Question

A charged particle enters a uniform magnetic field with velocity that makes an angle of ${45}^{\circ }$ with the magnetic field. The pitch of the helical path followed by the particle is $p.$ The radius of the helix is

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

Answer 1

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

The pitch $p$ of the helical path is given by

$p=\frac{2\pi mv\cos \theta }{qB}$

$\Rightarrow p=\frac{2\pi m}{qB}\left(v\cos {45}^{\circ }\right)=\frac{2\pi m}{qB}\left(v\sin {45}^{\circ }\right)$

$\because r=\frac{mv\sin \theta }{qB}$

$\Rightarrow p=r\times 2\pi$

$\Rightarrow r=\frac{p}{2\pi }$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.