A particle of charge $q$, mass $m$ enters in a region of magnetic field $B$ with velocity $V_0 \widehat i$. Find the value of $d$ if the particle emerges from the region of magnetic field at an angle $30^o$ to its ititial velocity:-
Diffcult
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As the initial velocity of the particle is perpendicular to the field, the particle will move along the arc of a circle as shown (fig). If $r$ is the radius of the circle, then
$\frac{m v_{0}^{2}}{r}=q v_{0} B_{0} \Rightarrow r=\frac{m v_{0}}{q B_{0}}$
Also, from geometry, $L=r \sin 30^{\circ} \Rightarrow r=2 L$
or $L=\frac{r}{2}=\frac{m v_{0}}{2 q B_{0}}$
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