{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

329lect17 - 17 Magnetization current Maxwells equations in...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 e ff ect 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
Background image of page 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.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}