A electron cyclotron has a frequency of 2450 Hz and a magnet

[anthonyslvtr]

Homework Statement

A electron cyclotron has a frequency of 2450 Hz and a magnetic field strength of 50T.?

a) what's the speed of the electron?

b) what was the voltage on the electron gun which projected the electron into the cyclotron?

Homework Equations

Givens:
r=.4m
B=50T
f=2450Hz
q=e=-1.6E-19C
m(e)=9.1E-31kg

The Attempt at a Solution

For a) I used :

f=ω/(2pi)

and ω=v/r

to find v and got v = 616m/s

for b)

I used v = sqrt((2qV)/m) and got 1.08E-6Volts

just trying to see if I did this right...thanks

 

[mfb]

B=50T
f=2450Hz

At least one of those values has to be wrong. They just don't fit unless you have highly relativistic electrons, but then the .4m don't fit.
Both are strange, 50 Tesla is extremely strong and 2450 Hz is extremely low.

The approach you posted is fine if you have those values and use radius and frequency, but something is wrong with the problem statement.

 

[anthonyslvtr]

Yeah this was a homework problem from a lecture book my professor wrote. Not sure if he meant for them to be realistic quantities but that's what was given. If you say the approach is right for the values then that answers my question and I appreciate it.

 

[mfb]

Well, it is not right for all the given values. Let's demonstrate that with an example where it is easier to see:

"You go from town A to town B with a constant speed of 50 kilometers per hour. The towns are 500 kilometers apart. You start at 1 pm and arrive there at 3 pm the same day. How long did your journey take?"

The numbers are clearly inconsistent. You can say "well, between 1 pm and 3 pm are two hours, so the trip took two hours!" - but you can also calculate how long it takes to go 500 km with 50 kilometers per hour - 10 hours. Which answer is correct? There is no way to tell, because the problem statement is inconsistent.
Your problem statement has the same issue. There is more than one way to calculate the speed and injection voltage, and they lead to different answers because the given numbers are inconsistent. You calculated one answer, but it is not the only one.