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A beam of protons with a velocity 4 x 10 5 m / sec enters a uniform magnetic field of 0.3 tesla at an angle of 60° to the magnetic field. 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 )

A beam of protons with a velocity 4 x 105 m / sec enters a uniform magnetic field of 0.3 tesla at an angle of 60° to the magnetic field. 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 )

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
Hello Student,
Please find the answer to your question
v1 is responsible for horizontal motion of proton
v2 is responsible for circular motion of proton
∴ mv22 / r = qv2 B
r = mv2 /qB = 1. 76 x 10-27 x 4 x 105 x √3 / 1. 6 x 10-19 x 0.3 x 2 = 0.012 m
Pitch of helix = v1 x T
Where T = 2πr / v2­ = 2πr / v sin θ
⇒ Pitch of helix = v cos θ x 2πr / v sin θ
= 2 πr cosθ = 2x 3.14 x 0.012 x cot 60° = 0.044 m
Thanks
Navjot Kalra
askIITians Faculty

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