E/M waves
What do charges have to do to create E/M radiation?
Accelerate!
A
Radiation from a single dipole
P1. Suppose that the two charges are moving apart at
this time. What is the direction of  0 E (displacement
t
current) at the center?
a) Up b) down
P2. What is the direction of induced
B at point A ?
a) out of page b) into page
c) right d) left
E
 B  0 J   0 0
t

path
A
B  dl  o I piercing
surface
d
ˆ
  o o
E  ndA

dt open surface
bounded
by path
Radiation from a single dipole
B
 E  
t
P3. What is the direction of the curl
of E near point A if B is increasing?
a) out of page b) into page
c) right d) left
A
Radiation from a single dipole
B
 E  
t
Inside the atom where e- is
moving:
E
 B  0 J   0 0
t
After light has left the atoms
(vacuum):
E
  B   0 0
t
Far from the dipole the field
lines straighten into plane
waves
E  r , t   Eo e
i k r t


B  r , t   Bo e


i k r t
What does
physically?
Eo e

i k r t
 mean
Review phasors
Two ways to indicate phase of wave
Beauty of using exponentials in uniform
plane waves

i  k x x  k y y  k z z t 
Eo e
t

i  k x x  k y y  k z z  t 
Eo e
x
A
 E  0

2
(remember these relations)
E vs B



Direction
E  r , t   Eo e
i k r t
Magnitude
B  r , t   Bo e

Phase
Bo
i k r t
A
(remember
the ratio of
Eo/Bo in a
plane wave)
Dipole radidation, antennas
The greatest intensity is
_______ to the line of
acceleration.
Index of refraction from polarization
2
2

J

E

P
2
P
 E   o o
 o
 o 2
2
t
t
t
n  1 
Assumption of a linear medium
(learn this derivation of n)
k
v
2

c
A

vac
 f 
n
  2 f

n 2
n

k
vac
n
Demo: waves in 1-D: wavelength, curvature vs
wave speed. http://phet.colorado.edu/sims/wave-ona-string/wave-on-a-string_en.html

c
Review
P.
f ( x, t)  f ( x  ct)is a solution to
It is also a solution to ____:
1)
3
1  3 f ( x, t)
x
2)
a)
b)
c)
d)
3
f ( x, t) 
c
3
t
3
0
4
1  4 f ( x, t)
f ( x, t)  4
0
4
4
x
c
t
eqn 1
eqn 2
both
neither
2
1  2 f ( x, t)
f ( x, t)  2
0
2
2
x
c
t