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Q.

A charged particle P leaves the origin with speed v = v0 at some inclination with the x-axis. There is a uniform magnetic field B along the x-axis. P strikes a fixed target T on the x-axis for a minimum value of B = B0. P will also strike T if

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a

B=2B0,v=2v0

b

B=2B0,v=v0

c

B=B0,v=2v0

d

B=B02,v=2v0

answer is A.

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Detailed Solution

Let d = distance of the target T from the point of projection. P will strike T if d is an integral multiple of the pitch. Pitch =2πmQBvcos⁡θ=kvBwhere k = constantInitially. pitch: d=kv0B0For the given options if pitch d′=d2,d3,d4,…, etc., then charge will hit the target.
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