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

  1. Jun 11, 2009 #1
    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. jcsd
  3. Jun 11, 2009 #2

    Cyosis

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    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?
     
  4. Jun 11, 2009 #3
    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?
     
  5. Jun 11, 2009 #4

    Cyosis

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    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 [itex]\omega=v/r[/itex]. 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?

    [tex]
    \frac{v}{r}=\frac{eB}{m}
    [/tex]

    Is correct.
     
  6. Jun 11, 2009 #5
    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.
     
  7. Jun 11, 2009 #6

    Cyosis

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

    You're welcome.
     
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