electromagnetic waves maxwell`s equations lecture 23 thursday: 8 april 2004
TRANSCRIPT
Electromagnetic WavesMaxwell`s Equations
Lecture 23
Thursday: 8 April 2004
ELECTROMAGNETIC WAVES
• E = Em sin(kx - t)
• B = Bm sin(kx - t)
k fT
ck
f
22
2
wave speed
k fT
ck
f
22
2
wave speed
POYNTING VECTOR
•This is a measure of power per area. Units are watts per meter2.
•Direction is the direction in which the wave is moving.
S E B 1
0S E B
1
0
POYNTING VECTOR
•However, since E and B are perpendicular,
S EB
E
Bc
Sc
Ec
B
1
1
0
0
2
0
2
and since
S EB
E
Bc
Sc
Ec
B
1
1
0
0
2
0
2
and since
INTENSITYS
cE kx t
S Ic
E
S Ic
E
EE
m
m
rms
rmsm
1
1
2
1
2
0
2 2
0
2
0
2
sin ( )
Intensity
Sc
E kx t
S Ic
E
S Ic
E
EE
m
m
rms
rmsm
1
1
2
1
2
0
2 2
0
2
0
2
sin ( )
Intensity
RADIATION PRESSUREF
p
t c
U
t cIA
FIA
c
FIA
c
1 1
2
(complete absorption)
(complete reflection)
Fp
t c
U
t cIA
FIA
c
FIA
c
1 1
2
(complete absorption)
(complete reflection)
RADIATION PRESSURE
Pressure =
(complete absorption
(complete reflection)
F
A
pI
c
pI
c
r
r
)
2
Pressure =
(complete absorption
(complete reflection)
F
A
pI
c
pI
c
r
r
)
2
RADIATION PRESSUREMomentum:
(complete absorption)
(complete reflection)
pU
c
pU
c
2
Momentum:
(complete absorption)
(complete reflection)
pU
c
pU
c
2
Comet: Picture taken WEDNESDAY 26 March
1997,at 2000 CST,at White Bear Lake,Minnesota.
MAXWELL’S EQUATIONSMAXWELL’S EQUATIONSMAXWELL’S EQUATIONSMAXWELL’S EQUATIONS
E A E s
B A B s
dq
dd
dt
d d id
dt
B
E
0
0 00
E A E s
B A B s
dq
dd
dt
d d id
dt
B
E
0
0 00
AMPERE’S LAWOriginal:
As modified by Maxwell:
B s
B s
d i
d id
dtE
0
0 0
Original:
As modified by Maxwell:
B s
B s
d i
d id
dtE
0
0 0
Reasons for the Extra Term SYMMETRY
CONTINUITY
SYMMETRY A time varying magnetic field produces an
electric field.
A time varying electric field produces a magnetic field.
SYMMETRYMaxwell' s Equations in Free Space
q i
d dd
dt
d dd
dt
B
E
0 0
0
0 0 0
E A E s
B A B s
Maxwell' s Equations in Free Space
q i
d dd
dt
d dd
dt
B
E
0 0
0
0 0 0
E A E s
B A B s
CONTINUITY
CONTINUITYWithout Maxwell' s modification:
At
At
At
P d i
P d
P d i
1 0
2
3 0
0
:
:
:
B s
B s
B s
Without Maxwell' s modification:
At
At
At
P d i
P d
P d i
1 0
2
3 0
0
:
:
:
B s
B s
B s
CONTINUITYWith Maxwell's modification:
At
At
At
"Displacement current"
P d i
P dd
dti
P d i
d
dti
Ed
Ed
1 0
2 0 0 0
3 0
0
:
:
:
B s
B s
B s
With Maxwell's modification:
At
At
At
"Displacement current"
P d i
P dd
dti
P d i
d
dti
Ed
Ed
1 0
2 0 0 0
3 0
0
:
:
:
B s
B s
B s
CONTINUITYi i
q CV
CA
dV Ed
qA
dEd AE
idq
dt
d
dti
d
E
Ed
0
0 0 0
0
i i
q CV
CA
dV Ed
qA
dEd AE
idq
dt
d
dti
d
E
Ed
0
0 0 0
0
AMPERE’S LAW
AMPERE’S LAWFor path 1:
For path 2:
For path 3:
since
B s
B s
B s
d i
d i i
d i i
i id
d
0
0 0
0 0
( )
( )
For path 1:
For path 2:
For path 3:
since
B s
B s
B s
d i
d i i
d i i
i id
d
0
0 0
0 0
( )
( )
ELECTROMAGNETIC WAVES
Maxwell' s Equations in Free Space
q i
d dd
dt
d dd
dt
B
E
0 0
0
0 0 0
E A E s
B A B s
Maxwell' s Equations in Free Space
q i
d dd
dt
d dd
dt
B
E
0 0
0
0 0 0
E A E s
B A B s
ELECTROMAGNETIC WAVES
E
x
B
t
B
x
E
t
E
B
E
Bc
c
m
m
0 0
0 0
8130 10. m/s
E
x
B
t
B
x
E
t
E
B
E
Bc
c
m
m
0 0
0 0
8130 10. m/s
MAXWELL’S EQUATIONSMAXWELL’S EQUATIONSMAXWELL’S EQUATIONSMAXWELL’S EQUATIONS
E A E s
B A B s
dq
dd
dt
d d id
dti i
B
E
d
0
0 0
0
0
( )
E A E s
B A B s
dq
dd
dt
d d id
dti i
B
E
d
0
0 0
0
0
( )
