Two uncharged parallel plates A and B are at the same electrical potential, and separated by a distance d. A uniform magnetic induction field B acts perpendicular to plane of paper (and parallel to plates) between the plates. Particles, each with charge q, mass m and kinetic energy
K are shot through a hole in A directly towards B, particle entering the hole perpendicular to plate A. An ammeter A_m connected to B and measures the current collected by the plate B, as the particles hit it. The limiting value of the field B for which the ammeter will stop showing a current is

Question

Infinity Learn · Accepted Answer

Obviously for the limiting field, the path of the particles will be $$semi-circular$$ arcs of radius equal to the distance between the plates.i.e., radius r of circular path is r $$=$$ d.Now, for a particle of charge q, mass m and kinetic energy K, where velocity $$v=2km$$, the radius r is $$r=d=mvqB$$ $$=$$  $$mqB2km$$ Hence,  $$B=$$  $$2Kmqd$$

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