What is the radius of the path of an electron (mass `9xx10^(-31)" kg and charge "1.6xx10^(-19)C)` moving at a speed of `3xx10^(7)m//s` in a magnetic field of `6xx10^(-4)T` perpendicular to it ?
What is its frequency ? Calculate its energy in keV. `(1 eV = 1.6xx10^(-19)J)`.

Explanation

Using Eq. r=mv/qb we find
`r=mv//(qB)=9xx10^(-31)kg xx3xx10^(7) ms^(-1)//(1.6xx10^(-19)Cxx6xx10^(-4)T)`
`=26xx10^(-2)m=28.4cm`
`v=v/(2pi r)=1.68xx10^(7s`E=(1//2)mv^(2)=(1//2)9xx10^(-31)kg xx9xx10^(14)m^(2)//s^(2)=40.5xx10^(-17)J`
`~~4xx10^(-16)J=2.5 keV.`