In a chamber, a uniform magnetic field of 8.0 G is maintained. An electron with speed of `4.0 times 10^(6)ms^(-1)` enters the chamber in a direction normal to the field.
(a) Describe the path of the electron.
(b) What is the frequency of revolution of the electron?
(c) What happens to the path of electron if it progessively loses its energy due to collisions with the atoms or molecules of the environment?

Explanation

Given : `B=8 times 10^(-4)T, v=4 times 10^(6)ms^(-1)`.
`theta=90^(@),m_(e)=9.1 times 10^(-31)kg`.
(a) The path of the electron is circular of radius `r=(mv)/(eB)`
`" "=(9.1 times 10^(-31) times 4 times 10^(-6))/(1.6 times 10^(-19) times 8 times 10^(-4))m`
`" "r=2.84 times 10^(-2)m.`
(b) `" "T=(2pir)/v`
`" "=(2 times 3.14 times 2.84 times 10^(-2))/(4 times 10^(6))`
i.e., `" "T=4.46 times 10^(-2-6)s`
`" "T=4.46 times 10^(-8)s`
`" Frequency"=1/T=1/(4.46 times 10^(-8))=0.224 times 10^(8)Hz`
i.e., `" Frequency" f=2.24 times 10^(7)Hz.`
The frequency is independent of the size of the orbit or energy.
(c) The electrons will follow either a helical or a spiral path.