Question

A positive charge ${}^{\prime }{q}^{\prime }$ of mass ${}^{\prime }{m}^{\prime }$ is moving along the $+x$ axis. We wish to apply a uniform magnetic field $B$ for time $\Delta t$ so that the charge reverses its direction crossing the $y$ axis at a distance $d$. Then :

• A. $B=\frac{m\upsilon }{qd}$ and $\Delta t=\frac{\pi d}{\upsilon }$
• B. $B=\frac{m\upsilon }{2qd}$and$\Delta t=\frac{\pi d}{2\upsilon }$
• C. $B=\frac{2m\upsilon }{qd}$and$\Delta t=\frac{\pi d}{2\upsilon }$
• D. $B=\frac{2m\upsilon }{qd}$and$\Delta t=\frac{\pi d}{\upsilon }$

Answer 1

Answer: (C)

$R=\frac{d}{2}$
$\therefore Bqv=\frac{m{v}^2}{d/2}$
or, $B=\frac{2mv}{qd}$
Time interval for which a uniform magnetic field is applied
$\Delta t=\frac{\pi .\frac{d}{2}}{v}$
(particle reverses its direction after time At by covering semi circle).
$\Delta t=\frac{\pi d}{2v}$