An `alpha-`particle is accelerated by a potential difference of `10^4 V.` Find the change in its direction of motion, if it enters normally in a region of thickness 0.1 m having transverse magnetic induction of 0.1 tesla. (Given: mass of `alpha-`particle `6.4xx10^(-27)`kg).

Explanation

The situation is shown in Figure. When a charged particle wit charge `q` is accelerated through a potential difference `V` volt, then
`(1)/(2)mv^(2)=qV ...(i) (or)v=sqrt(((2qV)/(m))) ...(i)`

`ul bar(alpha-"particle in magnetic field moves in a circle of radius R which is given by" )`
`R=(mv)/(qB) or R=(1)/(B)sqrt(((2mV)/(q))) ....(ii)`
The change in direction of `alpha-` particle `(theta)` from figure is given by `Sintheta=(l)/(R)=lB sqrt(((q)/(2mV)))`
Here `l=0.1m,B=.1 tesla,V=10^(4) vol t`
`q=2e=2xx1.6X10^(-19)=3.2xx10^(-19)C`
and `m=6.4xx10^(-2)kg`
`:. sin theta=0.1xx0.1xxsqrt(((3.2xx1-^(-19))/(2xx6.4xx10^(-27)xx10^(4))))=(1)/(2) or theta=30^(@)` .