ok

1
Physics
made by cand. jur. Jørgen Atke BA
2
PowerPoint slide show
to
Serway Faughn College Physics Saunders College
Publishing
and
Maksimov Hristakudis Physics Bulvest 2000,
Sofia 2001
3

Direction of the current
N-pole turns this direction
-
4
Place your right hand
with your fingertips in the currents direction
and the wire between the magnet and your palm
and the north pole will turn in the direction of
your thumb.
5

I
F
B
-
6
Place your right hand
with your fingertips in direction of the magnetic
field
and your thumb in direction of the current
and force will be out from your palm.
7
Electric field is defined as the electric force
per unit charge acting.
In a similar manner, we can descibe the
properties of the magnetic field, B, at some
point in terms of the magnetic force exerted on a
test charge at that point.
The test charge, q, moving with velocity v.
The strenght of a magnetic force on a particle is
propertional to the magnitude of the charge. q,
the magnitude of the velocity, v, and the
strength of the external magnetic field B, and
the sine of the angle q between the direction of
v and the direction of B.
The magnitude of the force is F qvB sin q
8
This expression can be used to define the
magnitude of the magnetic field as
F qv sin q
B
If F is in Newton, q in coulombs, and v in meter
per second, the SI unit of the magnetic field is
the tesla (T), also called the weber (Wb) per
square meter (1 T 1 Wb/m2).
If a 1-C moves through a magnetic field of
magnitude 1 T with a velocity of 1 m/s,
perpendicularly to the fields (sin q 1), the
magnetic force exerted on the charge is 1 N.
Wb
N
N
(B) T
m2
C m/s
A m
In practice the unit for magnetic fields is the
gauss (G) 1 T 104 G
9
If
l is the length of the conductor
I is the current flowing trough it
B stands for the strength of the magnetic field
also referred to as magnetic
induction
The magnitude of the force can be given by the
expression
F BIl
10
Bin
I 0
11
Bin
I
12
Bin
Remember
Fmax BIl
If the current and the magnetic field are at
right angel to each other.
I
13
Bin
A section of a wire containing moving charges in
an external magnetic field B.
q
vd
A
l
In this example each carrier in the wire
experience a force of magnitude Fmax qvdB,
where vd is the drift of the velocity of the
charge. To find the total force on the wire, we
multiple the force on one charge carrier by the
number of carriers in the segment. The volume of
the segment is Al, the numbers of carrier is nAl,
where n is number of carriers per unit volume.
The magnitude of the total magnetic force on the
wire of the length l is Total force (force on
each charge carrier)(total number of carriers)
Fmax (qvdB)(nAl)
The equation can only be used when the current
and the magnetic field are right angle to each
other.
14
B
q
I
If the wire is not perpendicular to the field but
some arbitrary angel, the magnitude of the force
on the wire is F BIl sin q
15
B
b
a
Carrying current is I
Magnitude of length a is zero as a is parallel
with B
16
I
B
b
a
17
a
2
F2
Magnitude force on length b are F1 F2 BIb
F1
18
The magnitude of the torque, Tmax, is
F1
a
a
Tmax F1 F2
2
2
a
a
a
2
(BIb) (BIb) BIab
2
2
O
B
F2
Tmax BIA as the area of the loop is A ab
19
If the field makes an angle of q with a line
perpendicular to the plane of the loop, the
moment arm for each force is given by (a/2) sin
q. The magnitude of the torque T BIA sin q
F1
q
A/2
B
A/2 sin q
F2
20
This result shows that the torque has the maximum
value, BIA, when the field is parallel to the
plane for the loop (q 900) and it is zero when
the field is perpendicular to the plane of the
loop (q 0)
The torque of a loop with N turns is T NBIA sin
q
21
The galvanometer is the basis of an ammeter and
a voltmeter
22
When a galvanometer is to be used as a voltmeter,
a resistor (Rs) is connected in series with the
galvanometer.
23
When a galvanometer is to be used as an ammeter,
a resistor (Rp) is connected in parallel with the
galvanometer.
24
6
2
V
A
25
Remember! Volt Joule/Coulomb Ampere
Coulomb/second
?
?
V
A
26
Bin
r


