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Faraday:
d
B
dt
LI
Inductance:
flux = (inductance) x (current)
Thur. Nov. 6, 2008
Lsolenoid o N 2 A /
Physics 208, Lecture 20
1
Inductance: a general result
Flux = (Inductance) X (Current)
LI
Change in Flux
= (Inductance) X (Change in Current)
LI
Faraday’s law:
d
dI
EMF
L
dt
dt
Thur. Nov. 6, 2008
Physics 208, Lecture 20
2
Question
The current through a solenoid is doubled.
The inductance of the solenoid
A. Doubles
B. Halves
C. Stays the same
Thur. Nov. 6, 2008
Physics 208, Lecture 20
3
Question
The potential at a is higher than at b. Which
of the following could be true?
A) I is from a to b, steady
B) I is from a to b, increasing
C) I is from a to b, decreasing
D) I is from b to a, increasing
E) I is from b to a, decreasing
Thur. Nov. 6, 2008
Physics 208, Lecture 20
4
Inductor circuit
Induced EMF extremely high
Breaks down air gap at switch
Air gap acts as resistor
Thur. Nov. 6, 2008
Physics 208, Lecture 20
5
Perfect inductors in circuits
I
Constant current flowing
I?
-
EMF needed to drive
current thru resistor
+
Thur. Nov. 6, 2008
All Voltage drops = 0
-IR + VL = 0
IR LdI/dt 0
dI/dt IR /L
Physics 208, Lecture 20
6
RL circuits
-
I?
dI
R
I
dt
L
R
dI I dt
L
+
Current decreases in time
Slow for large inductance
Slow for small resistance
(inductor fights hard, tries to keep constant current)
(no inductor EMF needed to drive current)
Time constant L/R
Thur. Nov. 6, 2008
Physics 208, Lecture 20
7
RL circuits
-
I(t)
I Ioet /(L / R ) Ioet /
+
Time constant
L/R
Thur. Nov. 6, 2008
Physics 208, Lecture 20
8
Faraday’s law
d
d
E ds B B dA
dt
dt
EMF around loop
Magnetic flux through
surface bounded by path
EMF no longer zero
around closed loop
Thur. Nov. 6, 2008
Physics 208, Lecture 20
9
EMF and E.ds in electrostatics
Remember,
work done by E-field = W AB
so
W
qtest
“EMF”
B
F
E ds V
B
A
B
Coulomb
ds qtest VB VA
VA
A
y
A
E ds E ds 0
A
A
Integral of E-field around closed
loop is zero in electrostatics
Thur. Nov. 6, 2008
Physics 208, Lecture 20
x
10
E dA
S
B dA
S
E ds
0
B
0
dB
dt
dE
B ds oI oo dt
E Qencl /o
Not only charges produce E-field
a changing B-field also produces an E-field
a changing E-field produces a B-field
Gauss’ law:
charges create E-fields
Ampere’s law:
currents create B-fields
Time-dependent
fields
Not only currents produce B-field
Thur. Nov. 6, 2008
Physics 208, Lecture 20
11
James Clerk Maxwell
Electricity and magnetism
were originally thought to
be unrelated
in 1865, James Clerk
Maxwell provided a
mathematical theory that
showed a close
relationship between all
electric and magnetic
phenomena
Thur. Nov. 6, 2008
Physics 208, Lecture 20
12
Maxwell’s Starting Points
Electric field lines originate on positive charges and
terminate on negative charges (E 1 / R2)
Gauss’s law for E
Magnetic field lines always form closed loops – they
do not begin or end anywhere
Gauss’s law for B
Magnetic fields are generated by moving charges or
currents
Ampère’s Law
A varying magnetic field induces an emf and hence
an electric field
Faraday’s Law
Thur. Nov. 6, 2008
Physics 208, Lecture 20
13
Maxwell’s Predictions
Electric and Magnetic fields play symmetric roles
in nature
light waves consist of fluctuating electric and
magnetic fields
each varying field induces the other
In vacuum, EM waves travel at
speed of light : 3x108 m/s
Thur. Nov. 6, 2008
Physics 208, Lecture 20
14
• A Transverse wave.
• Electric/magnetic fields perpendicular to
propagation direction
• Can travel in empty space
f = v/, v = c = 3 x 108 m/s (186,000 miles/second!)
Thur. Nov. 6, 2008
Physics 208, Lecture 20
15
Electromagnetic Waves
E and B fields are perpendicular
to each other
to propagation direction
E and B fields are ‘in phase’
Both reach their peak values simultaneously
Wave moves in space
Propagation direction is E B
Thur. Nov. 6, 2008
Physics 208, Lecture 20
16
Question:
At a particular instant, an EM wave has an
E-field pointing in the y-direction and a Bfield pointing in the x-direction. The
propagation direction is
z
A. z
D. -z
B. y
E. -y
C. X
F. -x
Thur. Nov. 6, 2008
Physics 208, Lecture 20
y
x
17
The EM
Spectrum
Note the overlap
between types of
waves
Visible light is a
small portion of
the spectrum
Types are
distinguished by
frequency or
wavelength
Thur. Nov. 6, 2008
Physics 208, Lecture 20
18
Sizes of EM waves
Visible light
typical wavelength of 500 nm = = 0.5 x 10-6 m
= 0.5 microns (µm)
AM 1310, your badger radio network,
has a vibration frequency of 1310 KHz = 1.31x106 Hz
What is its wavelength?
A. 230 m
B. 0.044
m
C. 2.3 m
D. 44m
Thur. Nov. 6, 2008
Physics 208, Lecture 20
19
Hertz’s Confirmation of
Maxwell’s Predictions
Generates and
detected
electromagnetic waves
Showed they have
same properties as
light waves
Thur. Nov. 6, 2008
Physics 208, Lecture 20
20
Hertz Trans & reciever
Receiver
spark gap
Transmitter
spark gap
EM wave
Magnified view of the spark gap
and dipole transmitting ("feed")
antenna at the focal point of the
reflector. The high voltage spark
jumped the gap between the
spherical electrodes. The electrical
impulse produced by the spark
generated damped oscillations in
the dipole antenna.
Thur. Nov. 6, 2008
Magnified view of the spark gap and
dipole receiving antenna at the focal
point of a receiving reflector similar to
the transmitting one. The width of the
small spark gap on the right is controlled
by the screw below it. The vertical dipole
antenna at the left was about 40
centimeters long.
Physics 208, Lecture 20
21
Transatlantic signals
Capacitor
banks
Induction
coils
Spark gap
Gulgielmo Marconi’s transatlantic transmitter
Thur. Nov. 6, 2008
Physics 208, Lecture 20
22
Transatlantic receiver
Left to right: Kemp, Marconi, and Paget pose in front of a kite that was
used to keep aloft the receiving aerial wire used in the transatlantic
radio experiment.
Thur. Nov. 6, 2008
Physics 208, Lecture 20
23
EM Waves from an Antenna
Two rods are connected to an ac source, charges oscillate
between the rods (a)
As oscillations continue, the rods become less charged, the field
near the charges decreases and the field produced at t = 0
moves away from the rod (b)
The charges and field reverse (c)
The oscillations continue (d)
Thur. Nov. 6, 2008
Physics 208, Lecture 20
24
Detecting EM waves
FM antenna
AM antenna
Oriented vertically for radio waves
Thur. Nov. 6, 2008
Physics 208, Lecture 20
25
EM Waves Question?
Which direction should I orient my loop
antenna to receive a signal from the
transmission tower?
+
A)
B)
C)
Thur. Nov. 6, 2008
Physics 208, Lecture 20
26