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 Fig. When a charged particle with charge q is accelerated through a potential difference V volt, then
`1/2 mv^2 = qV.....(i) " or " v = sqrt( (2qV)/(m) ) .....(i) `

`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 `sin theta = 1/R = lB sqrt( (q)/(2mV) )`
Here l = 0.1m, B = 0.1 tesla, `V =10^4` volt
`q = 2e = 2xx1.6xx10^(-19) = 3.2x10^(-19) = 3.2 xx 10^(-19)C` and `m= 6.4xx10^(-27) ` kg
` therefore sin theta = 0.1 xx 0.1 xx sqrt( (3.2 xx 10^(-19 ) )/(2 xx 6.4 xx 10^(-21) xx 10^4) ) = 1/2 " or " theta = 30^@`