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Q.

A charged particle $P$ leaves the origin with speed $v = v_{0}$ , 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 to a minimum value of $B = B_{0} P$ will also strike $T$ if

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a

Both are correct

b

$B = 2 B_{0}, v = 2 v_{0}$

c

Both are wrong

d

$B = 2 B_{0}, v = v_{0}$

answer is C.

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Detailed Solution

For minimum value of $B$ , it is colliding after one pitch. It will collide the target again if pitch is halved or remains same.

$P = (v \cos θ) (\frac{2 πm}{B q})$ or $P \propto \frac{v}{B}$

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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 to a minimum value of B=B0P will also strike T if