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  4. A beam of protons with speed 4 × 105 ms -1 enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. The pitch of the resulting helical path of protons is close to: (Mass of the proton =1.67 × 10-27 kg, charge of the proton =1.69 × 10-19 C

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Q. A beam of protons with speed $4 \times 10^{5} ms ^{-1}$ enters a uniform magnetic field of $0.3 T$ at an angle of $60^{\circ}$ to the magnetic field. The pitch of the resulting helical path of protons is close to: (Mass of the proton $=1.67 \times 10^{-27} kg$, charge of the proton $=1.69 \times 10^{-19} C$

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Solution:

Pitch $=\frac{2 \pi m }{ qB } v \cos \theta$
Pitch $=\frac{2(3.14)\left(1.67 \times 10^{-27}\right) \times 4 \times 10^{5} \times \cos 60}{\left(1.69 \times 10^{-19}\right)(0.3)}$
Pitch $=0.04 m =4 cm$