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. `(sqrt(2)mK)/(qd)`

Answer

A

Explanation

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

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