Question

A plane metallic sheet is placed with its face parallel to lines of magnetic induction B of a uniform field.A particle of mass 2m and charge q is projected with a velocity v from a distance d from the plane normal to lines of induction. Then the maximum velocity of projection for which the particle does not hit the plane is,​

Answer 1

Explanation:

The charged particle bends in a circle of radius r. \[Bqv\sin \frac{\pi }{2}=\frac{m{{v}^{2}}}{r}\] \[\Rightarrow \] \[r=\frac{mv}{Bq}\] The particle does not hit the plate if \[r\le d\] Or \[\frac{mv}{Bq}\le d\] Or \[v\le \frac{Bqd}{m}\] \[\therefore \] \[{{v}_{\max }}\le \frac{Bqd}{m}\]