Circularly Symmetrical Magnetic Field B Depends Only On

A circularly symmetrical magnetic field (B depends only on the distance from the axis), pointing perpendicular to the page, occupies the shaded region in Fig. 5.58. If the total flux (f B ∙ da) is zero, show that a charged particle that starts out at the center will emerge from the field region on a radial path (provided it escapes at all–if the initial velocity is too great, it may simply circle around forever). On the reverse trajectory, a particle fired at the center from outside will hit its target, though it may follow a weird route getting there.

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