Lecture3 - Lecture 3 4. Electromagnetic Fields 5. Basic...

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Unformatted text preview: Lecture 3 4. Electromagnetic Fields 5. Basic idea of Quantum Electrodynamics 4. Electromagnetic elds Maxwell equations: (Differential form): r " # r D = $ r " # B = r " % E + & B & t = r " % H = J + & D & t r D = " r E dielectric constant r B = r H permeability r J = # r E conductivity $ charge density J current density Useful formula 4.1. Wave equation Consider simplied case for no current or charge isotropic, uniform we obtain apply from the left and evaluate the expressions using vector relations and eq.4 4.1. Wave equation Consider simplifed case For no current or charge isotropic, uniForm r " # r D = $ r " # B = r " % E + & B & t = r " % H = J + & D & t r " # r D = r " # B = r " $ E + % B % t = r " $ H = % D % t r " # apply From the leFt r " # r D = r " # B = r " $ r " $ E + r " $ % B % t = r " $ H = % D % t and evaluate the expressions using vector relations and eq.4 r " # $ B $ t = $ r " # B ( ) $ t = o $ 2 D $ 2 t r " # r " # r E = r " ( r " $ r E ) % r " 2 r E = % r " 2 r E We obtain " 2 r E ( r r , t ) = # 2 r D ( r r , t ) # 2 t we can express this in 2 ways Using so we have: r D = " r E " 2 r E ( r r , t ) = # 2 r D ( r r , t ) # 2 t " 2 r E ( r r , t ) = 2 E ( r r , t ) 2 t " 2 r E ( r r , t ) 2 E ( r r , t )...
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Lecture3 - Lecture 3 4. Electromagnetic Fields 5. Basic...

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