Lecture 31 - Maxwell's equations. EM waves

Lecture 31 - Maxwell's equations. EM waves - Maxwells...

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1 Lecture 31 Maxwell’s equations Maxwell s equations. Electromagnetic waves. Maxwell’s equations 0 q E dA Gauss’s law for E 0 B dA Gauss’s law for B B d E dl dt   Faraday’s law 0 0 E d B dl I dt Ampere’s law In the absence of sources 0 E dA 0 B dA B d E dl d The symmetry is then very impressive: dt   0 0 E B dl dt   changing B -field induces E -field changing E -field induces B -field E produces B , B produces E Example: At some point P in space, the measured electric field as a function of time is: E P t This E field MUST be accompanied by a B field. But if the induced B field also changes with time, it induces an E field! This can be self-sustained ! “Perturbation” ( E or B field) propagates in space wave Very special wave, can propagate in vacuum: no medium !
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2 Electromagnetic waves Let us assume that we have: E -field in the y direction, uniform along yz plane B -field in the z direction, uniform along yz plane • propagation in the x direction Plane electromagnetic wave y x z E B E and B are the same at all points in this
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