F qvB mv2/r or r mv/qB
F
P

v
q
27
B (the direction of your fingertips)
V
Direction of the motion (the direction of your
thumb)

F (the direction of your palm)
28
B (the direction of your fingertips)
F (the direction of the back of your hand)
V
Direction of the motion (the direction of your
thumb)
-
29
Hold you right hand open with your thumb pointing
in the direction in which the particle moves and
your fingers stretched out in the direction of
the magnetic field B the magnetic force will
then be directed out of your palm, perpendicular
to it!
30
(No Transcript)
31
The magnet field strength at distance r from a
wire carrying current I is
I
m0I
B
2pr
The magnitude of the field is proportional to the
current and decreases as the distance from the
wire increases.
The proportionality constant m0, called the
permeability of free space, is defined to have
the value m0 4 p x 10-7 T m/A
If the wire is grasped in the right hand with the
thumb in the direction of the current, the
fingers will curl in the direction of the
magnetic field.
32
B
I

Amperes law The magnetic force on a straight
current-carrying conductor, placed perpendicular
to the fields lines of a uniform magnetic field,
is equal to the product of the magnitude B of the
magnetic field, the current I and the length l of
the conductor.
F
33
This figure shows circular path surrounding a
current. This path can be divided into many short
segments, each of length Dl.
Let us now multiply one of the length by the
component of the magnetic field parallel to the
that segment, where the products is labeled B D
l. According to Ampere, the sum of all such
products over the closed path is equal to m0
times the net current I, that passes through the
surface bounded by the closed path. The
statement, Amperes circuital law, can be
written SB D l m0 I Where SB D l means
that we take the sum over all the products around
the closed path.
34
Amperes Law can be used to derive the magnetic
field due to a long straight wire carrying a
current, I. The magnetic field lines forms a
circle with the wire as center. The magnetic
field is tangent to this circle at every point
and has the same value, B, over the entire
circumference of a circle of radius r.
The sum of SB D l can be calculated over a
circular path. Note that B can be removed from
the sum, as it has the same value for each
element on the circle. That gives SB D l B
S D l B (2pr) m0 I If both sides is divided
by 2pr, we obtain
m0 I
B
2pr
35
l
1
I1
B2
F1
I2
2
36
Magnitude of the magnetic field is
m0I2
B2
2pd
The magnetic force on wire 1 in the present of
field B2 due to I2 is
m0I1I2l
m0I2
(
)
F1 B2 I1l I1l
2pd
2pd
The force per unit length
F1
m0I1I2

2pd
l
37
If two long parallel wires 1 m apart carry the
same current, and the force per unit length on
each wire is 2 x 10-7 N/m, then the current is
defined to be 1 Ampere.
If a conductor carries a steady current of 1
ampere, then the quantity of charge that flows
through any cross-section in 1 second is 1
coulomb.
38
I
B
39
(No Transcript)
40
The expression for the field inside the solenoid
is
B m0nl
Where n N/l is the number of turns per Unit.

