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An uniform beam of positivley charged...

An uniform beam of positivley charged particles is moving with a constant velocity parallel to another beam velocity in opposite direction separated by a distance d the variation of magnetic field B along a perpendicular line draw between the two beams is best represented by

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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.