Question

A particle of mass m and charge q is lying at the origin in a uniform magnetic field B directed along x-axis .At time t=0,it is given a velocity $v_o$ at an angle $\theta$ with the y-axis in the xy-plane.Find the coordinates of the particle after one revolution.

• A. $(\frac{\pi m{v}_{o}sin\theta }{Bq},0,0)$
• B. $(\frac{8\pi m{v}_{o}sin\theta }{Bq},0,0)$
• C. $(\frac{2\pi m{v}_{o}cos\theta }{Bq},0,0)$
• D. $(\frac{4\pi m{v}_{o}sin\theta }{Bq},0,0)$

Answer 1

Answer: (C)

$(\frac{2\pi m{v}_{o}cos\theta }{Bq},0,0)$

Path is helix and after one rotation only x-coordinate will change by a distance equal to pitch.
$\therefore x=p=\left(v_{o}cos\theta \right)(\frac{2\pi m}{Bq})$