Two charged plates `A` and `B` are at the same electrical potential, and parallel and separated by a distance `d.` A unifrom magnetic induction field `B` acts perpendicular to plane of paper (and parallel to plates)n between the plates. Particels,each with charge `q`, mass `m` and kinetic energy `K` are shot throgh a hole in `A` directly towards `B`, each particle entering the hole perpendicular to `A`, An ammeter `AM` connected to an electrical network is connected to `B` and measures the current collected by the plate `B`, as the particles hit it. The limited value of the fied `B` for which the ammeter will stop showing a current is

Options

A. `(sqrt(2mK))/(qd)`
B. `(sqrt(3mK))/(qd)`
C. `(sqrt(mK))/(qd)`
D. `(2sqrt(mK))/(qd)`

Answer

A

Explanation

Obviously for the limiting field, the path of the particles will be semi`-` circular arcs of radius equal to the distance between the plates.

`(i.e.)` radius r of circular path is `r=d`
Now for a particle of charge q, mass m and kinetic energy K, where velocity `upsilon=u upsilon=sqrt((2K)/(m))`
r is `r=(m upsilon)/(qB)=(m)/(qB)sqrt((2K)/(m))`
Hence, `B=(m)/(qd)sqrt((2K)/(m))=(sqrt(2mK))/(qd)`