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 $m$ and charge $q$ is projected with a velocity $v$ from a distance $d$ from the plane normal to the lines of induction. Then, the maximum velocity of projection for which the particle does not hit the plate is :

• A. $\frac{2Bqd}{m}$
• B. $\frac{Bqd}{m}$
• C. $\frac{Bqd}{2m}$
• D. $\frac{Bqm}{d}$

Answer 1

Answer: (B)

$\frac{Bqd}{m}$

Answer 2

The charged particle bends in a circle of radius $r$ $B q v \sin \frac{\pi}{2} =\frac{m v^{2}}{r}$ $\Rightarrow r =\frac{m v}{B q}$ The particle does not hit the plate if $r \leq d$ or $\frac{m v}{B q} \leq d$ or $v \leq \frac{B q d}{m}$ $\therefore v_{\max } =\frac{B q d}{m}$