hw10 - and find the condition on y such that(c is much...

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Physics 273 Homework #10 Due: Monday, November 28, 2011 1. A particle of charge Q oscillates sinusoidally with frequency in the x -direction according to ) sin( ) ( 0 t X t x . We will study the resulting electromagnetic fields at a distance y perpendicular to the motion, with y >> X 0 . The static radial electric field at ( x =0, y ) is 2 0 4 y Q E near . The current-induced magnetic field (out of the page) at ( x =0, y ) is 2 0 4 ) ( y t x Q B near , where ) ( t x is the velocity of the oscillating charge. (a) Write down the amplitude of the Poynting vector at ( x =0, y ) associated with the “near- field” electromagnetic fields E near and B near . (b) Now write down the radiated electric and magnetic fields at position ( x =0, y ) associated with the acceleration of the charge. (c) Write down the amplitude of the Poynting vector at ( x =0, y ) from the radiation fields derived in (b). (d) How far away must we be for the intensity of the radiation fields to dominate over the intensity of the “near fields” ? [Hint: compare the radiation intensities from (a) and (c),
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Unformatted text preview: and find the condition on y such that (c) is much larger than (a). Use c = k to simplify, where the wavenumber k = 2 / 2. An early model of the hydrogen atom had a point-like electron undergoing uniform circular motion around a fixed proton at radius r = 5 10 11 m. The problem with this model is that the electron would radiate away all of its energy due to its centripetal acceleration v 2 / r , and get sucked into the proton. (Luckily for us, this serious deficiency is fixed by quantum mechanics.) Estimate ( only to an order of magnitude ) how long it would take for the atom to collapse – that is, how long does it take the initial kinetic energy of the electron ½ m e v 2 to be radiated away? You can assume that the power radiated is constant. 3. H&L 10-1 4. H&L 11-1 5. French 8-15...
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