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A long uniform cylindrical beam of radiu...

A long uniform cylindrical beam of radius R consists of positively charged particles each of charge q, mass m and velocity V along positive x direction. The axis of the beam is the x-axis. The beam is incident on a region having magnetic field in y-z plane. The magnetic field in the region is confined to `0lexleDeltax(Deltax "is small").` The field lines are circular in yz plane as shown. The magnitude of the field is given by
`B = B_(0) r` where `B_(0)` is a constant and r is distance from the origin.

Show that this magnetic field acts as a converging lens for the ion beam and obtain the expression for focal length. Neglect the divergence in the beam caused due to electromagnetic interaction of the charge particles.

Text Solution

Verified by Experts

The correct Answer is:
`f=(mV)/(qB_(0)Deltax)`
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