chapter 32.pdf

8/14/2019 Chapter 32.pdf

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Chapter 32Electromagnetic Waves

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Is the assumption consistent with

Faradays Law?

Consistent only with Faradays Law if the

wave speed and the magnitudes of the

perpendicular vectors Eand B are related.!Ea =!Bac It is then valid to say that,

(Electromagnetic wave

in vacuum)

During a time interval dt, the

wave front moves a distance

(c)dtto the right sweeping out

an area (ac)dtof the rectangle.The thus increases

during the time interval by,!

B

d!B =B(ac)dt

The rate of change of is,!Bd!

B

dt=Bac

E = cB

!Ed

!

l"! = "Ea Does our wave satisfies Amperes Law?

We move our rectangle so that it lies

in the xz-plane.We take the vector area dAin the y-direction thus we integrate

counterclockwise around the

rectangle.On side ef, Bis zero.

Only sideghcontributes to the

integral.

On side fgand he, Bis either zero or

perpendicular to dl.

There is no conduction current so,!Bd

!

l"! = 0!0d"

E

dt

!

Bd!

l"! =Ba

Does our wave satisfies Amperes Law?Only sideghcontributes to the integral.

The left-hand side of Amperes Law is

non-zero so the right-hand side must

also be non-zero.Eand Bmust be mutually

perpendicular.

It is then valid to say that,(Electromagneticwave in

vacuum)Obeys Amperes Law only if B, cand Eare

related.

!Bd

!

l"! =0!0d"

E

dt

!

Bd!

l"! =Ba

In a time interval dt, thethrough the rectangle increases by,!E

d!E =E(ac)dt

The rate of change of is,

!E

d!E

dt=Eac

Ba =0!0Eac

B =0!0Ec

Our EM wave must obey both Amperes and

Faradays Law!

It will only happen if,

That is,

MUST BE SATISFIED!!!B =

0!0EcE = cB ; B =

1

cE

1c

=0!0c

c =

1

0!0

c =1

8.85!10"12C

2/ Nm

2( ) 4!!10"7N/ A2( )= 299, 792, 458m / s


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Our assumed wave is consistent with all

Maxwells equations, provided that the wave

front moves with the SPEED OF LIGHT!!!c = 3.00!10

8m / s

Important features of all Electromagnetic Waves:The wave is transverse; both E and B are perpendicular to the

direction of propagation of the wave. The E and B fields are also

perpendicular to each other. The direction of propagation is the

direction of the vector product Ex B.There is a definite ratio between the magnitudes of Eand B: E= cB.The wave travels in vacuum with a definite and unchanging speed. Unlike mechanical waves, which need the oscillating particles of a

medium such as water or air to transmit a wave, electromagnetic

waves require no medium. Whats waving in an electromagnetic

wave are the electric and magnetic fields.

Sinusoidal Electromagnetic Waves

Electromagnetic waves produced by an oscillating point charge is an

example of sinusoidal waves that are not plane waves. The frequency, wavelength and speed of propagation of any periodic wave

is,c = !f

E0 ;*( +06;/4B0 ?=


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A( * 5*;''12 ; B = 0!0EcE = cB

X 6 S 0 0 + & O ? = 4 ( *

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E = vB ; B = !Ev

1

v

= !v !1

v2 =!

v2=

1

!

! v =1

!

v =

1

!m

0!"

0

=

1

!m!

1

0"0

=

c

!m!

A( * +40C0;7/4;2

X4(+0P &O /0O/*;@&(Y

v =

c

!m!

. & / 1 & 6 7

+40C0;7/4;2

!m !1

v =

c

!

^0;*'60 46 *C2

! vdielectric

< c 1

!

B

8

A( &S@;62c

v

= n


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