Transcript PHY 231 Lecture 29 (Fall 2006)

Physics 213
General Physics
Lecture 14
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Last Meeting: Electric Generators,
Alternating Current
Today: Electromagnetic Waves,
Maxwell’s Equations
2
Electromagnetic Properties, Summary
(1) Electric field Sources
1 Q
E 
40 r 2
(2) No magnetic field
sources
(3) Changing magnetic field
produces an electric field
(Faraday’s Law)
B
2rE  
t
(4) Moving charge (current) 2rB   I
0 C
produces magnetic fields.
Changing E field produces B field
2rB  0IC
E

2rB  0IC  0


t


 E
0
 id
t


A changing E field produces a
B field.
Can vied as formed from a
“displacement current”.
4
EM Waves by 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)
EM Waves by an Antenna, B field



Because the oscillating
charges in the rod produce
a current, there is also a
magnetic field generated
As the current changes,
the magnetic field spreads
out from the antenna
The magnetic field is
perpendicular to the
electric field
Electromagnetic Waves Can
Propagate in Free Space
A changing magnetic field produces an
electric field
 A changing electric field produces a
magnetic field
 These fields are in phase

 At
any point, both fields reach their maximum
value at the same time
Electromagnetic Waves are
Transverse Waves


The E andBfields are
perpendicular to each
other
Both fields are
perpendicular to the
direction of motion

Therefore, em waves
are transverse waves
Properties of EM Waves


Electromagnetic waves are transverse waves
Electromagnetic waves travel at the speed of
light (3x108 m/s)
c
 Because
1
o o
EM waves travel at a speed that is precisely
the speed of light, light is an electromagnetic wave
Properties of EM Waves, 2

The ratio of the electric field to the magnetic field
is equal to the speed of light
E
c
B

Electromagnetic waves carry energy as they
travel through space, and this energy can be
transferred to objects placed in their path
Properties of EM Waves, 3

Energy carried by EM waves is shared equally
by the electric and magnetic fields (Emax=cBmax)
Average power per unit area 
2
2
Emax Bmax
Emax
c Bmax
I 


2 o
2 o c
2 o
 Intensity
(I) is average power per unit area
The Spectrum of EM Waves

Forms of electromagnetic waves exist that
are distinguished by their frequencies and
wavelengths
c
= ƒλ
Wavelengths for visible light range from
400 nm to 700 nm
 There is no sharp division between one
kind of EM wave and the next

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
14
15
of
th
e
ab
o.
..
(1
/2
)A
No
n
0
(1
/2
1/
2)
A
A
21
/2
120
In an RLC circuit, the maximum current is 1
amp. What is the average current?
25% 25% 25% 25%
1. 21/2 A
2. (1/21/2) A
3. (1/2) A
4. Non of the above
16
A
25%
2.
0
A
A
4.
25%
5.
6
3.
25%
A
2.
25%
2.8 A
4.0 A
5.6 A
2.0 A
4.
0
1.
2.
8
120
An AC voltage source, with a peak output of 200 V, is
connected to a 50- resistor. What is the effective (or rms)
current in the circuit?
0
17
25%
H
m
1.
9
m
H
25%
19
H
4.
H
3.
25%
m
2.
25%
1.9 H
190 mH
19 mH
1.9 mH
19
0
1.
1.
9
120
A 100 Hz AC voltage source, with a peak output of 170 V,
is connected to an inductor. If the rms current through the
inductor is 1 A, what is the value of the inductor?
0
18
In a circuit made up of inductor L, resistance R, ammeter,
battery and switch in series, the current is greatest at which
of the following times, as measured after the switch is
25% 25% 25% 25%
closed?
1. Zero
co
ns
t..
.
/R
t=
L
e
tim
n
On
e
tim
e
co
ns
t..
.
Ze
ro
4.
Te
3.
One time constant
At time t=L/R
Ten time constants
e
2.
At
tim
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19