# Agk 2005 ecse 352 34 5 wave solutions obj100 obj101 p

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©AGK 2005 ECSE 352 3.4-5 Wave solutions Obj100 Obj101 p u k ϖ = k =wave number (m- 1): Homogeneous vector Helmholtz equations (from Maxwell): ϖ =angular frequency (rad/s) up =phase velocity (rad/m) . . ( 29 ( 29 ( 29 0 0 0 0 , Re cos (V/m) j t k z x z t E e E t k z ϖ ϖ - + + + = = - E Solution in 1D: Harmonic wave, traveling in z , E-field in x direction λ = 2 π k E 0 - E 0 z 0 Time dependence: ( 29 ( 29 t j e z t z ϖ E = , E λ ϖ f k u p = = REVIEW

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©AGK 2005 ECSE 352 3.4-6 E Transverse electromagnetic wave y z H x E and H are orthogonal Obj106 Obj107 Obj108 Impedance of free- space: Impedance describes ratio of electric field to magnetic field amplitude REVIEW Obey right-hand rule

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©AGK 2005 ECSE 352 3.4-8 Transverse EM waves Waves can travel anywhere in 3-dimensional space How do we describe this ? What do we mean by the wavefront of an electromagnetic wave ? What do we mean by a plane wave ?
©AGK 2005 ECSE 352 3.4-9 Transverse EM waves (plane waves) Wavefronts (planes of constant phase) have infinite extent E 0 - E 0 0 k Ε How do we describe a wave that does not travel on the z-axis ?

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