E

1
As the first half wavelength of the approaching
wavefront reaches the atom shown, the E-field
E
c
B
1) pushes the electron cloud up, the nucleus
down. 2) pushes the electron cloud left, the
nucleus right. 3) pushes the electron cloud
right, the nucleus left. 4) pushes the electron
cloud down, the nucleus up.
2
As the electrons move down under the influence of
the E-field, the oncoming B-field in the same
half wavelength pushes those electrons
E
1) toward the right of the screen. 2) toward the
left of the screen. 3) up. 4) down. 5) forward,
in the direction of c. 6) backward, into the
screen.
c
B
3
As the protons move up under the influence of the
E-field, the oncoming B-field in the same half
wavelength pushes those protons
E
1) toward the right of the screen. 2) toward the
left of the screen. 3) up. 4) down. 5) forward,
in the direction of c. 6) backward, into the
screen.
c
B
4
Wave Intensity
Intensity Energy transported per unit area per
second Power transported per unit area.
As the wave moves outward, energy gets spread out
over a wider and wider area, so the wave
intensity gets smaller.
Surface area of a sphere 4?R2
What is the intensity of EM waves?
5
Recall
Energy stored in the electric field within a
capacitor CV2
with C ?oA/d and VEd
so PEEfield (?oA/d)(Ed)2
?o(Ad)E2
1 2
1 2
uE ?oE2
Similarly
Energy stored in the magnetic field of a
solenoid LI2
where L NBA/I and BmoI(N/?)
1 2
so PEBfield (NBA/I)I2
NBA(B?/moN)2
1 2mo
PEBfield (A?)B2
uB B2
We say the energy density within the magnetic
field is
1 2mo
6
A
A
cDt
During a time Dt, an electromagnetic wave will
deliver energy to/through any surface A it
illuminates
AcDt(uB uB )
7
Since E (B) is continuously induced/created by B
(E) expect E?B
and since the total energy is continuously
exchanged between E and B we expect (for EM
waves), at every point in space uB uB
8

• The rate at which electromagnetic energy is being
  transferred by an EM wave through any given area
  is

Units W / m2
or
9
Compared to wave 1, the power transported by
wave 2 is about 1) half 2) the same 3)
double 4) quadruple
10

• The rate at which electromagnetic energy is being
  transferred by an EM wave at any given moment
  through any given area is

instantaneous field values!
Remember! E and B fields fluctuate with time!
11
You should recall that the time average of E(t)
is zero.
Eo2sin?
2
Eo
Eosin?
Eo
2
Eosin?
What is the average E2(t)?

1. 0
2. Eo
3. Eo

• 4) Eo
• ( Eo)2
• Eo2

12
Average Intensity and RMS values
Energy delivered
E field
Because intensity is constantly changing, we work
with the average intensity
Average over one full wavelength. Since E
varies sinusoidally, (E2)avg ??? (Emax2) .
(1/2)
13
Average Intensity and RMS values
Energy delivered
E field
Because intensity is constantly changing, we work
with the average intensity
Average over one wavelength. Because E is a sine
wave, the average is 1/2.
To get average, you have two choices 1. Remember
the factor of 1/2 2. Use rms values for E and B
and use standard equation S E2/?oc
Sav Erms2/?oc
14
Charge vibrates linearly along the direction
illustrated. This oscillating dipole emits
transverse waves preferentially in what
direction?
1
2
3
Waves are transmitted equally in all directions
4
5
15
The magnetron of a microwave horn generates a
horizontally varying B-field and oscillating
vertical E-field. We found which of the
aluminum gratings below let the microwaves pass?

1
2
16
4) pushes the electron cloud down, the nucleus up.
E-field up, so positive charges are pushed up,
negative charges down!
5) forward, in the direction of c.
B-field left, with electrons (use left hand!)
moving down.
5) forward, in the direction of c.
B-field still left, but use right hand now
for The positive protons moving up.
Intensity is proportional to the square of the E
or B fields.
4) quadruple
If the amplitude of the fields doubles, it must
mean 4x as much energy.

1. Eo2

Just look at the graph of E2 to judge where the
average of those oscillations are.
4
Most of the energy is transmitted perpendicular
to the direction the charge vibrates..
2
The vertical slats act as antenna absorbing
energy from the microwaves as current surges up
and down. The horizontal slats are ineffective
current paths, and let the microwave energy pass,
unused.