Question

A particle of mass $m$ and positive charge $q$, moving with a uniform velocity $v$, enters a magnetic field $B$ as shown in figure. $\left(a\right)$ Find the radius of the circular arc it describe in the magnetic field. $\left(b\right)$ Find the angle subtended by the arc at the centre. $\left(c\right)$ How long three parts of the above problem if the charge $q$ on the particle is to be negative.

Answer 1

(i)Magnetic Force = centripetal force

$BqV=\frac{M{V}^2}{r}$

$r=\frac{MV}{Bq}$

(ii) From the figure, angle subtended by arc is $\frac{\pi }{4}+\frac{\pi }{4}=\frac{\pi }{2}$

(iii) Angle subtended when charge is negative is $(2\pi -\frac{\pi }{2})=\frac{3\pi }{2}$

Angular velocity is constant $\omega$

$\omega =\frac{\pi /2}{T_q}=\frac{3\pi /2}{T_{-q}}$

$\Rightarrow T_{-q}=3T_q$

Time required by negative charge is three times the time required by positive charge.