Simple Nature - Light and Matter

Amp`ere’s lawis another way of relating static magnetic fields to the static currents that

created them, and it is more easily extended to nonstatic fields than is the Biot-Savart law.

Amp`ere’s law states that thecirculationof the magnetic field,

ΓB=

∑

sj·Bj,

around the edge of a surface is related to the currentIthroughpassing through the surface,

Γ =

4 πk

c^2

Ithrough.

In the general nonstatic case, the fundamental laws of physics governing electric and magnetic

fields areMaxwell’s equations, which state that for any closed surface, the fluxes through the

surface are

ΦE= 4πkqin and

ΦB= 0.

For any surface that is not closed, the circulations around the edges of the surface are given by

ΓE=−

∂ΦB

∂t

and

c^2 ΓB=

∂ΦE

∂t

+ 4πkIthrough.

The most important result of Maxwell’s equations is the existence ofelectromagnetic waves

which propagate at the velocity of light — that’s what light is. The waves are transverse, and

the electric and magnetic fields are perpendicular to each other. There are no purely electric or

purely magnetic waves; their amplitudes are always related to one another byB=E/c. They

propagate in the right-handed direction given by the cross productE×B, and carry momentum

p=U/c.

A complete statement of Maxwell’s equations in the presence of electric and magnetic ma-

terials is as follows:

ΦD=qfree

ΦB= 0

ΓE=−

dΦB

dt

ΓH=

dΦD

dt

+Ifree,

where the auxiliary fieldsDandHare defined as

D=E and

H=

B

μ

,

andandμare the permittivity and permeability of the substance.

Chapter 12, Optics, page 763

The ray model of light: We can understand many phenomena involving light without having

1086 Chapter Appendix 5: Summary