mriswith170wp

2023-01-28

A charged particle enters a uniform magnetic field with velocity vector at 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 will be

A) $\frac{p}{\sqrt{2}\pi}$

B) $\sqrt{2}p$

C) $\frac{p}{2\pi}$

D) $\frac{\sqrt{2}p}{\pi}$

A) $\frac{p}{\sqrt{2}\pi}$

B) $\sqrt{2}p$

C) $\frac{p}{2\pi}$

D) $\frac{\sqrt{2}p}{\pi}$

Fislisb0a

Beginner2023-01-29Added 3 answers

The correct option is c:

$\frac{p}{2\pi}$

$p=\frac{2\pi m}{Bq}(v\mathrm{cos}{45}^{\circ})=\frac{2\pi m}{Bq}(v\mathrm{sin}{45}^{\circ})$

$\frac{mv\mathrm{sin}{45}^{\circ}}{Bq}=\frac{p}{2\pi}=\text{radius of helix}$

$\frac{p}{2\pi}$

$p=\frac{2\pi m}{Bq}(v\mathrm{cos}{45}^{\circ})=\frac{2\pi m}{Bq}(v\mathrm{sin}{45}^{\circ})$

$\frac{mv\mathrm{sin}{45}^{\circ}}{Bq}=\frac{p}{2\pi}=\text{radius of helix}$

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