Pathfinder Magnetism BYU 8

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In a hollow rigid cylinder of radius R gravity is absent and a uniform magnetic field of induction B is established everywhere parallel to the axis of the cylinder. The cylinder is made of an insulating material and is fixed by some external means. A very small ball of mass m and charge q is projected normally from a point P on the inner surface of the cylinder. If the ball returns to the point P after a certain number of elastic collisions with the cylinder, find range of velocity v of projection of the ball.