A slightly divergent beam of non-relatistic charged particles accelearated by a potential difference `V` propagates from a point `A` along the axis of a straight solenoid. The beacm is brought into focus at a distance `l` from the point `A` at two successive values of magnetic induction `B_(1)` and `B_(2)`. Find the spefic charge `q//m` of the particles.

Explanation

The charged particles will traverse a helical trajectroy and will be focussed on the axis after traversing a number of turns. Thus
`(l)/(v_(0)) = pi. (2pi m)/(q B_(1)) = (pi + 1) (2pi m)/(q B_(2))`
So, `(n)/(B_(1)) = (pi + 1)/(B_(2)) = (1)/(B_(2) - B_(1))`
Hence, `(l)/(v_(0)) = (2pi m)/(q(B_(2) - B_(1)))`
or, `(l^(2))/(2qV//m) = ((2pi)^(2))/((B_(2) - B_(1))^(2)) xx (1)/((q//m)^(2))`
or, `(q)/(m) = (8 pi^(2) V)/(l^(2) (B_(2) - B_(1))^(2))`