Question

A charged particle enters a uniform magnetic field with velocity vector at an angle of ${45}^o$ with the magnetic field. The pitch of the helical path followed by the particle is $p.$ The radius of the helix will be

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

Answer 1

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

Pitch of the helix is product of velocity component along the magnetic field and the time period $T.$

$p=\frac{2\pi m}{Bq}\left(v\cos {45}^o\right)$

$=\frac{2\pi m}{Bq}\left(v\sin {45}^o\right)$

$\therefore r=\frac{mv\sin {45}^o}{Bq}$

$r=\frac{Psin{45}^0}{Bq}$

$\therefore p=2\pi r$

$=\frac{p}{2\pi }=$ radius of helix