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# HW18Sol - Jim Guinns PHYS2212 Assignment#18 Solutions 1 An...

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Jim Guinn’s PHYS2212 Assignment #18 Solutions 1. An electromagnetic wave has an intensity of 1.00x10 2 W/m 2 . Find the magnitude of the electric and magnetic field. (You are actually getting the average magnitude. More on this later.) The energy density of the wave is then given by U = S / c = (100W/m 2 ) / (3.00x10 8 m/s) = 3.33x10 -7 J/m 3 , half of which, 1.67x10 -7 J/m 3 , is in the electric field and half in the magnetic field. So U E = (1/2) ε o E 2 or E = √ (2U E / ε o ) = E = 194V/m , and B = E / c = B = 6.47x10 -7 T . 2. The intensity of the sunlight at the top of Earth's atmosphere is 1390 W/m 2 . What is the amplitude of the electric and magnetic field at this point? You may treat the light as having a single wavelength. The intensity of a light source is given by S = c u , where u = the light's energy density, so u = S / c = 1390 W/m 2 / 3.00x10 8 m/s = 4.63x10 -6 J/m 3 . The energy density is given by u = ε o E rms 2 , so E rms = √(u/ ε o ) = 724. N/C , and E o = √2 E rms = E o = 1020 N/C . The amplitude of the magnetic field is then given by B o = E o / c = (1020 N/C) / (3.00x10 8 m/s) = B o = 3.40x10 -6 T . 3. An electromagnetic wave has an electric field amplitude of 1.00V/m . What is the average intensity of the wave? The magnetic field amplitude is given by

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