A tightly-wound, long solenoid has n turns per unit length, a radius r and carries a current i. A particle having charge q and mass m is projected from a point on the axis in a direction perpendicular to the axis. What can be the maximum speed for which the particle does not strike the solenoid?

Explanation

Magnetic field `B = mu_(0) n i`, along axis of solenoid.
Since `v` is `_|_^(ar)` to `B`, particle moves in a circle of radius
`R = (mv)/(Bq) = (mv)/(mu_(0)niq)`
If particle does not strike solenoid
`R le (r )/(2)`
`(mv)/(mu_(0) niq) le ( r)/(2)`
`v le (mu_(0)niqr)/(2m)`
`v_(max) = (mu_(0)niqr)/(2m)`