A beam of protons with a velocity 4 x 10⁵ m/s enters a uniform magnetic field of 0.3 T at an angle 60° to the magnetic field. Find the radius of the helical path taken by the proton beam. Also find the pitch of the helix mp = 1.67 x 10^–27 kg.

Given, the velocity of protons, v = 4 x 10⁵ m/s
Uniform magnetuc field, B = 0.3 T
Angle made by particle with magnetic field = 60^o
The magnetic force will act like centripetal force.
Therefore,

Using the formula,

r = \frac{mv}{qB}

r = \frac{1.67 \times 10^{- 27} \times 4 \times 10^{5} \sin 60 °}{1.6 \times 10^{- 19} \times 0.3} = 1.2 \times 10^{- 2} = 1.2 cm

Pitch is the distance moved along the magnetic field in one rotation.

Therefore,

T = \frac{2 πr}{v \sin θ} = 2.175 \times 10^{- 7} S

∴

P = v \cos θ . T

= 4 \times 10^{5} \times \frac{1}{2} \times 2.175 \times 10^{- 7} = 4.35 cm

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A beam of protons with a velocity 4 x 10⁵ m/s enters a uniform magnetic field of 0.3 T at an angle 60° to the magnetic field. Find the radius of the helical path taken by the proton beam. Also find the pitch of the helix mp = 1.67 x 10^–27 kg.