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A charged particle enter a uniform magnetic field with velocity vector making an angle of 45^{\circ} with the magnetic field. The particle describes a helical path of trajectory of pitch 'a'. The radius of the helix be

Option: 1

\frac{a}{\pi}


Option: 2

\frac{2 a}{\pi}


Option: 3

\frac{a}{2 \pi}


Option: 4

\frac{a}{3 \pi}


Answers (1)

best_answer

\text { Pitch } a^{\prime}=\frac{2 \pi m v \cos 45^{\circ}}{q B}=\frac{2 \pi m v}{q B}: \frac{1}{\sqrt{2}} \text { (1) }

and Radius (R) = \frac{m v \sin 45^{\circ}}{q B}

=\left(\frac{m v}{q B}\right) \frac{1}{\sqrt{2}}

=\left(\frac{\sqrt{2} a}{2 \pi}\right) \frac{1}{\sqrt{2}} \cdot \text { (from 1) }

=\frac{a}{2 \pi}

 

 

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