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A problem with a magnetic field and a revolving stick

  1. Nov 9, 2006 #1
    Helle there!
    Elektrodynamics is giving me a hard time. I have been trying to figure the following question out by using textkooks like Haliday, Schaum's Outline and even my professor's script ;)
    But unfortunately, I do not know how to solve it.

    Problem:

    A stick of length 0,1 m is revolving around one of its ends in a constant magnetic field of B=(0;0;1) mT. The stick's angular velocity is [tex]\omega=(0;0;1) s^1[/tex].
    What is the voltage between the two ends?
    (5 microV).

    Since I have absolutely no clue, I would appreciate if someone could give me a hint where to start and lead me in a few steps to the result.

    Many thanks in advance to this great community!
     
  2. jcsd
  3. Nov 9, 2006 #2

    OlderDan

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    You have probably already done the problem of finding the emf of a stick sliding on a rectangular loop of wire. Does that give you any ideas?
     
  4. Nov 9, 2006 #3
    Let's see if I am getting close:

    According to Faraday's Law, the magnetic flux is [tex]\phi_b= BA[/tex] when B is normal to the surface A.
    My problem here is that I first have to get the surface which the magnetic lines go through.
    l=length of the stick
    The surface of one radiant is [tex]A_{rad}=\frac{\pi l^2}{2\pi}=\frac{l^2}{2}[/tex]
    with that I get the surface related to the time:
    [tex]A(t)=\frac{l^2\omega t}{2}[/tex]

    So the magnetic flux is
    [tex]\phi_B=\frac{ Bl^2\omega t}{2}[/tex]

    And the EMF is
    [tex]U_{ind}=\frac{\delta}{\delta t}\frac{ Bl^2\omega t}{2}=\frac{ Bl^2\omega}{2}= 0.05 microVolts [/tex]

    What am I missing? Is this even close?
     
    Last edited: Nov 9, 2006
  5. Nov 9, 2006 #4

    OlderDan

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    You are just missing the [itex] \omega t [/itex] in a couple of places (flux and derivative of flux) but you got it back in the end.
     
  6. Nov 9, 2006 #5
    latex was leaving them out. Now they are there. Sorry about that ;)
    and I got confused by the units. But thank you very much for your help!
    I am soo glad I finally figured it out! Right in time for the class tomorrow morning ;)
     
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