=255 ns
The centripetal force of circular motion must be equal to the magnetic force:
qvB = mv^2/r
=> v/r = Bq/m
Remember angular speed is:
ω = v/r = 2π/T
Where T is the period of a single orbit.
Thus:
2π/T = B(q/m)
=> T = 2π/(B(q/m))
q/m = 1.76x10^11 C/kg for an electron, and
B = 1.4 G = 1.4 (1x10^-4) T = 1.4x10^-4 T (T in this case is obviously the SI unit Tesla, unrelated to the period T, sorry 'bout that).
So we have the period:
T = 2π/(1.4x10^-4 x 1.76x10^11)
= 2.55 x10^-7 s
= 255 ns .
Therefore period is 255 ns
T = 2π/(1.4x10^-4 x 1.76x10^11) = 2.55x10^-7 s
Explanation
1. The centripetal force must be equal.
The centripetal force of circular motion must be equal to the magnetic force hence:
qvB = mv^2/r
v = (qBr)/m
Since angular speed is: ω = v/r = 2π/T
2. v = 2πr/T
Where T is the period of a single orbit. Thus substituting equation 2 in equation 1 and making T the subject:
3. T = 2π/(B(q/m))
Substituting B = 1.4 G => 1.4 x 10^-4 T
and q/m = 1.76x10^11 C/kg in equation 3
T = 2π/(1.4x10^-4 x 1.76x10^11) = 2.55x10^-7 s
