lecture6 - Lecture 6 Expression of field Superposition of...

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Unformatted text preview: Lecture 6 Expression of field Superposition of waves 1. 1 = 2 2. 1 2 3. Waves of several frequencies Phase and group velocities Expression of field E (x,y,z;t)= E o (x,y,z) cos ( t k r + ) or E (x,y,z;t)= E o (x,y,z) sin ( t k r + ) Direction and amplitude of fields, Vector E o , V/m Frequency , f in Hz, =2 f, in rad/s Direction of propagation , vector k Phase , in radians Irradiance , = < S > =(1/2)c o | E o | 2 , W/m 2 E 1 =E o1 sin( 1 t k 1 x 1 ) , < E 1 2 > = (1/2) E o1 2 E 2 =E o2 sin( 2 t k 2 x + 2 ), < E 2 2 > = (1/2) E o2 2 E t = E 1 + E 2, < E t 2 > =? Superposition of two fields Two sinusoidal fields 1. Superposition of two fields of same frequency 1 = 2 = k 1 = k 2 = k, same direction But 1 and 2 may be different 2 1 2 2 2 1 2 2 1 2 ) ( ) ( ) ( E E E E E E 2 1 2 2 2 1 2 2 1 2 ) ( ) ( ) ( E E E E E E ) cos( ) cos( ) sin( ) sin( 2 B A B A B A E 1 =E o1 sin( 1 t k 1 x 1 ) E 2 =E o2 sin( 2 t k 2 x + 2 ) 1. Superposition of1....
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This note was uploaded on 02/12/2012 for the course ECE 414 taught by Professor Alenxendra during the Spring '11 term at Purdue University-West Lafayette.

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lecture6 - Lecture 6 Expression of field Superposition of...

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