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Math Help - Lienard Wienchert Potentials

  1. #1
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    Lienard Wienchert Potentials

    I would post on the Physics help forum, but Latex does not work there! Perhaps a mathematician needs to help them out?

    My text asks me to obtain the Lienard-Wiechert Potentials. The potentials are quoted as:

    \phi= \left[\frac q {r(1+u_r/c)}\right]_{ret} and \underline w= \left[\frac {q \underline u} {r(1+u_r/c)}\right]_{ret}

    This seems wrong to me, I get the following

    \underline w= \left[\frac {q \underline u/c} {r(1+u_r/c)}\right]_{ret}

    Is my text incorrect?
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  2. #2
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    Two thoughts:

    1. Is your textbook using a c=1 convention? If not, then
    2. You should be able to distinguish between those two potentials using dimensional analysis. The one you put forth has an extra sec/m multiplying it, but is otherwise the same.
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  3. #3
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    \phi and \underline w can be combined into the 4-vector (-\underline w,\phi) so I expect that \phi and \underline w must have the same units (coulombs per meter). This is why I think the additional c is required and the text is wrong?

    The text (Rindler; Relativity Special, General and Cosmological) does not use c=1.
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  4. #4
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    I would agree that the components of a 4-vector must all have the same units. Otherwise, when you compute the dot product of a 4-vector with itself (thus producing a Lorentz invariant), you'd be adding up terms that didn't have the same units.

    So the only question left is this: what are the units of \underline{u}? If its units are, as I suspect, [m/s], then you are correct and the book must be wrong. If, on the other hand, \underline{u} is dimensionless, then the book is correct.

    That's my verdict.
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