• # question_answer A charged particles 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) $\frac{\sqrt{3}x}{2\pi }$

Pitch$X=\frac{2\pi m\upsilon \cos {{30}^{o}}}{qB}=\frac{2\pi m\upsilon }{qB}.\frac{\sqrt{3}}{2}$(1) Radius $r=\frac{m\upsilon \sin {{60}^{o}}}{qB}=\frac{m\upsilon }{2qB}$                  (2) From Eqs. (1) and (2), we get $r=\frac{x}{2\sqrt{3}\pi },$which is choice [c]. Hence, the correction option is [c].