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Math Help - Help With Sources

  1. #1
    Rhymes with Orange Chris L T521's Avatar
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    Help With Sources

    I just started Physics III yesterday, and I talked to my professor about doing research for the class. He recommended that I write a paper on how Maxwell came up with the equation dP=\frac{dU}{c}, where P is momentum, U is energy (forget which one at the moment) and c is the speed of light. After this, he wants me to do the following:

    dP=\frac{dU}{c} \implies E=mc^2

    He wants me to derive Einstein's Famous equation from Maxwell's. Can anyone give suggestions on how to start, or even suggestions on books that I can take a look at?

    Thanks in Advance!

    --Chris
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    I just started Physics III yesterday, and I talked to my professor about doing research for the class. He recommended that I write a paper on how Maxwell came up with the equation dP=\frac{dU}{c}, where P is momentum, U is energy (forget which one at the moment) and c is the speed of light. After this, he wants me to do the following:

    dP=\frac{dU}{c} \implies E=mc^2

    He wants me to derive Einstein's Famous equation from Maxwell's. Can anyone give suggestions on how to start, or even suggestions on books that I can take a look at?

    Thanks in Advance!

    --Chris
    If you ever find out how to do this I'd like to know. I don't think it can be done. As I recall your given equation only holds for massless particles. You see given your original equation:
    dp = \frac{dU}{c}

    \frac{dU}{dp} = c

    U = pc
    where U is the total internal energy of the particle, ie. U = E, and this is indeed true for a massless particle.

    E = pc also comes from Einstein's equation. The actual equation derived by Einstein is
    E^2 = (pc)^2 + (mc^2)^2

    If the particle is massless we have E = pc like we had above. If the particle is at rest (ie. no momentum) we get the celebrated E = mc^2.

    I cannot think where the Maxwell equation would be found, but Maxwell's work in this case is for bosons (subatomic particles with integer spins) and probably would be found under a search on spin-statistics correlations. You can find a derivation of Einstein's equation in just about any Modern Physics text. That will give you a starting point anyway.

    -Dan
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