Question

A charged particle enters a uniform magnetic field with velocity vector at an angle $30°$ with the magnetic field. The pitch of the helical path is ${}^{\prime }{p}^{\prime }$, the radius of helix will be

• A. $\frac{p}{\pi \sqrt{3}}$
• B. $\frac{p\pi }{2\sqrt{3}}$
• C. $\frac{p}{2\pi }$
• D. $\frac{p}{2\pi \sqrt{3}}$

Answer 1

The correct option is D $\frac{p}{2\pi \sqrt{3}}$


The average radius of the helix is given by
$r=\frac{M{v}_y}{qB}$
The pitch is given as
$p=\frac{2\pi M}{qB}{v}_x$
So, we have
$\frac{r}{p}=\frac{\frac{M{v}_y}{qB}}{\frac{2\pi M{v}_x}{qB}}=\frac{v_y}{2\pi v_x}=\frac{v\sin {30}^{\circ }}{2\pi v\cos {30}^{\circ }}$

$\therefore r=\frac{p}{2\sqrt{3}\pi }$
Hence, option $\left(B\right)$ is correct.