What is the radius of the path of an electron (mass `9 xx 10^(-31)` kg and charge `1.6 xx 10^(-19)C)` moving at a speed of `3 xx 10^(7)m//s` in a magnetic field of `6 xx 10^(-4)T` perpendicular to it? What is its frequency? Calculate its energy in `keV.(1eV = 1.6 xx 10^(-19)J)`.

Explanation

Radius, `r=mv//(qB)`
`= 9.1 xx 10^(-31)` kg `xx3 xx 10^7 ms^(-1)//(1.6 xx 10^(-19) C xx 6 xx 10^(-4) T)` = 20 cm
`v=v//(2pir) = 1.7 xx 10^7` Hz
`E = (1//2) mv^2 = (1//2) 9xx 10^(-31) kg xx 9 xx 10^(14) m^2 //s^2`
`= 40.5 xx 10^(-17) J = 4 xx 10^(-16) J = 2.5` KeV.