32 lecture lam - university of hawaiʻiplam/ph272_summer/l12/32_lecture_lam.pdf · electromagnetic...

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

PowerPoint® Lectures for

University Physics, Twelfth Edition

– Hugh D. Young and Roger A. Freedman

Lectures by James Pazun

Chapter 32

ElectromagneticWaves

Modified P. Lam 8_11_2008


Topics for Chapter 32

• Maxwell’s equations and wave equation

• Sinusoidal electromagnetic waves

• Passage of electromagnetic waves through matter

• Energy and momentum of electromagnetic waves

• Formation of standing electromagnetic wave

inside a conducting cavity.


Maxwell’s equations

• James Clark Maxwell penned a set of four equations that draw

Gauss, Ampere, and Faraday’s laws together in a comprehensive

description of the behavior of electromagnetic waves.

• The four elegant equations are found at the bottom of page 1093.

(r E • ˆ n )

closedsurface

dA =Qenclosed

o

(r B • ˆ n )

closedsurface

dA = 0

r E • d

r l

Closedloop

= (

r B

tOpensurface

• ˆ n )dA

r B • d

r l

Closedloop

= μoIenclosed μo o (

r E

tOpensurface

• ˆ n )dA


Creating electromagnetic waves

• Classical Theory: An accelerating charge (eq. a charge moving in a

circular motion, a charge oscillates back and forth in an alternating

current circuit) creates electromagnetic wave.

Concept :

r E

t

r B (t)

r B

t

r E (t)

Quantum Theory: When an excited atom and molecule returns back

to the ground state, they generate electromagnetic waves.


Properties of Electromagnetic waves in vacuum

(1) Wave speed = 1

oμo3x108 m

sc

(2) Does not require a medium to carry the wave.

(3) Transverse wave - r E and

r B are to direction of propagation.

ˆ E ˆ B = ˆ v

(4) Definite ratio between the magnitudes of r E and

r B :

r E = c

r B


Spherical wave and Sinusoidal Plane waves

Sinusoidal plane wave :r E = ˆ j Emax cos(

2x 2 f t)

r B = ˆ k Bmax cos(

2x 2 f t)

c =T

= f


Electromagnetic waves occur over a wide range

• Where wavelength is large, frequency is small.

• The range extends from zero to infinite frequency. Common lowfrequency waves are radio and television waves generated by Accurrents; high frequency waves are X-ray and gamma raysgenerated by de-excitation of electrons inside an atom and de-excitation of the nucleus.

f = c


The visible spectrum

• The visible spectrum is a very small range compared to the entireelectromagnetic spectrum.

• Visible light extends from red light at 700 nm to violet light at400 nm.


Numerical example.

• Follow Example 32.1. An electromagnetic wave propagates in thenegative x-direction, its wavelength is 10.6x10-6 m, the electricfield is along the z-direction with maximum E-field=1.5x106

V/m.

• Write the equation for E and B-fields.


Propagation of electromagnetic wave in a linear medium

In a medium such as water or glass,

the electromagnetic wave speed is not c (3x108 m

s).

= K o μ = Kmμo

v =1

μ=

1

KKm oμo=

c

KKm

< c

KKm n = index of refraction of the medium.

For example :

When an electromagnetic wave enters from vacuum

into glass, the frequency is unchanged but the new

wavelength is different from the orignal wavelength.

=cf, '=

vf

=c

KKm f,


Energy in an EM wave, the Poynting vector

Energy is stored in E and B - fields :

Energyvolume

u =1

2 oE 2 +1

2μo

B2

Use E = cB u =12 oE 2 +

12μo

E 2

c 2=12 oE 2 +

12 oE 2

energy stored in E - field = energy stored in B - field.

Energy intensity =energy

area * time=

energyvolume

*wave speed = uc

= oE 2c = oEBc 2 =EB

μo

This energy flows in the direction given by r E

r B , hence

define a energy flow vector (called Poynting vector)r S

1

μo

r E

r B


Numerical example.

• An electromagnetic wave propagates in the negative x-direction, itswavelength is 10.6x10-6 m, the electric field is along the z-direction withmaximum E-field=1.5x106 V/m.

• Find the instantaneous energy density, the time average energy density.

• Find the instantaneous Poynting vector, the time average intensity.


Electromagnetic wave also carries momentum - “Solar sail”


Standing EM waves inside a conducting cavitySimilar to standing waves of a vibrating string.

The "allowed"wavelengths are fixed by the dimension of the cavity.

For example : Two parallel conducting plates are separated

by a distance L apart (in the x - direction.).

The allowed wavelengths are :

1 = 2L, 2 =2L

2, 3 =

2L

3, ..., n =

2L

na set of allowed frequencies :

fn =c

n

= nc

2L(n =1,2,3,...)

32 lecture lam - university of hawaiʻiplam/ph272_summer/l12/32_lecture_lam.pdf · electromagnetic...

Documents