hertz’s discoveries
TRANSCRIPT
Ampere’s Law Updated Hertz’s Discoveries Plane Electromagnetic Waves Energy in an EM Wave Momentum and Radiation Pressure The Electromagnetic Spectrum
Id 0. sB
Ampère’s Law
For S1, Id 0. sB
For S2, 0. 0 Id sB
(No current in the gap)
But there is a problem if I varies with time!
Consider a parallel plate capacitor
Call I as the conduction current.
Specify a new current that exists when a change in the
electric field occurs. Call it the displacement current.
dt
dI E
d
0
Electrical flux through S2:
00
QA
A
QEAE
Idt
dQ
dt
dI E
d
0
Magnetic fields are produced by
both conduction currents and by
time-varying electrical fields.
dt
dIIId E
d
0000. sB
Now the generalized form of Ampère’s Law, or Ampère-Maxwell Law becomes:
BvEF
qq Lorentz Force Law
Faraday’s Law dt
dd B
sE
.
Ampère-Maxwell Law dt
dId E 000. sB
Gauss’ Law for Magnetism –
no magnetic monopoles 0. AB
d
Gauss’ Law 0
.
Qd AE
By supplying short voltage bursts from the coil
to the transmitter electrode we can ionize the
air between the electrodes.
In effect, the circuit can be modeled as a LC circuit,
with the coil as the inductor and the electrodes as
the capacitor.
A receiver loop placed nearby is able to receive
these oscillations and creates sparks as well.
Circular (or Spherical in 3D) Waves
Plane Waves
dt
dd B
sE
.
dt
dId E 000. sB
Free Space: I = 0, Q = 0
dt
dd E
00. sB
t
E
x
B
t
B
x
E
00
2
2
002
2
002
2
t
E
x
E
t
E
tx
B
tt
B
xx
E
2
2
002
2
t
B
x
B
tkxBB
tkxEE
cos
cos
max
max
2k Wavenumber
00
1
c Speed of Light
f 2 Angular Frequency
f
c Wavelength
tkxBB
tkxEE
cos
cos
max
max
ck
tkxBB
tkxEE
cos
cos
max
max
t
E
x
B
t
B
x
E
00
ckB
E
B
E
BkE
max
max
maxmax
The solutions to Maxwell’s equations in free space are wavelike
Electromagnetic waves travel through free space at the speed of light.
The electric and magnetic fields of a plane wave are perpendicular to each other and the direction of propagation (they are transverse).
The ratio of the magnitudes of the electric and magnetic fields is c.
EM waves obey the superposition principle.
MHzf 40
a) =?, T=?
sf
T
mf
c
8
6
6
8
105.21040
11
5.71040
103
b) If Emax=750N/C, then Bmax=?
Tc
EB 6
8
maxmax 105.2
103
750
Directed towards the z-direction
c) E(t)=? and B(t)=?
)1051.2838.0cos(105.2cos
)1051.2838.0cos(/750cos
86
max
8
max
txTtkxBB
txCNtkxEE
sradf
mradk
/1051.2104022
/838.05.7
22
86
BES
0
1
Poynting Vector (W/m2)
For a plane EM Wave: 2
00
2
0
Bc
c
EEBS
2
max
00
2
max
0
maxmax
222B
c
c
EBESI av
The average value of S
is called the intensity:
S is equal to the rate of EM energy flow per unit area
(power per unit area)
0
2
2
BuB
2
2
0EuE
2
0
2
0
00
0
2
2
1
22EE
cEuB
0
22
022
1
BEuu BE
For an EM wave, the instantaneous
electric and magnetic energies are
equal.
0
22
0
B
Euuu BE
0
2
max2
max0
2
022
1
BEEu avav
avav cuSI
Total Energy Density of an EM Wave
The intensity is c times the
total average energy density
Which gives the largest average energy density
at the distance specified and thus, at least
qualitatively, the best illumination
1. a 50-W source at a distance R.
2. a 100-W source at a distance 2R.
3. a 200-W source at a distance 4R.
c
E
AI av
0
2
max
2
P
P lamp= 150 W, 3% efficiency
A = 15 m2
mVA
cE av /42.18
2 0max
P
Wlampav 5.403.0 PP
Tc
EB 8max
max 1014.6
A
c
Tp ER Momentum for complete absorption
dt
dp
AA
FP
1
A
dtdT
cc
T
dt
d
AP ERER 11
c
SP
Pressure on surface
For complete reflection: c
Tp ER2
c
SP
2
P laser= 3 mW, 70% reflection, d = 2 mm
2
2/955
001.0
003.0mW
AS
P
26
8/104.5
103
9557.1
7.17.0
mNP
c
S
c
S
c
SP
The fundamental mechanism for electromagnetic radiation is
an accelerating charge
Reading Assignment
Chapter 35: Nature of Light and Laws of Geometric Optics
WebAssign: Assignment 12