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A charged particle P leaves the origin w...

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 for a minimum value of `B=B_0`. P will also strike T if

A

`B = 2B_(0), v = 2 v_(0)`

B

`B = 2B_(0), v = v_(0)`

C

`B = B_(0), v = 2v_(0)`

D

`B = B_(0)//2, v = 2v_(0)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
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 `= (2 pi (m)/(QB)) V cos theta`. (Hence, m, Q and `theta` are constants)
Pitch `= k ((v)/(B))` (where k = constant)
Initially, `d = k ((V_(0))/(B_(0)))`
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