Question

A beam of protons with a velocity $4\times {10}^5$m/s enters a uniform magnetic field of $0.3$ tesla at an angle ${60}^o$ to the magnetic field. Find the radius of the helical path taken by the proton beam. Also find the pitch of the helix(which is the distance travelled by a proton in the beam parallel to the magnetic field during one period of rotation).

Answer 1

For circular motion, $F=qvB\sin \theta =\frac{m{v}^2}{r}$

$⟹r=\frac{mv}{qB\sin \theta }$

$⟹r=\frac{1.67\times {10}^{-27}\times 4\times {10}^5\times 2}{1.6\times {10}^{-19}\times 0.3\times \sqrt{3}}$

$⟹r=1.6\times {10}^{-2}m=1.6cm$

Pitch, $P=v\cos \theta \times T$

$T=\frac{2\pi r}{v\sin \theta }$

$⟹P=\frac{2\pi r}{\tan \theta }=\frac{2\times \pi \times 1.6\times {10}^{-2}}{\sqrt{3}}$

$⟹P=5.8\times {10}^{-2}m=5.8cm$