Question

The cyclotron frequency is the number of revolutions the particle makes in one second. calculate the cyclotron frequency for this particle

Answer 1

Answer:

f=qB/2$\pi$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  $F_{lorentz} =F_{centripetal}$

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

$2\pi *f*r$=qBr/m

f=qB/2$\pi$m

the cyclotron frequency is therefore f=qB/2$\pi$m

the period(the time it take to make a complete oscillation) will be the inverse of frequency

T=2$\pi$m/qB