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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 righthanded 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 lightminutes. D EVELOP A lightminute (abbreviated as cmin) is approximately equal to 8 10 1 cmin (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 cmin, SE R can be rewritten as 11 10 1cmin (1.5 10 m) 8.33 cmin 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 roundtrip 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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This note was uploaded on 09/12/2009 for the course PH PH101 taught by Professor Prof.kim during the Spring '09 term at Korea Advanced Institute of Science and Technology.
 Spring '09
 Prof.Kim
 Physics, Current

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