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

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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 = μ r H permeability r J = # r E conductivity $ charge density J current density Useful formula 4.1. Wave equation • Consider simpli¡ed 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 = μ 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 ) = μ # 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 ) = μ # 2 r D ( r r , t ) # 2 t " 2 r E ( r r , t ) = μ ¡ ¢ 2 E ( r r , t ) ¢ 2 t " 2 r E ( r r , t ) £ μ ¡ ¢ 2 E ( r r , t ) ¢...
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Lecture3 - Lecture 3 4 Electromagnetic Fields 5 Basic idea...

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