EMsource - EM sources Electromagnetic Waves and Optics 1...

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Unformatted text preview: EM sources Electromagnetic Waves and Optics 1 Generation of EM Waves EM Waves in Matter Revisited radiation of accelerated charges resonance and dispersion group velocity optical properties of metals EM sources Electromagnetic Waves and Optics 2 EM radiation in one dimension switch on current in xy-plane: resulting fields: appearance of fields delayed by t =z/c ( ) = > = otherwise , , z t J i t r J r r ( ) ( ) 2 , 1 with , , cB E c ct z ct z B j t r B ct z ct z E i t r E = = > < = > < = r r r r z y x J z y ct : = = > B E ct z r r x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x EM sources Electromagnetic Waves and Optics 3 EM Radiation by Charged Particles charges at rest static E-field charges in uniform motion static B-field accelerating charges EM radiation e.g., sudden shift of charge at t = 0 new field for r < ct distances r > ct remember old field transverse E-field travelling kink in field lines E coplanar with accel. no kink parallel to accel. + + r = ct EM sources Electromagnetic Waves and Optics 4 EM Radiation by Accelerating Charge continuous acceleration expected properties of E-field energy conservation: proportional to charge: prop. to transverse component of historical acceleration: direction: a k a k a k E r r r r r r r for strongest radiation || for radiation no coplanar , , ) , 1 for ( 4 c v kr c r t a k k r q E << >> = r r sin ) / ( c r t a E r E 1 q E EM sources Electromagnetic Waves and Optics 5 EM Radiation by Oscillating Charge far field: r >> ) ( 2 , sin 4 qx p r e p E e x x t kr i t i = = = ) / ( sin 4 c r t a a r a q E = = E r k r r B r 2 2 4 2 2 sin 32 r p c S = EM sources Electromagnetic Waves and Optics...
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EMsource - EM sources Electromagnetic Waves and Optics 1...

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