` or `Bge(sqrt2)/(n)tesla`, where `n=1, 2, 3.....`