Lecture 10 Maxwell Eqns

Lecture 10 Maxwell Eqns - Lecture Lecture10...

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cture 10 Lecture 10 Maxwell’s Equations Part 2: Plane Wave model and reflection from normal cidence at boundaries incidence at boundaries Hayt CH 12 1 McGill ECSE 352, Fall 2011, D. Davis
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lane Wave Solution Plane Wave Solution In the previous lecture we discussed the Vector tepe ous ectu e e d scussed te ecto Wave Equation (also known as the Helmholtz Wave Equation). We will now introduce a solution to the wave equation. The plane wave. The plane wave propagates along a straight line path until it encounters a discontinuity. The electric field and magnetic field extend across an entire plane (effectively an infinite sized ea) area). McGill ECSE 352, Fall 2011, D. Davis 2
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lane Wave Solution Plane Wave Solution e direction of propagation is a straight line, The direction of propagation is a straight line, for example travelling along the z axis. avelling along the z is would be expressed Travelling along the z axis would be expressed as: െߛݖ ݆߱ݐ െߙݖ െ݆ߚݖ The term on the left of the equality uses the ropagation coefficient notation, the term on propagation coefficient notation, the term on the left uses the attenuation coefficient + the phase coefficient notation. McGill ECSE 352, Fall 2011, D. Davis 3
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lane Wave Solution Plane Wave Solution e electric field portion of a plane wave has a The electric field portion of a plane wave has a magnitude and direction (electric forces are ctor fields) as well as propagating wave vector fields) as well as propagating wave behaviour. r example an electric field propagating in For example an electric field propagating in the z direction with polarization in the x irection and a field strength of 10 V/m is direction and a field strength of 10 V/m is written as: ܧ ሺݖ,ݐሻൌܽ ݔ 10݁ െߙݖ ݁ െ݆ߚݖ ݁ ݆߱ݐ McGill ECSE 352, Fall 2011, D. Davis 4
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lane Wave Solution Plane Wave Solution e magnetic field can be obtained from The magnetic field can be obtained from substitution of the electric field into Faraday`s w: Law: ݔ െߙݖ െ݆ߚݖ ݆߱ݐ This will lead to a magnetic field of: ܪሺݖ, ݐሻൌܽ ݕ 10൫ඥ݆߱ߤሾߪ൅ ݆߱߳ሿ ߤ ݁ െߙݖ ݁ െ݆ߚݖ ݁ ݆߱ݐ This can be simplified to: ሺ݆߱ߤሻ McGill ECSE 352, Fall 2011, D. Davis 5
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Lecture 10 Maxwell Eqns - Lecture Lecture10...

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