329lect17 - 17 Magnetization current Maxwell’s equations in material media • Consider the microscopic-form Maxwell’s equations ∇ D = ρ

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Unformatted text preview: 17 Magnetization current, Maxwell’s equations in material media • Consider the microscopic-form Maxwell’s equations ∇· D = ρ Gauss’s law ∇· B = 0 ∇× E =- ∂ B ∂t Faraday’s law ∇× H = J + ∂ D ∂t , Ampere’s law where D = o E B = μ o H . • Direct applications of these equations in material media containing a colossal number of bound charges is impractical. • Macroscopic-form Maxwell’s equations suitable for material media are obtained by first expressing ρ and J above as the macroscopic quantities ρ = ρ f-∇· P and J = J f + ∂ P ∂t + ∇× M where 1 – subscripts f indicate charge and current density contributions due to free charge carriers, – the term-∇· P denotes the bound charge density , – the term ∂ P ∂t denotes the polarization current density due to oscillating dipoles (already discussed in Lecture 11), and – ∇× M is a “magnetization current density” also due to bound charges, an effect that we will discuss and clarify later in this section. Using these expressions in Gauss’s and Ampere’s laws ∇· o E = ρ Gauss’s law ∇× μ- 1 o B = J + ∂ o E ∂t , Ampere’s law we obtain ∇· ( o E + P ) = ρ f Gauss’s law ∇× ( μ- 1 o B- M ) = J f + ∂ ∂t ( o E + P ) , Ampere’s law. Now, re-define D and H as D = e E + P = E and H = μ- 1 o B- M = μ- 1 B , 2 respectively, and drop the subscripts f which will no longer be needed. Using these new definitions, the full set of Maxwell’s equations now read as (the same form as before) ∇· D = ρ Gauss’s law ∇· B = 0 ∇× E =- ∂ B ∂t Faraday’s law ∇× H = J + ∂ D ∂t , Ampere’s law with D = E B = μ H , where ρ and J are understood to be due to free charge carriers only....
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This note was uploaded on 07/19/2010 for the course ECE ECE329 taught by Professor Kudeki during the Summer '10 term at University of Illinois at Urbana–Champaign.

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329lect17 - 17 Magnetization current Maxwell’s equations in material media • Consider the microscopic-form Maxwell’s equations ∇ D = ρ

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