A particle of mass m and charge q moves with a constant velocity v along the positive $$x-direction$$. It enters a region containing a uniform magnetic field B directed along the negative $$z-direction$$, extending from x $$=$$ a to x $$=$$ b. The minimum value of v required so that the particle can just enter the region x b, is

Question

A particle of mass m and charge q moves with a constant velocity v along the positive $$x-direction$$. It enters a region containing a uniform magnetic field B directed along the negative $$z-direction$$, extending from x $$=$$ a to x $$=$$ b. The minimum value of v required so that the particle can just enter the region x > b, is

Infinity Learn · Accepted Answer

In the figure, the $$z-axis$$ points out of the paper, and the magnetic field is directed into the paper, existing in the region between PQ and RS. The particle moves in a circular path of radius r in the magnetic field. It can just enter the region x > b  for r ≥ b−aNow,   $$r=mvqB$$  ≥  b−aor     v ≥  qb−aBm  ⇒   vmin  $$=$$  qb−aBm

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