Answer:
f=qB/2[tex]\pi[/tex]m
Explanation:
The cyclotron frequency is the number of revolutions the particle makes in one second. calculate the cyclotron frequency for this particle
solution
The Lorentz force [tex]F_{lorentz} =F_{centripetal}[/tex]
is the centripetal force
and makes the particles path to revolve in a circle:
qvB=mv^2/r
radius=r
m=mas of the particle
B=magnetic flux
q=quantity of charge
v=velocity of the particle
v=qBr/m
where v is the velocity of the particle
recall the velocity v=rω
v=2*Pi*f*r
[tex]2\pi *f*r[/tex]=qBr/m
f=qB/2[tex]\pi[/tex]m
the cyclotron frequency is therefore f=qB/2[tex]\pi[/tex]m
the period(the time it take to make a complete oscillation) will be the inverse of frequency
T=2[tex]\pi[/tex]m/qB
