ls1_unit_1 - ON CLASSICAL ELECTROMAGNETIC FIELDS I. P...

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O N C LASSICAL E LECTROMAGNETIC F IELDS I. PRELIMINARIES: A R EVIEW OF SOME BASIC CONCEPTS AND METHODS : THE MICROSCOPIC MAXWELL'S EQUATIONS IN THE TIME DOMAIN: r ∇× r E r r , t ( 29 =- t r B r r , t ( 29 [ I-1a ] r ∇× r B r r , t ( 29 0 r J r r , t ( 29 0 μ 0 t r E r r , t ( 29 [ I-1b ] r ∇⋅ r E r r , t ( 29 = 1 ε 0 ρ r r , t ( 29 [ I-1c ] r ∇⋅ r B r r , t ( 29 [ I-1d ] where the meaning of fields r E r r , t ( 29 and r B r r , t ( 29 is ultimately defined in terms of the Lorentz force on a charge q moving at a velocity r u -- viz., r F r r , t ( 29 = q r E r r , t ( 29 + q r u × r B r r , t ( 29 [ I-2 ] THE MACROSCOPIC MAXWELL'S EQUATIONS IN THE TIME DOMAIN Following common practice, we set forth a particular set of macroscopic Maxwell’s equations that applies in the high frequency or optical regime . 1 r ∇× r E r r , t ( 29 t r B r r , t ( 29 = -μ 0 t r H r r , t ( 29 [ I-3a ] r ∇× r B r r , t ( 29 0 r ∇× r H r r , t ( 29 = μ 0 r J r r , t ( 29 + t r P r r , t ( 29 0 μ 0 t r E r r , t ( 29 [ I-3b ] 1 All bound current effects are included in the polarization density, since magnetization density "ceases to have any physical meaning at relatively low frequencies." See Section 62 in L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media , Pergamon Press (1960).
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ON CLASSICAL ELECTROMAGNETIC FIELDS PAGE 2 R. Victor Jones, March 11, 2003 r ∇⋅ r E r r , t ( 29 = 1 ε 0 ρ r r , t ( 29 - r ∇⋅ r P r r , t ( 29 [ ] [ I-3c ] r ∇⋅ r B r r , t ( 29
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ls1_unit_1 - ON CLASSICAL ELECTROMAGNETIC FIELDS I. P...

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