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Homework Help: Relativistic-Strength EM Field

  1. Oct 5, 2008 #1
    1. The problem statement, all variables and given/known data

    Demonstrate (qualitatively) that an electron in a linearly polarized EM beam that is driven transversely at \omega will also oscillate longitudinally at 2*\omega (due to the B field, apparently).

    2. Relevant equations

    I want to use a phasor form for the fields: [tex]\vec{E} = \vec{E_0} e^{i \omega t} [\tex], etc for B and velocity.

    [tex] F = q E + q v \cross B [\tex]

    3. The attempt at a solution

    A hint given is that v is pi/2 out of phase with B, and to focus on the magnetic term in the Lorentz expression.

    My guess was that, when v and B are multiplied as phasors, the frequency becomes 2 \omega. However, this doesn't use the fact that v is pi/2 out of phase! So what's the hint for?
  2. jcsd
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