-
41
Galvanometer
Switch
Primary coil
Secondary coil

-
Iron (Fe)
Battery
42

-
43
The emf induced by a change in a quantity called
the magnetic flux rather than simply by a change
in the magnetic field.
If we have a loop of wire in the presence of a
uniform magnetic field B and the loop has an area
of A, the magnetic flux, f, through the loop is
defined as
F BA BA cos q
Where B is the component of B perpendicular to
the plane of the loop.
44
q
B
q
Where B is the component of B perpendicular to
the plane of the loop an q is the angle between B
and the normal (perpendicular) to the plane of
the loop.
B
45
B
q
B
This is an end view of the loop and the
penetrating magnetic field lines.
46
When the field is perpendicular to the plane of
the loop
f 0 and f has a maximum value, fmax BA.
47
When the plane of the loop is parallel to B, q
90o and f 0
Since B is in teslas, or weber per square meter,
the unit of flux are T x m2, or webers.
We too see that the most lines pass through the
loop when the plane is perpendicular to the
field, and so the flux has its maximum value. If
no lines pass through the loop ( the loop is
parallel to the field) f 0.
48
The value of the magnetic flux is proportional to
the total number of lines passing through the
loop.
49
(No Transcript)
50
(No Transcript)
51
If a circuit contains N tightly wound loops and
the flux through each loop changes by the amount
Dq during the interval Dt the average emf induced
in the circuit during time Dt is
The instantaneous emf induced in a circuit equals
the rate of change of magnetic flux through the
circuit.
Dq
e -N
Dt
52
The ground fault interrupter (GFT) is an
interesting safety device. Wire 1 leads from the
wall outlet to the appliance to be protected, and
wire 2 leads from the appliance back into the
wall outlet. An iron ring ring surrounds the two
wires. So as to confine the magnetic field set up
by each wire. A sensitive coil, which can be
activate a circuit breaker when charges in
magnetic flex occur, is wrapped around part of
the iron ring. Because the current in the wires
are in opposite direction, the magnetic firld
through the sensing coil due to the currents is
zero. If a short circuit occurs in the appliance
so that there is no returning current, the
magnetic field through the sensing coil is no
longer zero. Because the current ids alternating,
the magnetic flux through the sensing coil
changes with time, producing an induced voltage
in the coil. This induced voltage is used to
trigger a circuit breaker, stopping the current
before it reaches level that might be harmful to
the person using the appliance.
Circuit breaker
Sensing coil
1
A.C.
2
Iron ring
53
Lenz Law
The Polarity of the induced emf is such that it
produces a current whose magnetic field opposes
the change in magnetic flux through the loop.
That is, the induced current tends to maintain
the original flux through the circuit.
54
A straight conductor of length l moving with
velocity v through a uniform magnetic field B,
directed perpendicular to v. The vector F is the
force on an electron in the conductor. An emf of
Blv induced between the end of the bar.


-
v
l
F
-
-
55
The magnetic force moves the electron to the
lower and accumulate there, leaving a net
positive charge at the upper end. That cause an
electric field in the conductor. The charge at
the end build up until the downward magnetic
force qvB is balanced to the upward electric
force qE. At this point the charge stop flowing
and the condition for equilibrium requires
that qE qvB or E vB Since the electric field
is constant, the field in the conductor is
related to the proportional difference acoress
the the ends by VEl, thus VElBlv
A potential difference is maintained acroos the
conductor as long as there is motion through the
field. If the motion is reversed, the polarity of
the potential difference is also reversed.
56
v
l
R
Fm
Fapp
I
I
x
R
(e) Blv
57
In the previous slide the moving conductor is a
part of the closed conducting part. You have to
consider a circuit consisting of a conducting bar
of length l, sliding along two fixed parallel
conducting rails. The moving bar has zero
resistance and the stationary part of the circuit
has resistance R. A uniform magnetic field B is
applied perpendicularly to the plane of the
circuit. As the bar is pulled to the right with
velocity v under the influence of an applied
force Fapp the free charges in the bar experience
a magnitude force along the length of the bar.
This force in turns set up an induced current
because the charges are free to move in a closed
conducting path. The changing magnetic flux
through the loop and the corresponding induced
emf across the moving bar arise from the change
in area of the loop as the bar moves through the
magnetic field.
58
Assume that the bar moves a distance of Dx in the
time Dt. The increase of in flux Df through the
loop in that time is amount of flux that now
passes through the portion in the circuit that
has area lDx Dx BA BlDx If there is one loop
(N1) the induced emf has the magnitude e Df/
Dt Bl(Dx/Dt) Blv
The induced emf is often called a motional emf.
l
R
Dx
59
(No Transcript)
60
V sin q
v
q
B
A
a/2
C
v
B
D
l
A
A loop rotating at a constant angular velocity in
an external Magnetic field. The emf induced in
the loop varies sinusoidally with time.
61
e
t
62
Thus shows that the emf varies sinusoidally with
time. The maximum emf has it value emax
NBAw When wt 900 or 2700. e emax when the
plane of the loop is parallel to the magnetic
field and the emf is zero when wt 00 or 1800,
that is when the magnetic field is perpendicular
to the plane of the loop.
63
The expression for the emf generated in the
rotating loop is as the motional emf, e Blv
2Blv sin q

