Since T = 2πm/Be the period of revolution of the electron is independent of velocity and radius of path
For an electron moving in a uniform magnetic field, the force on the electron is given by
F = Bev where
Also, this magnetic force equals the centripetal force on the electron, F'
F' = mv²/r where
Since both forces are equal,
F = F'
Bev = mv²/r
Be = mv/r
We know that angular speed, ω = v/r. So,
Be = mω
Also, angular speed, ω = 2π/T where T = period of revolution of electron
So, Be = m2π/T
Making T subject of the formula, we have
T = 2πm/Be
so, since T = 2πm/Be the period of revolution of the electron is independent of velocity and radius of path
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