s71 - Solutions to Homework#7 Chapter 25 38 Picture the...

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Solutions to Homework #7 Chapter 25 38. Picture the Problem: To obtain optimal reception of a 66.0-MHz TV signal, the length of the antenna should be equal to half a wavelength. Strategy: Set the length of the antenna equal to half a wavelength, where the wavelength is given in terms of the frequency using equation 25-4. Solution: Calculate the length of the antenna: ( 29 8 7 1 3.00 10 m/s 2.27 m 2 2 2 6.60 10 Hz c L f λ = = = = Insight: To listen to an FM radio station at 107 MHz the antenna should be 1.40 m long. 44. Picture the Problem: The radiation pressure exerted by beam of light 1 is half the radiation pressure of beam of light 2. Strategy: Use the expressions 2 0 I c E ε = (equation 25-10) and av av pressure I c = (equation 25-12) to determine the rms electric field in beam 2. Solution: We note from equation 25–12 that the radiation pressure depends on the intensity of a wave. The intensity, in turn, depends on the square of the fields, as equation 25–10 shows. Therefore, the electric field in beam 2 has a magnitude of 0 2 . E 2. (b) The intensity of an electromagnetic wave, on the other hand, depends on the square of the electric and magnetic fields. As a result, doubling the fields quadruples the intensity of the wave. We conclude the rms average intensity of the wave changes by a multiplicative factor of 4.00. Insight: The answer can also be determined by a ratio: av, 2 0 av, 2 av, 2 av, 2 2 2 2 0 1 1 0 av, 1 av, 1 av, 2 2 av, 1 0 pressure pressure 2 2 pressure pressure I c I c E E E E E E I c I c ε ε = = = = = = = 62. Picture the Problem: A 75.0-W light bulb emits electromagnetic waves uniformly in all directions. Strategy: Use equation 14-7 to calculate the intensity of the light 2.5 m from the source. Insert the intensity into equation 25-10 to calculate the rms electric field, and then solve equation 25-9 for the magnetic field. Solution: 1. Divide the power by area: ( 29 2 av av 2 75.0 W 0.955 W/m 4 2.50 m P I A π = = = 2. Calculate the electric field: ( 29 ( 29 2 av 0 rms 2 av rms 8 12 2 2 0 0.955 W/m 19.0 V/m 3.00 10 m/s 8.85 10 C / Nm I c E I E c ε ε - = = = = 3. Find the magnetic field: 8 rms rms 8 19.0 V/m 6.33 10 T 63.3 nT 3.00 10
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