A charged particle having kinetic energy `E` enters normally a region of uniform magnetic field between two plates `P_(1)` and `P_(2)` as shown in the figure. If the particle just misses hitting the plate `P_(2)`, then the magnetic field `B` in the region between the plates is

Options

A. `(2mE)/(q d)`
B. `(mE)/(q d)`
C. `(sqrt(mE))/(q d)`
D. `(sqrt(2mE))/(q d)`

Answer

D

Explanation

`R = (sqrt(2mK))/(Bq) = (sqrt(2m E))/(Bq)`
If particle just misses the plate `P_(2)`,
`R le d`
`(sqrt(2mE))/(Bq) le d`
`B ge (sqrt(2mE))/(qd)`
`B_(min) = (sqrt(2mE))/(qd)`