Chapter 34

Electromagnetic Waves and light

Electromagnetic waves in our life Microwave oven, EM wave is used to deliver energy. Radio/TV, cell phones, EM wave is used to carry

information. Telephone and internet: electrical signal in copper

wires is NOT EM wave, but fiber optics is the backbone of the network.

The wireless connection for your laptop, the bluetooth headset for your iPod, …

Without EM wave, there would be no life on Earth.

– why?

Plane EM waves, the simplest formA review: a wave is a disturbance that propagates through space and time, usually with transference of energy

PLAYACTIVE FIGURE

An EM wave is the oscillation between electric and magnetic fields.The electric field oscillates in the x-y plane, along the y direction; the magnetic field oscillates in the x-z plane and along the z direction. The EM wave propagates along the x axis, with the speed of light c, in vacuum.

E

B

Wave propagationA sinusoidal EM wave moves in the x direction with the speed of light c, in vacuum.

PLAYACTIVE FIGURE

The electric field direction (here the y axis direction) is called the polarization direction. When this polarization direction does not change with time, it is said that the EM wave is linearly polarized. Another common polarization is the circular polarization, when the electric field direction moves in a circle

The magnitudes E and B of the fields depend upon x (the location in the wave) and t (time) only:

maxE E cos kx t maxB B cos kx t Here k is the wave number.

Rays, wave front and plane wave

A ray is a line along which the wave travels.

In a homogeneous medium for EM waves (vacuum being one), rays follow straight lines.

The surface that connects points of equal phase in a group of rays (waves) is called the wave front. When this wave front is a geometric plane, this collection of waves is called a plane wave.

Maxwell’s equations of EM waves

Gauss’s Law of electric field:0

E AE

qd

Gauss’s Law of magnetic field: B A 0B d

Here the emf is actually distributed over the conducting ring. From the definition of potential,we know that the emf here equals:

E sV d

E semf d

Faraday’s Law of induction:Bd

emfdt

So Faraday’s Law of induction now reads:

E s Bdd

dt

Maxwell’s modification to Ampere’s LawAmpere’s Law of magnetic field: 0B sd I

Here the current flows in a wire.

Now let’s examine the case when there is a capacitor in the current path:Ampere’s Law applies to the wire part. The current flows into the upper plate of the capacitor, flows out from the lower plate, creating charge accumulation in the capacitor and build up the electric field. Constructing a Gaussian surface which has two parts: S1 and S2.

Maxwell’s modification to Ampere’s Law

2 20

E SE

qES

Gauss’ Law says that:

So one has:

0 0 0

1 1Ed

d d q dqI

dt dt dt

Here Id is called the displacement current. With it, the Ampere’s Law is now completed as:

0 0 0 0B s Ed

dd I I I

dt

It is often called Ampere-Maxwell Law

Maxwell’s equations of EM waves

Gauss’s Law of electric field:

Gauss’s Law of magnetic field:

Faraday’s Law of induction:

Ampere-Maxwell Law:

0

E Aq

d

B A 0d

E s Bd

ddt

0 0 0B s Edd I

dt

These four equations are called Maxwell’s Equations. These are the integral forms. The differential forms are:

0

Eq

B 0

BE

t

0 0 0

EB J

t

With Lorenz force Law,

we complete the laws of classical electromagnetism.

F E v Bq q

James Clerk Maxwell 1831 – 1879 Scottish physicist Provided a mathematical theory

that showed a close relationship between all electric and magnetic phenomena

His equations predict the existence of electromagnetic waves that propagate through space

His equations unified the electric and magnetic fields, and provide foundations to many modern scientific studies and applications.

Energy in EM waves

From Maxwell’s equations, one can prove:

The speed of light is 0 0

1c

The electric field to magnetic field ratio is E

cB

The energy flow in an EM wave is described by the Poynting vector

0

1S E B

2 2

0 0 02 2 2max max max max

av

E B E cBI S

c

The wave energy intensity is

The energy density is2

20

0

1

2 2B E

Bu u E

Producing EM waves through an antenna

Use a half-wave antenna as an example Two conducting rods are connected to a

source of alternating voltage The length of each rod is one-quarter of

the wavelength of the radiation to be emitted

The oscillator forces the charges to accelerate between the two rods

The antenna can be approximated by an oscillating electric dipole

The magnetic field lines form concentric circles around the antenna and are perpendicular to the electric field lines at all points

The electric and magnetic fields are 90o out of phase at all times

This dipole energy dies out quickly as you move away from the antenna

The EM wave Spectrum

Radio waves

Microwaves

Infrared

Ultraviolet, UV

Visible light

Gamma and X rays

Notes on the EM wave Spectrum Radio Waves

Wavelengths of more than 104 m to about 0.1 m

Used in radio and television communication systems

Microwaves Wavelengths from about 0.3 m to 10-4 m Well suited for radar systems Microwave ovens are an application

Infrared waves Wavelengths of about 10-3 m to 7 x 10-7 m Incorrectly called “heat waves” Produced by hot objects and molecules Readily absorbed by most materials

Visible light Part of the spectrum detected by the human

eye Most sensitive at about 5.5 x 10-7 m (yellow-

green) Ultraviolet, X-rays and Gamma rays

More About Visible Light Different frequencies (or wavelengths in vacuum)

correspond to different colors The range of wavelength in vacuum is from red (λ

~ 7 x 10-7 m) to violet (λ ~4 x 10-7 m)

More notes on the EM wave Spectrum

Ultraviolet light Covers about 4 x 10-7 m to 6 x 10-10 m Sun is an important source of uv light Most uv light from the sun is absorbed in the

stratosphere by ozone X-rays

Wavelengths of about 10-8 m to 10-12 m Most common source is acceleration of high-

energy electrons striking a metal target Used as a diagnostic tool in medicine

Gamma rays Wavelengths of about 10-10 m to 10-14 m Emitted by radioactive nuclei Highly penetrating and cause serious damage

when absorbed by living tissue Looking at objects in different portions of the

spectrum can produce different information

More notes on the EM wave Spectrum

Wavelengths and Information

These are images of the Crab Nebula

They are (clockwise from upper left) taken with x-rays visible light radio waves infrared waves