What is the Magnetic Field Strength of a Magnetron at a Resonant Frequency?

[Hellphish]

Homework Statement

A magnetron is a microwave source in which a "bunch" of electrons travel on a circular orbit in a uniform magnetic field. As the electrons pass the electrodes, a high-frequency alternating voltage difference occurs. Suppose the resonant frequency is f = 2.82×10^10 s-1; that is, the electron period of revolution is T = 3.55×10^-11 s. What is the corresponding strength of the magnetic field?
The electron charge is -1.6E-19 C and the electron mass is 9.1E-31 kg.

Homework Equations

f=qv * b
where q is the charge, v is the velocity, and b is the magnetic field

The Attempt at a Solution

I think I need to set a centripetal force equal to the magnetic force. The only equation I know for centripetal force is f=m(v^2 / r) and I'm not sure how to solve that with the period. I'm really just not sure if I'm even going about this right or how I can solve for v and r. Any help would be appreciated.

 

[nrqed]

Homework Statement

A magnetron is a microwave source in which a "bunch" of electrons travel on a circular orbit in a uniform magnetic field. As the electrons pass the electrodes, a high-frequency alternating voltage difference occurs. Suppose the resonant frequency is f = 2.82×10^10 s-1; that is, the electron period of revolution is T = 3.55×10^-11 s. What is the corresponding strength of the magnetic field?
The electron charge is -1.6E-19 C and the electron mass is 9.1E-31 kg.

Homework Equations

f=qv * b
where q is the charge, v is the velocity, and b is the magnetic field

The Attempt at a Solution

I think I need to set a centripetal force equal to the magnetic force. The only equation I know for centripetal force is f=m(v^2 / r) and I'm not sure how to solve that with the period. I'm really just not sure if I'm even going about this right or how I can solve for v and r. Any help would be appreciated.

You are only missing one equation (which is quite simple). Consider a particel going in a circle of radius r. If it takes a time T to go around once, what is the speed of the particle?

 

[Hellphish]

Oh wow, I didn't even think of that. Thanks.