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# problem_2 - ASTRONOMY 822 Electromagnetic Radiation Problem...

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ASTRONOMY 822 Electromagnetic Radiation Problem Set 2 due Wednesday, October 12 at class time 1) Consider a plane electromagnetic wave of the form ~ E = ˆ e y E 0 cos( kx - ωt ) and ~ B = ˆ e z E 0 cos( kx - ωt ) . The wavelength of the light is measured to be λ = 700 nm and its time averaged energy density is h u i = 20 erg cm - 3 . a) An electron is placed at the origin, initially at rest ( ~x = 0 and ~v = 0 at t = 0). Let’s start by assuming that the motions of the electron are highly nonrelativistic, and that the magnetic forces can be ignored. What is the force exerted on the electron, in this case? What is the maximum displacement of the electron from the origin? What is the maximum velocity of the electron? Was our assumption of nonrelativistic motions justiFed? b) The most powerful “petawatt” lasers can produce energy densities as large as h u i ≈ 3 × 10 17 erg cm - 3 . Assuming this energy density is provided by a single plane wave of wavelength λ = 1000 nm, what would be the

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problem_2 - ASTRONOMY 822 Electromagnetic Radiation Problem...

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