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Electromagnetism question, what formula

  1. Dec 15, 2009 #1

    fluidistic

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    I'd like to know what formula to use in order to find the following :
    Imagine a uniform magnetic field. I am moving with a constant velocity perpendicularly through it. Do I see only an electric field? A magnetic field? Both? Or both of them?
    What if I move in the sense of the magnetic field with a constant velocity?

    What if my velocity changes with time?
    What if, instead of the magnetic field, it's an electric field?

    I do not expect the answer to all these questions, rather I'd like a formula to check it out myself. But if you have to say a word or even give the answer, I'm all ears.
    Thanks in advance.
     
  2. jcsd
  3. Dec 15, 2009 #2

    Pythagorean

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    What velocity are you traveling with? If it's much lower than the speed of light:

    9cab6787646062d6e658cd1e83ad468f.png
     
  4. Dec 15, 2009 #3

    fluidistic

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    Thanks a lot. I'm a bit confused, if B is uniform, if I move, [tex]\frac{\partial B}{\partial t}=0[/tex] or I'm wrong?
     
  5. Dec 15, 2009 #4

    jtbell

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    Staff: Mentor

  6. Dec 15, 2009 #5

    fluidistic

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  7. Dec 15, 2009 #6
    To look at EM in another velocity you need to use a lorentz transformation of the field. If you are familiar with vectors, J.D. Jackson p. 558 gives a useful form:

    [tex]\vec{E}' = \gamma (\vec{E} + \vec{\beta} \times \vec{B}) - \frac{\gamma^2}{\gamma + 1} \vec{\beta} (\vec{\beta} \cdot \vec{E})[/tex]

    [tex]\vec{B}' = \gamma (\vec{B} - \vec{\beta} \times \vec{E}) - \frac{\gamma^2}{\gamma + 1} \vec{\beta} (\vec{\beta} \cdot \vec{B})[/tex]

    [tex]\vec{\beta} = \vec{v}/c[/tex]
    [tex]\gamma = \frac{1}{\sqrt{1 - \beta^2}}[/tex]

    So, you see if you have one frame where E = 0, and only B != 0. Then in every other frame E' != 0, and B' != 0, since B appears in both terms.
     
  8. Dec 15, 2009 #7

    fluidistic

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    Ok thank you very much. I'm going to try to grasp this. I took vector calculus. I'm taking the 1 year EM course on next term (in March). I thought I would need it for the intro to EM course, but I'm not sure now. Anyway, I'll do an effort to learn this part.
     
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