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

Step-by-step solution

The magnetic field inside a long solenoid is uniform and directed along its axis. B = ₀ n i When a particle of charge q and mass m is projected from the axis perpendicular to the magnetic field with speed v , it moves in a circular path. The radius of this circular path is given by: R = mv qB Since the particle is projected from the axis, the axis lies on the circumference of its circular trajectory. The maximum distance of the particle from the axis is equal to the diameter of its circular path, which is 2R . For