Calculating Magnetic Field Strength of Magnetron

[Wizardofwaz]

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 = 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.

Homework Equations

mv^2/r= qv*b

The Attempt at a Solution

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

 

[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?

 

[Wizardofwaz]

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

 

[rock.freak667]

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

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 ?

 

[Wizardofwaz]

kinetic engergy

1/2mv
______
r

 

[rock.freak667]

kinetic engergy

1/2mv
______
r

no no, I went a bit over your head there.

Do you know of angular velocity?

 

[Wizardofwaz]

ω = θ / t (2a)

where

ω= angular velocity (rad/s)

θ = angular displacement (rad)

t = time (s)

 

[rock.freak667]

ω = θ / t (2a)

where

ω= angular velocity (rad/s)

θ = angular displacement (rad)

t = time (s)

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?

 

[Wizardofwaz]

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

 

[rock.freak667]

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

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?

 

[Wizardofwaz]

so s=360 T= 5.24×10-11 s

 

[rock.freak667]

so s=360 T= 5.24×10-11 s

ω=θ/T

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

 

[Wizardofwaz]

2pie

 

[rock.freak667]

2pie

Nice! (2pi=2π)

so now ω=2π/T


so can we find ω now?


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

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

 

[Wizardofwaz]

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

 

[Wizardofwaz]

but how di i find r

 

[rock.freak667]

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

no no

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

so your formula changes to?