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 $\frac{p}{n\pi }$. Find $n$.

• A. 2.00
• B. 2
• C. 2.0

Answer 1

Answer: (A), (B), (C)

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

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

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

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

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

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