• If the loop rotates with a constant angular
  velocity of w, the relation q wt can be used.
  Every point at wire and BC and DA rotates in a
  circle about the axis with the same regular
  velocity, w, v rw (a/2)w where a is the
  length of side AB and CD.
• The expression can be reduced to
• 2Blv(a/2)w sin wt Blaw sin wt
• If the loop has N turns, the emf is N turns as
  large because each loop has the same emf induced
  it. Since the area of the loop is Ala the total
  emf is
• NBAw sin wt

64

-
65
Pivot
An apparatus that demonstrates the formation of
eddy currents in a conductor moving through a
magnetic field. As the plate enters or leaves the
field, the changing magnetic flux sets up an
induced emf, which causes the eddy currents in
the plates.
66
(No Transcript)
67
(No Transcript)
68
emf
time
69
B
I
e
S
R
After the switch in the circuit is closed, the
current produces its own magnetic flux through
the loop. As the current increases toward its
equilibrium value, the flux changes in time and
induced an emf in the loop.
70
A current in the coil produces a magnetic field.
-

If the current increases, the coil act as a
source of emf directed as shown by the dashes
battery.

-
The emf of the coil changes its polarity if the
current drecreases
71

• According to Faradays law the induced emf is
• -N (Df/Dt)
• The magnetic flux is proportional to the magnetic
  field, which is proportional to the current in
  the circuit. Thus, the self-induced emf must be
  proportional to the time rate of change of the
  current.
• -L (DI/Dt)
• Where L is a proportional constant called the
  inductance of the device. The negative sign
  indicates that a changing current induces an emf
  in opposition to the change.
• If the current is increasing (DI positive), the
  induced emf is negative, indicative of opposition
  to the increase in current. If the current is
  decreasing (DI negative), the sign of the induced
  emf is positive to indicate that the emf is
  acting to oppose the decrease.

72
The inductance of a coil depends on the
cross-sectional area of the coil and other
quantities, which all can be grouped under the
general heading of geometric factors. The unit of
inductance is the Henry (H), which is equal to 1
volt-second per ampere. 1 H 1 V x s/A The
expression for L is N(Df/Dt) L(DI/Dt) L
N(Df/DI) Nf/I When f 0 and I 0 at t 0
73
Carbon brushes Hidden two slip rings
I
Time t
I 0
74
I
Time t
I max
75
I
Time t
I 0
76
I
Time t
I max
77
I
Time t
I 0
78
I
Tmax
T
0
t
T/2
79
The electric current changes its direction at the
point where the graph crosses the x-axis. This is
the moment when when the loop is perpendicular to
the field lines. Before it stands in this
position, the number of the lines increases and
then it begin to decrease after the loop has gone
beyond. According the Lenz law, the induced
current changes its direction exactly at this
moment. The current is at its maximum when the
loop is parallel to the field lines. The maximum
value of the current Imax is called the amplitude
of the current.
80
You know, that the uniform rotation of a body
around its axis is a periodic motion
characterized by its period T and frequency v
1/T. To perform complete cycle of rotation (in
time interval T) the current increases until it
reaches its maximum value, then decreases to zero
and after changing its direction it increases
again to reach is maximum value. Then it becomes
zero at the end of the period T. The induced emf,
which generates electric current after the
circuit is closed, changes in the same way.
81
The magnitude I of the direct current, releasing
the same amount of heat in a conductor as
alternating current does, is called the effective
value of the alternating current. Alternating
current is usually characterized by its effective
value. Therefore, we tend to say, that the
current through a heater is 10A, meaning that the
thermal efficiency of that alternating current is
equal to the efficiency of a 10 A direct
current. From the definition of efficient
current, Joule-Lenz law is equally applicable to
direct and alternating currents. Q I2Rt Where I
is the effective value of alternating current.
82
The laws of direct current are also valid the the
effective values of alternating currents and
voltages. Ohms Law U RI R is the resistance
in a wire carrying an alternating current with an
effective value I and the effective value U of
the alternating voltage between both ends of the
wire. The power P of alternating current is given
by the formulae P UI P I2R or P
U2/R Where I is the efficient current, U the
efficient voltage and R is the resistance of the
device.
83
It can be proved that the effective values of the
alternating current I and the alternating voltage
U are related to the amplitudes of the
alternating current Imax and the alternating
voltage Umax by the ratios I Imax /square root
2 U Umax / square root 2
84
1/100 s
3 A

