# Introduce the wave vector k agk 2005 ecse z what is

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Introduce the wave vector k

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©AGK 2005 ECSE 352 3.4-10 0 z What is the plane for which the phase is constant ? Write the wave as: Transverse EM waves
©AGK 2005 ECSE 352 3.4-11 E Magnetic field of transverse wave The associated magnetic field is given by: Obj110 k H

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©AGK 2005 ECSE 352 3.4-12 An EM wave is traveling in the x-z plane. The wave vector is directed at 45° to the z-axis. The frequency is 300 MHz What is the E-field at a point (3,0,2) ? Example 0 z k r P a n 45° x 2 3

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©AGK 2005 ECSE 352 3.4-14 Transverse EM wave: summary E and H are orthogonal E and H are related through the impedance of the medium. Direction of propagation is described by the wave vector The plane of constant phase is perpendicular to the wave vector E and H are perpendicular to the wave vector ( 29 ( 29 r k E r E . exp 0 j = 0 z k r P a n
©AGK 2005 ECSE 352 3.4-15 Self-test questions Can you define the term ‘wave vector’ ? Can you define the term ‘wave front’ ? See the WebCT self-test to check.

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©AGK 2005 ECSE 352 3.4-16 Summary A wavefront is a plane of constant phase The wave vector defines the direction of the wave Wavefronts are orthogonal to the wave vector Plane waves have planar wavefronts A plane EM wave is called a transverse electromagnetic wave (TEM)
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