Electromagnetic Waves

James Clerk Maxwell

• Scottish theoretical physicist

• 1831-1879

• Famous for the Maxwell-Boltzman Distribution and Maxwell’s Equations

Source: en.wikipedia.org

Maxwell’s Equations

o

E

B 0

BE

t

o o o

EB J

t

Guass’ Law:

The total electric field through a closed surface is proportional to the charge enclosed

Coulomb’s Law can be derived

Guass’ Law for Magnetism:

The total magnetic flux through a closed surface is always zeroThere are no magnetic monopoles

Faraday’s Law of Induction:

A changing magnetic field produces an electric field (which can cause electrons to flow)

Ampere’s Law:

An electric current produces a magnetic field A changing electric field produces a magnetic field

E – electric field strength 0 – magnetic permeability

B – magnetic field strength 0 – electric permittivity

– charge density J – current density

Electromagnetic Waves

2 2x x

o o2 2

E E

z t

• Combining Faraday’s Law and Ampere’s Law (with correction):

2 2y y

o o2 2

B B

z t

• These are wave equations! Electric and magnetic fields can be described as a wave!

Electromagnetic Waves

Antenna

• An accelerating charge will produce an electromagnetic wave (i.e. radiation)

• Radiation is a form of energy transfer

Radiation

Electromagnetic Waves

• An electromagnetic wave consists of an electric field and magnetic field changing in time

• The electric field and magnetic field are perpendicular to each other and in phase

• Both the electric and magnetic fields are perpendicular to the direction of propagation (i.e. EM waves are transverse)

Electromagnetic Waves

• From the wave equation, the speed of an electromagnetic wave is:

• Where and

• That means that , which is the speed of light!

• Light is an electromagnetic wave!

0

0 0

1c

7 20 4 10 N A 12 2 2

0 8.85 10 C Nm

80c 3.00 10 m s

Electromagnetic Waves

• At first scientists thought light travelled through a medium they called the “luminiferous ether”

• Michelson and Morley attempted to measure Earth’s movement through the ether

• They hypothesized light would travel different distances depending on the direction Earth moves through the ether

Electromagnetic Waves

• They found that there was no change in propagation distance with direction

• The ether did not exist!

• LIGHT DOES NOT NEED A MEDIUM TO PROPAGATE

• Even null results are significant!

Electromagnetic Spectrum

• Light, microwaves, x-rays, etc. are all electromagnetic waves with different wavelengths (and frequencies)

Electromagnetic Spectrum

• Humans perceive the wavelength of electromagnetic waves in the visible range as COLOUR

400–484 THz620–750 nmred

484–508 THz590–620 nmorange

508–526 THz570–590 nmyellow

526–606 THz495–570 nmgreen

606–668 THz450–495 nmblue

668–789 THz380–450 nmviolet

FrequencyWavelengthColor

EM Waves in Media

• As EM waves travel through media other than a vacuum, the waves are constantly absorbed and re-emitted.

• The electric field of the incident wave accelerates the electrons.

• Accelerating electrons produce EM waves.

EM Waves in Media• It takes time to absorb and re-emit the EM waves causing

the wave to propagate slower than it would in a vacuum.

• Different molecules absorb and re-emit EM waves a different rates causing differences in the speed of light in these media.

cn

v

Index of Refraction:

n – index of refraction

c – speed of light in a vacuum

v – speed of light in a medium