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(C) The pitch $x$ of a helical path is given by the distance traveled along the magnetic field direction in one time period $T$: $x = v \cos 	heta \c

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$\frac{x}{2\sqrt{3}\pi}$

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(C) The pitch $x$ of a helical path is given by the distance traveled along the magnetic field direction in one time period $T$: $x = v \cos 	heta \cdot T = v \cos 	heta \cdot \frac{2\pi m}{qB}$.The radius $R$ of the helical path is given by: $R = \frac{mv \sin 	heta}{qB}$.Dividing the expression for $R$ by the expression for $x$:$\frac{R}{x} = \frac{mv \sin 	heta / qB}{2\pi mv \cos 	heta / qB} = \frac{\sin 	heta}{2\pi \cos 	heta} = \frac{	an 	heta}{2\pi}$.Given $	heta = 30^o$,we have $	an 30^o = \frac{1}{\sqrt{3}}$.Therefore,$R = x \cdot \frac{	an 30^o}{2\pi} = x \cdot \frac{1/\sqrt{3}}{2\pi} = \frac{x}{2\sqrt{3}\pi}$.

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

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