Slide 1

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CHAPTER� 34� -� ELECTROMAGNETIC� WAVES

INSERT� SLIDE� ON� MAXWELL�S� EQUATIONS

SECTION� 34.2 � MAXWELL�S� EQUATIONS

=
NOT= E: The equations are in integral form in the
�� text� p. 955

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Maxwell�s� Equations� III� and� IV� with� J� =3D� 0� are:

In� Free� Space

SECTION� 34.3�� -�� PLANE� E-M WAVES

=
Con= sider� E� with a� y� component� only� perpendicular� to� B� which has
a� z� component� only

+y

E_y

+x

E_x� =3D� E_z� =3D� 0

B_y� =3D� B_x� =3D� 0

B_z

<= /td>	=
Wav= e propagation in this case will be in
the= x dimension only. One dimensional
pro= pagation is characteristic of PLANE

WAVES

+z

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+y

E_y

+x

B_z

differentiate� (3)� with respect to x:

<= /td>		<= /td>
(5= )	is = the linear wave equation in

�� one dimension

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E_y

where� v� is the phase velocity of the wave

+x

B_z

=	<= /td>
The= solution to equation (5) would be a
wave functio= n of E propagating

in = the x dimension at phase speed, v

=		<= /td>
A t= ime-dependent E and a time
-de= pendent B that are orthoganol
wil= l result in a wave in the electric

and= magnetic fields that propagate
at = phase speed, c (free space) in
a d= irection perpendicular to both
E and B. In our case, the

pro= pagation direction is +x.

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E_y

=
One solution of= equation (6) is:

(7)= �� E_y� =3D� E_m sin ( kx � ωt )

+x

B_z

=
The magnetic fi= eld solution is:

(8)= �� B_z� =3D� B_m sin ( kx � ω t )

<= /td>	=	<= /td>
Equ= ations (7)� and (8)� show that

= E and B� are perpendicular
= traveling waves propagating in a
dir= ection that is perpendicular to
both

ω� and� k� are� the same for both� E and B

Also<� E and B� �are� in phase

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<= /td>
EXAMPLES:=
(i)= �� Light has a wavelength of 1 micr= on in a vacuum. what is its frequency ?

f λ� =3D� c�� in a vacuum

f� =3D� c / λ� =3D� (3x10⁸ m/s) / (10^-6= m)

Is this light v= isible ?

f� =3D� 3 x 10¹⁴� s-1� =3D� 3 x 10¹⁴ Hz

<= /td>	=
(i= i)	Pyr= ex glass has a dielectric constant, K =3D 5.6. What is the speed
�� of light in this glass ?=

=
Assume� μ� =3D� μ₀<= span style=3D'mso-spacerun:yes'>� (meaning the medium is non-magnetic= which is
�� approximately valid in most media we�ll consider)

ε� =3D� Kε₀

v� =3D� 1.26 x 10⁸ m/s

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(7)�� E_y� =3D� E_m sin ( kx � ωt )

(8)�� B_z� =3D� B_m sin ( kx � ω t )

Equations� (7) and (8) and� Maxwell�s equations show that:

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<= /td>		<= /td>
EXAM= PLE �

�� The amplitude of the electric fi= eld, E_m of an E-M wave is 10 N/C. What is
Bm ?

E_m / = B_m� =3D� c

B_m� =3D� E_m / c� =3D� 10 N/C / (3x10⁸ m/s)

B_m� =3D� 3.3 x 10^-8� N= /C / m/s�� =3D�� 3.3x10^-8 T

B_m &l= t; <� E_m

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INSERT� SLIDES� ON� SECTION� 34.4 � ENERGY IN E-M WAVES

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<= /td>
Visible

Spec= trum

<= /td>	<= /td>
Elec= tromagnetic
�� Spectrum
SEE = SEC.34.7

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= CHAPTER 34 - ELECTROMAGNETIC WAVES

INSERT SLIDE ON MAXWELL’S EQUAT= IONS

SECTION 34.2 – MAXWELL’S EQUATIONS

NOTE: The equations are in integral form in the

= ; text p. 955

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Maxwell’s Equations III and IV with J =3D 0 are:

In Free Space

= Consider E with a y component only perpendicular to B which has= 3;

a z component only

Ey

Bz

+x

+y

+z

= Ex<= /span> =3D Ez =3D 0

By<= /span> =3D Bx =3D 0

Wave propagation in this case will be in th= e x dimension only. One dimensional

propagation is characteristic of PLANE

WAVES

SECTION 34.3 - PLANE E-M WAVES

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Ey

Bz

+x

+y

<= ![endif]>

differentiate (3) with respect to x:

(5)is the linear wave equation in &#= 13;

one dimension

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=

Ey

Bz

+x

where v is the phase velocity of the wave

The solution to equation (5) would be a

wave function of E propagating

in the x dimension at phase speed, v

=

A time-dependent E and a time

-dependent B that are orthoganol

will result in a wave in the electric

and magnetic fields that propagate

at phase speed, c (free space) in

a direction perpendicular to both

E and B. In our case, the

propagation direction is +x.

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Fig 34-2, p.1069

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