Chapter3_9 - of the conductor. This implies that ) sin( =...

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PHY3063 R. D. Field Department of Physics Chapter3_9.doc University of Florida E&M wave bouncing back and fourth in cavity! Number of modes increases as λ decreases! Rayleigh-Jeans Theory: Number of Modes Traveling Waves: The electric and magnetic fields for a plane wave traveling in the +x direction with frequency f and wavelength λ and speed c = f λ are given by r r Ext E k x ty Bxt B k x tz (,) s i n ( ) $ (,) s i n ( ) =− =− 0 0 ω ω where k = 2 π / λ , ω = 2 π f , T = 1/f , and E 0 = cB 0 . Standing Waves: Now consider the superposition of a wave moving in the +x direction with one moving in the –x direction as follows: ) cos( ) sin( 2 ) sin( ) sin( ) , ( 0 0 0 t kx E t kx E t x E y ω ω ω = + + =
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Unformatted text preview: of the conductor. This implies that ) sin( = ka and hence kL = n where n = 0, 1, 2, 3, and n L = 2 where n = 0, 1, 2, . Cubic Conducting Cavity: For a cavity consisting of a conducting cube with sides of length L get 2 2 2 2 2 z y x n n n c Lf L + + = = where n x , n y , n z = all positive integers . This equation describes all possible wavelengths (or frequencies) of electromagnetic radiation in the cubical conducting cavity. We must count the number of allowed frequencies in the cavity. x-axis y-axis z-axis E B Direction of Propagation One Dimensional Conducting Box . 5 1 n = 1 n = 2 n = 3 y-axis z-axis x-axis O L L L...
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.

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