Chapter 21Chapter 21

Electromagnetic WavesElectromagnetic Waves

General Physics

Exam IIExam II

Curve: +30

General Physics

Electromagnetic WavesElectromagnetic Waves

Ch 21, Secs 8–12Ch 21, Secs 8–12

General Physics

James Clerk MaxwellJames Clerk Maxwell 1831 – 18791831 – 1879 Electricity and magnetism Electricity and magnetism

were originally thought to be were originally thought to be unrelatedunrelated

In 1865, James Clerk Maxwell In 1865, James Clerk Maxwell provided a mathematical provided a mathematical theory that showed a close theory that showed a close relationship between all relationship between all electric and magnetic electric and magnetic phenomenaphenomena

Electromagnetic theory of lightElectromagnetic theory of light

General Physics

Maxwell’s Starting PointsMaxwell’s Starting Points

Electric field lines originate Electric field lines originate on positive charges and on positive charges and terminate on negative terminate on negative chargescharges

Magnetic field lines always Magnetic field lines always form closed loops – they do form closed loops – they do not begin or end anywherenot begin or end anywhere

General Physics

Can electric fields Can electric fields form closed loops?form closed loops?

1 2

50%50%1.1. YesYes

2.2. NoNo

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

General Physics

Maxwell’s Starting PointsMaxwell’s Starting Points

Magnetic fields are generated Magnetic fields are generated by moving charges or by moving charges or currents (Ampère’s Law)currents (Ampère’s Law)

A varying magnetic field A varying magnetic field induces an emf and hence induces an emf and hence an electric field (Faraday’s an electric field (Faraday’s Law)Law)

General Physics

Turning Faraday’s Law upside Turning Faraday’s Law upside down, Maxwell hypothesized down, Maxwell hypothesized that a changing electric field that a changing electric field would produce a magnetic would produce a magnetic field (Maxwell-Ampère’s Law)field (Maxwell-Ampère’s Law)

Maxwell’s HypothesisMaxwell’s Hypothesis

General Physics

Maxwell EquationsMaxwell Equations

closed surface enclosed charge closed surface no mag. charge

• Conservation of energy

closed loop linked current + flux

• Conservation of charge

Lorentz force law

closed loop linked flux

General Physics

Maxwell’s PredictionsMaxwell’s Predictions Maxwell concluded that visible light and all Maxwell concluded that visible light and all

other electromagnetic (EM) waves consist of other electromagnetic (EM) waves consist of fluctuating electric and magnetic fields, fluctuating electric and magnetic fields, with each varying field inducing the otherwith each varying field inducing the other

Accelerating charges generate these time Accelerating charges generate these time varying E and B fieldsvarying E and B fields

Maxwell calculated the speed at which Maxwell calculated the speed at which these electromagnetic waves travel in a these electromagnetic waves travel in a vacuum – speed of light c = 3.00 x 10vacuum – speed of light c = 3.00 x 1088 m/s m/s

General Physics

Hertz’s Confirmation of Hertz’s Confirmation of Maxwell’s PredictionsMaxwell’s Predictions

1857 – 18941857 – 1894 First to generate and First to generate and

detect electromagnetic detect electromagnetic waves in a laboratory waves in a laboratory settingsetting

Showed radio waves Showed radio waves could be reflected, could be reflected, refracted and diffractedrefracted and diffracted

The unit Hz is named for The unit Hz is named for himhim

General Physics

Hertz’s Experimental Hertz’s Experimental ApparatusApparatus

An induction coil is An induction coil is connected to two large connected to two large spheres forming a spheres forming a capacitorcapacitor

Oscillations are initiated Oscillations are initiated by short voltage pulsesby short voltage pulses

The oscillating current The oscillating current (accelerating charges) (accelerating charges) generates EM wavesgenerates EM waves

General Physics

Hertz’s ExperimentHertz’s Experiment Several meters away Several meters away

from the transmitter is from the transmitter is the receiverthe receiver This consisted of a single This consisted of a single

loop of wire connected loop of wire connected to two spheresto two spheres

When the oscillation frequency of the When the oscillation frequency of the transmitter and receiver matched, energy transmitter and receiver matched, energy transfer occurred between themtransfer occurred between them

General Physics

Hertz’s ConclusionsHertz’s Conclusions Hertz hypothesized the energy transfer was in Hertz hypothesized the energy transfer was in

the form of wavesthe form of waves These are now known to be electromagnetic wavesThese are now known to be electromagnetic waves

Hertz confirmed Maxwell’s theory by showing Hertz confirmed Maxwell’s theory by showing the waves existed and had all the properties of the waves existed and had all the properties of light waves (e.g., reflection, refraction, light waves (e.g., reflection, refraction, diffraction)diffraction) They had different frequencies and wavelengths They had different frequencies and wavelengths

which obeyed the relationship v = f λ for waveswhich obeyed the relationship v = f λ for waves v was very close to 3 x 10v was very close to 3 x 1088 m/s, the known speed of m/s, the known speed of

lightlight

General Physics

EM Waves by an AntennaEM Waves by an Antenna

Two rods are connected to an oscillating source, charges Two rods are connected to an oscillating source, charges oscillate between the rods (a)oscillate between the rods (a)

