Editing Maxwell's equations (section)

=== Bound charge and current ===
{{Main|Current density|Polarization density#Polarization density in Maxwell's equations|Magnetization#Magnetization current|l2=Bound charge|l3=Bound current}}
[[File:Polarization and magnetization.svg|thumb|300px|''Left:'' A schematic view of how an assembly of microscopic dipoles produces opposite surface charges as shown at top and bottom. ''Right:'' How an assembly of microscopic current loops add together to produce a macroscopically circulating current loop. Inside the boundaries, the individual contributions tend to cancel, but at the boundaries no cancelation occurs.]]

When an electric field is applied to a [[dielectric|dielectric material]] its molecules respond by forming microscopic [[electric dipole]]s – their [[atomic nucleus|atomic nuclei]] move a tiny distance in the direction of the field, while their [[electron]]s move a tiny distance in the opposite direction. This produces a ''macroscopic'' ''bound charge'' in the material even though all of the charges involved are bound to individual molecules. For example, if every molecule responds the same, similar to that shown in the figure, these tiny movements of charge combine to produce a layer of positive [[Bound charge#Bound charge|bound charge]] on one side of the material and a layer of negative charge on the other side. The bound charge is most conveniently described in terms of the [[polarization density|polarization]] {{math|'''P'''}} of the material, its dipole moment per unit volume. If {{math|'''P'''}} is uniform, a macroscopic separation of charge is produced only at the surfaces where {{math|'''P'''}} enters and leaves the material. For non-uniform {{math|'''P'''}}, a charge is also produced in the bulk.<ref>See {{cite book|author=David J. Griffiths|title=Introduction to Electrodynamics|url=https://archive.org/details/introductiontoel00grif_0|url-access=registration|edition=third|section=4.2.2|publisher=[[Prentice Hall]]|year=1999|isbn=9780138053260|author-link=David J. Griffiths}} for a good description of how {{math|'''P'''}} relates to the [[Bound charge#Bound charge|bound charge]].</ref>

Somewhat similarly, in all materials the constituent atoms exhibit [[magnetic moment|magnetic moments]] that are intrinsically linked to the [[gyromagnetic ratio|angular momentum]] of the components of the atoms, most notably their [[electron]]s. The [[magnetic field#Magnetic dipoles|connection to angular momentum]] suggests the picture of an assembly of microscopic current loops. Outside the material, an assembly of such microscopic current loops is not different from a macroscopic current circulating around the material's surface, despite the fact that no individual charge is traveling a large distance. These ''[[Bound current#Magnetization current|bound currents]]'' can be described using the [[magnetization]] {{math|'''M'''}}.<ref>See {{cite book|author=David J. Griffiths|title=Introduction to Electrodynamics|url=https://archive.org/details/introductiontoel00grif_0|url-access=registration|edition=third|section=6.2.2|publisher=[[Prentice Hall]]|year=1999|isbn=9780138053260}} for a good description of how {{math|'''M'''}} relates to the [[bound current]].</ref>

The very complicated and granular bound charges and bound currents, therefore, can be represented on the macroscopic scale in terms of {{math|'''P'''}} and {{math|'''M'''}}, which average these charges and currents on a sufficiently large scale so as not to see the granularity of individual atoms, but also sufficiently small that they vary with location in the material. As such, ''Maxwell's macroscopic equations'' ignore many details on a fine scale that can be unimportant to understanding matters on a gross scale by calculating fields that are averaged over some suitable volume.