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. The maximum speed of the particle for which the particle does not strike the solenoid is

Step-by-step solution

Magnetic force on the charged particle is given as F_ B =q(v B)=q v B Here, =90^ F_ B =q v B 90^ =q v B Since, the particle is projected perpendicular to the field, so its trajectory will be circular in nature, where necessary centripetal force =F_ B m v² r^ =q v B m v² ( r 2 ) =q v B ( r^ = r 2 ) v= q B r 2 m ...(i) Magnetic field inside the solenoid is given as, B= ₀ n I Substituting the value of B in Eq. (i), we get v= ₀ n I q r 2 m