As oscillations continue, the rods become less charged, the As oscillations continue, the rods become less charged, the field near the charges decreases and the field produced at t = field near the charges decreases and the field produced at t = 0 moves away from the rod (b)0 moves away from the rod (b)

The charges and field reverse (c) – the oscillations continue (d)The charges and field reverse (c) – the oscillations continue (d)

General Physics

EM Waves by an Antenna, EM Waves by an Antenna, finalfinal

Because the oscillating charges in Because the oscillating charges in the rod produce a current, there the rod produce a current, there is also a magnetic field generatedis also a magnetic field generated

As the current changes, the As the current changes, the magnetic field spreads out from magnetic field spreads out from the antennathe antenna

The magnetic field is The magnetic field is perpendicular to the electric fieldperpendicular to the electric field

General Physics

Electromagnetic Waves, Electromagnetic Waves, SummarySummary

A changing magnetic field produces A changing magnetic field produces an electric fieldan electric field

A changing electric field produces a A changing electric field produces a magnetic fieldmagnetic field

These fields are These fields are in phasein phase At any point, both fields reach their At any point, both fields reach their

maximum value at the same timemaximum value at the same time

General Physics

Electromagnetic Waves are Electromagnetic Waves are Transverse WavesTransverse Waves

TheThe and fields are and fields are perpendicular to each perpendicular to each otherother

Both fields are Both fields are perpendicular to the perpendicular to the direction of motiondirection of motion Therefore, EM waves are Therefore, EM waves are

transverse wavestransverse waves

E

B

Active Figure: A Transverse Electromagnetic Wave

General Physics

Properties of EM WavesProperties of EM Waves

Electromagnetic waves are transverse Electromagnetic waves are transverse waveswaves

They travel at the speed of lightThey travel at the speed of light

This supports the fact that light is an EM This supports the fact that light is an EM wavewave

1

o o

c

General Physics

Properties of EM Waves, 2Properties of EM Waves, 2 The ratio of the electric field to the magnetic field The ratio of the electric field to the magnetic field

is equal to the speed of lightis equal to the speed of light

Electromagnetic waves carry energy as they Electromagnetic waves carry energy as they travel through space, and this energy can be travel through space, and this energy can be transferred to objects placed in their pathtransferred to objects placed in their path

max

max

B

E

B

Ec

General Physics

Properties of EM Waves, 3Properties of EM Waves, 3

Energy carried by EM waves is Energy carried by EM waves is shared equally by the electric and shared equally by the electric and magnetic fieldsmagnetic fields

Average power per unit areaAverage power per unit area

0

2max

0

2max

0

maxmax

222 cB

c

EBEI

A

Pave

General Physics

Properties of EM Waves, Properties of EM Waves, finalfinal

Electromagnetic waves transport Electromagnetic waves transport linear momentum as well as energylinear momentum as well as energy For complete absorption of energy U For complete absorption of energy U

p = U/c p = U/c F = P F = Paveave/c/c For complete reflection of energy UFor complete reflection of energy U

p = (2U)/c p = (2U)/c F = 2P F = 2Paveave/c/c Radiation pressures (forces) can be Radiation pressures (forces) can be

determined experimentallydetermined experimentally

General Physics

Determining Radiation Determining Radiation PressurePressure

This is an apparatus This is an apparatus for measuring for measuring radiation pressureradiation pressure

In practice, the system In practice, the system is contained in a is contained in a vacuumvacuum

The pressure is The pressure is determined by the determined by the angle at which angle at which equilibrium occursequilibrium occurs

General Physics

Summary of Properties ofSummary of Properties ofElectromagnetic (EM) Electromagnetic (EM)

WavesWaves They travel at the speed of lightThey travel at the speed of light They are transverse wavesThey are transverse waves

E, B perpendicular to each other and velocityE, B perpendicular to each other and velocity Ratio of E and B field magnitudes: E/B=cRatio of E and B field magnitudes: E/B=c

Electric and magnetic fields carry equal energyElectric and magnetic fields carry equal energy They carry both energy and momentumThey carry both energy and momentum

Can deliver U and p to a surfaceCan deliver U and p to a surface

General Physics

The Spectrum of EM WavesThe Spectrum of EM Waves Forms of electromagnetic Forms of electromagnetic

waves exist that are waves exist that are distinguished by their distinguished by their frequency and wavelengthfrequency and wavelength c = ƒλc = ƒλ

Wavelengths for visible light Wavelengths for visible light range from 400–700 nmrange from 400–700 nm

a small portion of the spectruma small portion of the spectrum

WavelengthsWavelengths 1 km = 101 km = 10-3-3 m (radio) electronic m (radio) electronic 1 1 m = 10m = 10-6-6 m (visible, IR) m (visible, IR) 1 nm = 101 nm = 10-9-9 m (UV, X-ray) m (UV, X-ray) 1 Å = 101 Å = 10-10-10 m (X-ray) atomic m (X-ray) atomic 1 fm =101 fm =10-15-15 m ( m (-ray) nuclear-ray) nuclear