A beam of protons moving with a velocity of `4 times 10^(5)ms^(-1)`, enters a uniform field of 0.3T at an angle of `60^(@)` to the direction of the magnetic field. Find (i) the radius of the helical path of the proton beam and (ii) pitch of the helix. (Mass of proton =`1.67 times 10^(-27)kg`, charge on proton `=1.6 times 10^(-19)C`).

Explanation

(i) `" "Bq(vsintheta)=(m(vsintheta)^(2))/r`
i.e., `" "r=(mvsintheta)/(qB)=(1.67 times 10^(-27) times 4 times 10^(5) times sin60^(@))/(1.6 times 10^(19) times 0.3)`
i.e., the radius of helix `=1.2 times 10^(-2)m.`
(ii) Pitch of helix `=(vcostheta)` (time period)
`" "=vcostheta times (2pim)/(qB)`
`" "=(4 times 10^(5) times cos60^(@) times 2 times 3.142 times 1.67 times 10^(-27))/(1.6 times 10^(-19) times 0.3)`
`" "=4.37 times 10^(-2)m`