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fall_03_exam3_sol_phy2054

fall_03_exam3_sol_phy2054 - Solution to Exam 3 Paul Avery...

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Solution to Exam 3 Paul Avery, Art Hebard PHY2049, Fall 2003 Nov. 21, 2003 1. A small transmitter in a secret location broadcasts a signal uniformly in all directions with 1 W of power. If a receiving antenna can detect a minimum signal intensity of 10 - 8 W / m 2 , what is the maximum distance in meters that the transmitter signal can be detected? Solution: Since the transmitter broadcasts uniformly in all directions, the intensity S at a distance d is S = P/ 4 πd 2 , where P = 1 Watt is the radiated power. Using S = 10 - 8 W/m 2 yields a maximum distance of 2820 meters. 2. A solenoid with radius r and length l is wound with copper wire having a resistance of 10 Ω/m. The number of turns of wire per unit length of solenoid is n . Similar wire with the same winding density n is used to fabricate a second solenoid with twice the radius and four times the length of the first solenoid. The relaxation time of the second solenoid, L/R , is how much larger than the relaxation time of the first solenoid? Solution: The inductance is proportionate to n 2 Al , where n is the number of turns per meter, A is the area and l is the length of the solenoid. With A and l both 4 times bigger, L is 16 times bigger for the second solenoid compared to the first. The resistance R is 8 times larger (2 from radius and 4 for length), making
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