# The magnetron

1. Oct 22, 2009

### Wizardofwaz

1. The problem statement, all variables and given/known data
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 = 1.91×1010 s−1; that is, the electron period of revolution is T = 5.24×10-11 s. What is the corresponding strength of the magnetic field?
Set the centripetal force equal to the magnetic force. The electron charge is -1.6E-19 C and the electron mass is 9.1E-31 kg.

2. Relevant equations
mv^2/r= qv*b

3. The attempt at a solution

none i can't find away to find the radius or speed

2. Oct 22, 2009

### rock.freak667

So in

$$\frac{mv^2}{r}=BQv$$

does anything happen to cancel out?

Do you know a relation between some sort of velocity and period?

3. Oct 22, 2009

### Wizardofwaz

just one V is i am solving for b and the only thing i know is what is at the begging

4. Oct 22, 2009

### rock.freak667

good good. So now we have

$$\frac{mv}{r}=Bq$$

Right?

so do you know any other formula where 'something' is equal to v/r ?

5. Oct 22, 2009

### Wizardofwaz

kinetic engergy

1/2mv
______
r

6. Oct 22, 2009

### rock.freak667

Do you know of angular velocity?

7. Oct 22, 2009

### Wizardofwaz

ω = θ / t (2a)

where

t = time (s)

8. Oct 22, 2009

### rock.freak667

so if θ=s/r (s= arc length)

then ω=(s/r)/t = (s/t)/r

Since s is a distance, what does distance/time give?

9. Oct 22, 2009

### Wizardofwaz

velocity, but how do i find that out from what i know

10. Oct 22, 2009

### rock.freak667

Now if s/t=v

then ω=v/r right?

Now what is ω with what you have?

If ω is the angular displacement in one revolution/time taken to make one revolution, what is ω equal to?

11. Oct 22, 2009

### Wizardofwaz

so s=360 T= 5.24×10-11 s

12. Oct 22, 2009

### rock.freak667

ω=θ/T

Right right, we're reaching somewhere. In one revolution, how many radians does it rotate?

13. Oct 22, 2009

### Wizardofwaz

2pie

14. Oct 22, 2009

### rock.freak667

Nice! (2pi=2π)

so now ω=2π/T

so can we find ω now?

Can we replace v/r by ω in this formula?

$$\frac{mv}{r}=BQ$$

15. Oct 22, 2009

### Wizardofwaz

m*(2pi/t)/r= Bq

16. Oct 22, 2009

### Wizardofwaz

but how di i find r

17. Oct 22, 2009

### rock.freak667

no no

$$\omega= \frac{v}{r}=\frac{2\pi}{T}$$