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Unformatted text preview: MAXWELLS EQUATIONS AND ELECTROMAGNETIC WAVES E XERCISES Section 29.2 Ambiguity in Ampres Law 13. I NTERPRET In this problem we are asked to find the displacement current through a surface. D EVELOP As shown in Equation 29.1, Maxwells displacement current is ( ) E d d d EA dE I A dt dt dt = = = E VALUATE The above equation gives 2 12 2 2 (8.85 10 C /N m )(1 cm )(1.5 V/m s) 1.33 nA d dE I A dt - = = = A SSESS Displacement current arises from changing electric flux and has units of amperes (A), just like ordinary current. 14. The electric field is approximately uniform in the capacitor, so ( / ) , and / E D E EA V d A I t = = = = 12 2 ( / ) / (8.85 10 F/m)(10 cm) (220 V/ms)/(0.5 cm) 3.89 A. A d dV dt - = = Section 29.4 Electromagnetic Waves 15. I NTERPRET We are given the electric and magnetic fields of an electromagnetic wave and asked to find the direction of propagation. D EVELOP The direction of propagation of the electromagnetic wave is the same as the direction of the cross product . E B r r E VALUATE When E r is parallel to j and B r is parallel to , i the direction of propagation is parallel to , E B r r or j i k . = - A SSESS For electromagnetic waves in vacuum, the directions of the electric and magnetic fields, and of wave propagation, form a right-handed coordinate system. 16. (a) The peak amplitude is the magnitude of ( ), E i j + which is 2. E Note that 2 , i j n + = where n is a unit vector 45 between the positive x and y axes. (b) When E r is parallel to n (for sin( ) kz t - positive) B r points 45 into the second quadrant (so that , and is in the direction). E B E B z + r r r r Thus, B r is parallel to the unit vector ( )/ 2. i j- + Section 29.5 Properties of Electromagnetic Waves 17. I NTERPRET This problem is about measuring the distance between the Sun and the Earth using light-minutes. D EVELOP A light-minute (abbreviated as c-min) is approximately equal to 8 10 1 c-min (3 10 m/s)(60 s) 1.8 10 m = = On the other hand, the mean distance of the Earth from the Sun (an Astronomical Unit) is about 11 1.5 10 m. SE R = E VALUATE In units of c-min, SE R can be rewritten as 11 10 1c-min (1.5 10 m) 8.33 c-min 1.8 10 m SE R = = 29.1 29 29.2 Chapter 29 A SSESS The result implies that it takes about 8.33 minutes for the sunlight to reach the Earth. 18. Assuming the satellite is approximately overhead, we can estimate the round-trip travel time by / t r c = = 5 (2 36,000 km)/(3 10 km/s) 0.24 s. = 19. I NTERPRET In this problem we want to deduce the airplanes altitude by measuring the travel time of a radio wave signal it sends out....
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