An electron moving with a kinetic energy of `1.5 xx 10^(3)` eV enters in a region of uniform magnetic field of induction `4 xx 10^(-3) Wb//m^(2)` at right angles to the direction of motion of the electron . The radius of circular path of the electron in the magnetic field is

Explanation

(1) The pitch p is the distance the electron travels parallel to the magnetic field `vec(B)` during one period T of circulation.
(2) The period T is given by for any nonzero angle between `vec(v)` and `vec(B)`.
Calculations : Using 28-12 and 28-9, we find
`p = v_(B)T = (v cos phi) (2pi m)/(|q|B)`.
Calculating the electron.s speed v from its kinetic energy, we find that `v = 2.81 xx 10^(6)m//s`, and so eq. 28-13 gives us
`p = (2.81 xx 10^(6)m//s) (cos 65^(@)) xx (2pi(9.11 xx 10^(-31) kg))/((1.60 xx 10^(-19)C)(4.55 xx 10^(-4)T))`
`= 9.16 cm`