# Expression: Number of revs per second of electron entering a region of magnetic field

1. Jun 11, 2009

### FelixISF

1. The problem statement, all variables and given/known data
An electron of speed v enters a region of magnetic field B directed normally to its velocity and is deflected into a circular path.
Find an expression for the number of revolutions per second the electron will make. If the electron is replaced by a proton, how does your answer change?

2. Relevant equations
revolutions per second = angular velocity = v/r
I also know, that the answer should be f=eB/2pi(m)
F=eBv sin(theta), where e=charge of an electron

3. The attempt at a solution

I figured, that one needs to replace v by 2(pi)r, which is angular velocity.
So, ma=eB2(pi)r

From then, I do not know how to go farther, please help with your suggestions or even solutions!

Thank you before hand!

2. Jun 11, 2009

### Cyosis

Re: expression: Number of revs per second of electron entering a region of magnetic f

In this case the magnetic field forces the particle into a circular orbit. There is a general name and expression for a force that keeps a particle in an orbit. Do you know what it is?

3. Jun 11, 2009

### FelixISF

Re: expression: Number of revs per second of electron entering a region of magnetic f

Well, this force is certainly known as centripetal force :)

I expect that I need to set up an equation of magnetic force and centripetal force and solve it for v/r which is the angular velocity or the revolutions per second.
The problem is, that I get the following answer:

v/r = eB/m...
now my book says, that the answer is f=eB/2(pi)m
where does the 2(pi) come from. any suggestions?

4. Jun 11, 2009

### Cyosis

Re: expression: Number of revs per second of electron entering a region of magnetic f

You're correct about the centripetal force and you're also correct that $\omega=v/r$. Now note that the answer in the book does not calculate omega, but it calculates f, frequency. Do you know how omega and f are related?

$$\frac{v}{r}=\frac{eB}{m}$$

Is correct.

5. Jun 11, 2009

### FelixISF

Re: expression: Number of revs per second of electron entering a region of magnetic f

omega = 2(pi)f

Thank you so much for your support, I finally got the answer.

I am new to the forum, and will recommend it among my friends, as I find it highly effective.

6. Jun 11, 2009

### Cyosis

Re: expression: Number of revs per second of electron entering a region of magnetic f

You're welcome.

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