phy1020.DVI

Chapter 42

Electromagnetism

42.1 Electromagnetic Waves

As mentioned in Chapter 36, the theory of classical electricity and magnetism is based on four equations
calledMaxwell’s equations, named for the 19th-century Scottish physicist James Clerk Maxwell. Around the
time of the American Civil War (1865) Maxwell collected the four equations together, and realized that there
was a crucial term called thedisplacement currentmissing from Ampere’s law that was required to make it self-consistent. After adding this term to Ampere’s law, Maxwell was able to show that the four equations
could be combined to derive awave equation, which describes a wave moving with speed

1

p

" 0  0

DcD299;792;458m=s; (42.1)

which is the speed of light in vacuum. This is a remarkable result: by combining equations that summarized
the results of laboratory experiments on electric and magnetic fields, Maxwell was able to demonstrate that
light is anelectromagnetic wave, thus connecting the fields of electromagnetism and optics.
Specifically, the classical view of electromagnetic waves (including visible light) is that it consists of
a transverse electric wave; the electric wave in turn creates a perpendicular magnetic wave, which in turn
produces the electric wave, and so on. In other words, light (and other electromagnetic waves) consist of
electric and magnetic waves that sustain each other as they propagate through space, so that no material
medium is required. (Fig. 42.1.) Light can propagate in a vacuum.
Visible light is just one of many forms of electromagnetic wave. Electromagnetic waves are categorized
(somewhat arbitrarily) according to their wavelength, as shown in Table 42-1. It’s important to realize,
though, that all these waves are really the same thing: they differ only in their wavelength, and the different
names we give them are for our own convenience.

Table 42-1. Electromagnetic waves and their wavelengths. Wavelength increases going down the table from

top to bottom; frequency and energy increase going up the table from bottom to top.

Wave Wavelengths

Gamma rays <0.1 nm (shortest ; highestf;E)

X-rays 0.1 – 10 nm

Ultraviolet 10 – 400 nm

Visible 400 – 700 nm

Infrared 0.7 – 100m

Submillimeter 0.1–1mm

Microwaves 1 mm – 1 m

Radio >1 m (longest ; lowestf;E)