A beam of protons with a velocity `4 xx 10^(5) m//sec` enters a uniform magnetic field of `0.4 T` at an angle of `37^(@)` to the magnetic field. Find the radius of the helical path taken by proton beam. Also find the pitch of helix.
`sin 37^(@) = 3//5 cos 37^(@) = 4//5`. `m_(p) ~= 1.6 xx 10^(-27) kg`.

Explanation

Radius of the helical path taken by the proton beam
`r=(m(vsintheta))/(qB)=1.2cm`
Time period `T=(2pir)/(vsintheta)=2.175xx10^(-7)s`
`therefore` pitch of the helix `p=vcostheta.T`
`impliesp=4xx10^(5)xx(1)/(2)xx2.175xx10^(-7)=4.35cm`