Question

A charged particle enters into 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. $\frac{\sqrt{2p}}{\pi }$

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 $T$.

Pitch: $p=\frac{2\pi m}{qB}v\cos \theta =\frac{2\pi P\cos \theta }{qB}=\frac{2\pi P\cos {45}^0}{qB}$

Here $P$ denotes momentum

Radius of the helix$:r=\frac{mv\sin \theta }{qB}=\frac{mv\sin {45}^0}{qB}=\frac{P\sin {45}^0}{qB}$

$\therefore p=2\pi r$

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