A beam of protons with a velocity of `4 X 10 ^5 ms^(-1)` enters a uniform magnetic field of 0.3 T. The velocity makes an angle of `60^@` with the magnetic field. Find the radius of the helicla path taken by the proton beam and the pitch of the helix.

A beam of protons with a velocity of `4 X 10 ^5 ms^(-1)` enters a unif

1.	A beam of protons with a velocity of `4 X 10 ^5 ms^(-1)` enters a uniform magnetic field of 0.3 T. The velocity makes an angle of `60^@` with the magnetic field. Find the radius of the helicla path taken by the proton beam and the pitch of the helix.
Answer» Velocity component along the field `V_(\|\|) = 4 xx 10^(5) xx cos 60^(@)` `= 2 xx 10^(5) m//s` and `v_(bot) = (4 xx 10^(5)) sin 60^(@) = 2 sqrt3 xx 10^(5) m//s` Proton will describe a circle in plane perpendicular to magnetic field with radius `r = (mv_(bot))/(qB) = ((1.67 xx 10^(-27) kg) xx (2 sqrt3 xx 10^(5) m//s))/((1.6 xx 10^(-19) C) xx (0.3 T))` `= 1.2 cm` Time taken to complete one revolution is `T = (2pi r)/(v_(bot)) = (2 xx 3.14 xx 0.012)/(2 sqrt3 xx 10^(5) m//s)` Because of `v_(\|\|)` protons will also move in the direction of magnetic field. Pitch of helix `= v_(\|\|) xx T` `= (2 xx 10^(5) xx 2 xx 3.14 xx 0.012)/(2 sqrt3 xx 10^(5) m//s)` `= 0.044 = 4.4 cm`

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A beam of protons with a velocity of `4 X 10 ^5 ms^(-1)` enters a uniform magnetic field of 0.3 T. The velocity makes an angle of `60^@` with the magnetic field. Find the radius of the helicla path taken by the proton beam and the pitch of the helix.

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