110217_hw5 - x direction in vacuum, has an electric field...

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February 17, 2011 PHYS 4132 Homework 5 Due date: February 24, 2011 1. Consider electromagnetic waves in free space of the form E ( r ,t) = E 0 (x,y) e i( kr - ω t) , B ( r ,t) = B 0 (x,y) e i( kr - ω t) , where E 0 and B 0 are in the xy plane. Find the relation between k and ω , as well as the relation between E 0 (x,y) and B 0 (x,y). Show that E 0 (x,y) and B 0 (x,y) satisfy the equation for electrostatics and magnetostatics in free space. 2. A transverse electromagnetic wave in a non-conducting, uncharged medium is a. linearly polarized, E = E o sin(kz – ωt) b. circularly polarized, E = E o [cos(kz- ωt) e x + sin(kz – ωt) e y ]. Calculate the magnetic field B ( r ,t) and the Poynting vector S ( r ,t) in both cases. 3. A plane electromagnetic harmonic wave of green light, propagating in the positive
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Unformatted text preview: x direction in vacuum, has an electric field amplitude of 41.42 V/m. The wave is linearly polarized such that the plane of oscillation of the electric field is at 45 o to the xz plane. a. Write expressions for E and B using numerical values for all quantities. b. Verify explicitly that all directional requirements are satisfied. 4. A metal string of length L is fixed on both ends. The string oscillates in a plane perpendicular to a homogeneous B-field. Determine the voltage induced at the ends of the conducting string. Hint: The amplitude u(x,t) at position x of the string at time t is a solution to the wave equation....
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