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An electron undergoes an oscillatory circular motion in the xy plane, dictated by a uniform constant...

An electron undergoes an oscillatory circular motion in the xy plane, dictated by a uniform constant magnetic field B applied in the z direction, and by a circularly polarized electromagnetic wave that propagates in the z direction. The electric field of the wave is given by E = Eo[cos(kz - wt)x - sin(kz - wt)y]. Note that at z=0, where the electron moves, this electric field is E = Eo[cos(wt)x + sin(wt)y].

(a) This part of the problem is classical mechanics, not electrodynamics. Write down the equation of motion for the electron and solve it. In the solution, express the radius ro of the oscillatory circular orbit in terms of w and the cyclotron resonance frequency wc = qB/m, where q and m are the charge and the mass of the electron. Assume q>0.

(b) Find the power P radiated by the electron by using the Larmor formula generalized by Lienard, instead of starting from scratch.

(c) Write the time average of the Poynting vector <S> of the electromagnetic wave in terms of Eo. Multiply <S> by the area pi*ro2 of the circle defined by the motion of the electron to estimate the power Po available to the electron, and compare the P you found in part (b) with Po.

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genius_generous answered 2 years ago
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