Question

A charged particle enters a uniform magnetic field with velocity vector making an angle of ${30}^{\circ }$ with the magnetic field. The particle describes a helical trajectory of pitch x. The radius of the helix is

• A. $\frac{x}{2\pi }$
• B. $\frac{x}{2\sqrt{2}\pi }$
• C. $\frac{x}{2\sqrt{3}\pi }$
• D. $\frac{\sqrt{3}x}{2\pi }$

Answer 1

The correct option is C $\frac{x}{2\sqrt{3}\pi }$

Radius,$R=\frac{mvsin{30}^{\circ }}{qB}$
$=\frac{mv}{2qB}$
Pitch,
$x=\frac{2\pi mvcos{30}^{\circ }}{qB}$
$=\frac{\sqrt{3}\pi mv}{qB}$
$x=\sqrt{3}\pi \left(2R\right)$
$\Rightarrow R=\frac{x}{2\sqrt{3}\pi }$