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A particle of mass m and charge q moves ...

A particle of mass m and charge q moves with a constant velocity v along the positive x-direction. If entres a region of uniform magnetic field B directed alon the negative z-direction and extanding from `x=a` to `x=b`. Find the minimum value of v so that the particle can just enter the region `x gt b`.

Text Solution

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When a charged particle entes a uniform magnetic field directed perpendicular to its velocity, then it moves in a circular path. Let r be radius of the circular path.
If `(b-a) ger` then the partical cannot enter the region `x gt b`. So to enter the region `x gt b`, r should be greater than `(b-a)`.
Now we know, `r=(mv)/(Bq)`
So, `(mv)/(Bq) gt (b-a) :. v gt (q(b-a)B)/(m)`
So the minimum value of v is `(q(b-a)b)/(m)`
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