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

Options

A. `B=2B_0 ,v=2v_0`
B. `B=2B_0 ,v=v_0`
C. `B=B_0,v=2v_0`
D. `B=(B_0)/2 ,v=2v_0`

Answer

(a,b)

Explanation

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=((2pim)/(QB)) v cos theta`
`=k(v/B)`
where k=constant
Initially, pitch: `d=k((v_0)/(B_0))` For the given options if pitch `d'=d/2,d/3,d/4,`.........,etc. then charge
will hit the target.