# sol03 - 1 University of California, Berkeley Physics H7C...

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Unformatted text preview: 1 University of California, Berkeley Physics H7C Spring 2011 ( Yury Kolomensky ) SOLUTION TO PROBLEM SET 3 EM Waves, Light Propagation Maximum score: 200 points Due: February 11, 2011 Composed and formatted by Yu. Kolomensky, and T.R. Beals 1. (20 points) ( Hecht 3.9 ) Using the relation between the amplitudes of electric and magnetic fields in an EM wave, prove that the en- ergy densities of the electric and magnetic fields are equal. 1. Solution The relationship for the magnitudes of the electric and magnetic fields of an electromagnetic field in vacuum is just | E | = c | B | . The energy in an electric field is U E = 1 2 R E 2 , while the energy in a magnetic field is U B = 1 2 R 1 μ B 2 . Since 1 μ B 2 = 1 c 2 μ E 2 = E 2 , we see that U E = U B . 2. (20 points) ( Hecht 3.26 ) Using energy arguments, show that the amplitude of a cylindrical wave must vary inversely with √ r . Draw a diagram indicating what’s happening. 2. Solution From application of Gauss’s law, we know that the intensity (energy per unit time per unit area) passing through the surface of a cylinder (with an axial source at the center) must just be inversely proportional to the area of the cylinder (excluding the ends), since energy is conserved. The area varies with r , so the intensity varies as 1 /r . Since intensity varies as the square of amplitude, the amplitude varies with 1 / √ r . 3. (30 points) ( Hecht 3.32 ) A surface is placed perpendicular to a beam of light of constant irradiance (intensity) I . Suppose that the fraction of the irradiance absorbed by the surface is α . Show that the pressure on the surface is given by P = (2- α ) I/c . 3. Solution The amount of momentum per unit area per unit time of a beam of light is just I/c . A photon that is absorbed by the surface transfers all of its momentum to the surface, while a photon that is reflected transfers twice its mo- mentum to the surface (since it leaves with momentum equal in magnitude but opposite in sign). If the frac- tion of the photons that are absorbed is α , then the pres- sure exerted (the momentum transferred per unit time per unit area) is P = (2- α ) I/c . 4. (30 points) ( c.f. Hecht 3.36 ) Consider the plight of an astronaut floating in free space 10 m away from the space station, with no lifeline to pull him back. Suppose the astronaut is lucky enough to be on the sunny size of the station, where the intensity of the solar radiation is 1.4 kW/m 2 . Estimate whether it is possible for the astronaut to reach the station using solar radiation for propulsion in a reasonable time (i.e. before the oxygen supply runs out in a few hours). Make reasonable assumptions about astronaut’s mass and sur- face area....
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## This note was uploaded on 03/28/2012 for the course PHYSICS H7c taught by Professor Staff during the Spring '08 term at Berkeley.

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sol03 - 1 University of California, Berkeley Physics H7C...

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