ELECTROMAGNETIC WAVES (Chapter 24 in text)
James Maxwell (1831-1879)
r
r
• found behaviour of E and B described by 4 equations
•
equations combine to give wave equation
speed of wave ≡ c =
1
ε 0 µ0
= 2.99 × 108 m/s = speed of light)
•
Maxwell’s discovery showed that light is an electromagnetic wave
•
First step was to “complete” Ampere’s law
“GENERALIZED” AMPERE’S LAW
Ampere’s law before Maxwell (and so far in this course):
r r
B
∫ ⋅ ds = µ 0 I enclosed
around
loop
Maxwell noticed a problem: consider 2 plates charging as current flows
•
•
as current flows, electric flux through
surface between plates changes
dΦ E
ε
found that 0 d t acts like a current
Result: General version of Ampere’s Law:
+
E
-
I
I
r r
dΦ E
⋅
=
µ
+
µ
ε
B
d
s
I
0
0 0
∫
dt
IMPORTANT: says that magnetic field is produced in TWO ways:
• around current in a wire
• around surface through which electric flux Φ E is changing.
r
r
MAXWELL’S EQUATIONS: link between E and B
In free space with no conductor, no charge, no dielectric or magnetic material:
r r
Gauss’s Law: no flux through empty closed surface
∫ E ⋅ dA = 0
r r
∫ B ⋅ dA = 0
r
dΦ B
E
ds
⋅
=
−
∫
dt
closed
Like Gauss’s Law: no magnetic “charges”
r r
Faraday’s Law of induction (because ε = ∫ E ⋅ ds )
path
r r
dΦ E
⋅
=
+
B
d
s
I
µ
µ
ε
0
0 0
∫
dt
Ampere’s Law
r
r
1 two say flux of E and B through a closed surface is zero
st
r r
r r
2 two say sum of E ⋅ ds or B ⋅ ds around a closed path is linked to rate of
change of the “other” flux.
nd
MAXWELL’S EQUATIONS imply ELECTROMAGNETIC WAVES (24.3 in text)
What are the properties of electromagnetic waves?
r
r
r r
• Perpendicular E and B propagate through space in direction of E × B
r
r
o Oscillating E induces B
r
r
o Oscillating B induces E
r
r
Representation: “envelopes” represent magnitudes of E and B along wave
y
x
z
E
B
c
x
Alternate representation with Field Lines:
c
E field lines
•
•
B field lines
as electromagnetic wave passes point in space:
r
o E oscillates with the frequency of the wave
r
o B oscillates with same frequency, perpendicular direction
r r
REMEMBER: direction of propagation is E × B
Electromagnetic waves are emitted from oscillating electric charges
r
• If all waves emitted in a given direction have E field oscillating along
same axis:
E
o Resulting radiation (light) is LINEARLY POLARIZED
B
for all waves
•
r
If waves are emitted with E fields pointing along all directions
perpendicular to direction of propagation
E
E
E
o Resulting radiation (light) is UNPOLARIZED
E
E
E
PLANE WAVES:
•
If waves travelling in a certain
direction are in phase
everywhere on a given plane
perpendicular to that direction
o Form plane waves
SPHERICAL WAVES:
•
Waves emitted in phase in all
directions from a point source
o Form spherical waves
λ