Question

A particle of mass $m$ and positive charge $q$, moving with a uniform velocity $v$, enters a magnetic field $B$ as shown in the figure.
(a) Find the radius of the circular arc it describes in the magnetic field
(b) Find the angle subtended by the arc at the center
(c) How long does the particles stay inside the magnetic field?
(d) Solve the three parts of the above problems if the charge $q$ on the particle is negative.

Answer 1

The particles of mass is m and charge q is moving with a uniform velocity v. This particle is entering in a magnetic field. Then the radius of circular arc described by particle in magnetic field is

(a)

$qvB=\frac{m{v}^2}{r}$

$r=\frac{mv}{qB}$

(b) From the figure,

$\angle MAO=90$

$\angle NAC=90$

$\angle AOC=180-(\frac{\pi }{4}+\frac{\pi }{4})$

$=90$

(c) Distance covered by particle inside magnetic field

$l=r\theta$

$l=\frac{mv}{qB}\times \frac{\pi }{4}$

$=\frac{\pi mv}{4qB}$

$t=\frac{l}{v}=\frac{\pi m}{4qB}$

(d) if charge is negative then

$r=\frac{mv}{qB}$

Angle subtended will be

$180+(\frac{\pi }{4}+\frac{\pi }{4})$

$=270$

$t=\frac{3\pi m}{2qB}$