[2.] Consider a model of a solid where electrons are attached to stationary ions by a...

 

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[2.] Consider a model of a solid where electrons are attached to stationary ions by a spring of spring constant x, so that each electron has a resonant frequency wo = √k/m. Assume there are # electrons per unit volume (and an equal number of positively charged ions per unit volume, but the ions are too massive to move in response to the wave electric and magnetic fields). The equation of motion for an electron in this system would then be: in dü di =-**- eE (a) Find the current density = -ned that arises in the material in the presence of an electromagnetic plane wave, E = R(Es(7) exp(-iwt)) Assume the electron position 7 and velocity have the same time behavior as the plane wave: 7 = R (7o exp(-iwt)} 5 = R (¾ exp(—iwt)) (Hint: approach this problem using Fourier notation.) [2.] Consider a model of a solid where electrons are attached to stationary ions by a spring of spring constant x, so that each electron has a resonant frequency wo = √k/m. Assume there are # electrons per unit volume (and an equal number of positively charged ions per unit volume, but the ions are too massive to move in response to the wave electric and magnetic fields). The equation of motion for an electron in this system would then be: in dü di =-**- eE (a) Find the current density = -ned that arises in the material in the presence of an electromagnetic plane wave, E = R(Es(7) exp(-iwt)) Assume the electron position 7 and velocity have the same time behavior as the plane wave: 7 = R (7o exp(-iwt)} 5 = R (¾ exp(—iwt)) (Hint: approach this problem using Fourier notation.)

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Solution Using Fourier notation to find the current ... View the full answer