?
6 A
?
36 w
6 V
-
12 V
Primary Coil
Secondary Coil
Windingsprimary
uprimary
Isecondary


Windingssecondary
usecondary
Iprimary
85
(No Transcript)
86
(No Transcript)
87
3 loops
300,000 loops
88
(No Transcript)
89
(No Transcript)
90
Wavelength
Crest
Trough
Amplitude
91
A
B
A movement from A to B is called a swinging.
If the swinging takes 1 second the frequency ( f
) is 1 Hertz ( Hz ).
The relation between the period and the frequency
is given by the formula f 1/T
92
A spring pendulum
3
x
A
1
A
2
93
The position 1, in which the ball rest, is
referred to as equilibrium position
The distance x between the equilibrium and the
position of the ball at definite moment is called
a displacement.
The amplitude A is equal to the maximum
displacement x of the ball from the equilibrium
position.
The time the ball takes to complete one full
cycle of motion, I.e. to move from 1 to 2 to 1 to
3 and back to 1, is referred to as the period of
oscillation T.
The frequency f equals the number of oscillations
per unit time, I.e. it shows how many times per
second (1 s) the cycle of the motion is repeated.
The relation between the period and the frequency
is given in the formula
f 1/T
The unit of frequency is the hertz (Hz).

The frequency is 1 Hz when one cycle of motion is
completed in 1 s.
94
How does the displacement x vary in time t ? A
pen is attached to the ball of a spring pendulum.
The paper moves horizontally with a constant
velocity and the pendulum oscillates vertically.
The pen draws a wave line on the paper,
representing graphically the displacement x of
the pen (the pendulum) as a function of the time.
95
Experiments show that the elastic force Fe with
which the spring acts on a ball is directly
proportional to the deformation (to the change in
the length extension or compression) x of the
spring.
The relation was established in 1678 by Robert
Hooke and was named Hookes law.
The constant k is called the coefficient of
elasticity or the spring constant. The SI unit of
k is newton per meter (N/m)
96
A harmonic oscillation or harmonic motion
x
A
t
A
¼ T
½ T
¾ T
T
97
Example Find the spring constant k for the
spring of the pendulum. The mass of the ball is m
50 g. The displacement of the spring from the
equilibrium position of the pendulum is xo 5 cm.
k
Solution Two forces act on the ball the force
of weight G mg and the force of elasticity F0
kx0. In the equilibrium position of the pendulum,
the two forces are equal in magnitude kx0 mg.
xo
F0 kx0
Consequently, k mg/x0
(0,05 kg)(10 m/s2)/0,05 m
10 N/m.
m
G mg
98
Restoring Force
When the pendulum is displaced from its
equilibrium position, an additional elastic force
F kx appears, wherein x stand for the
displacement. This is the force that causes the
harmonic motion of the ball.
F
F 0
O
F
The force F is always directed toward the
equilibrium position O tending to return the ball
to this position when the ball is below O, the
force F is directed vertically upward and when
the ball is above O, it is directed vertically
downward.
Equilibrium position
99
The harmonic motion can be defined by the force,
which causes it
Harmonic motion is a repetitive motion, caused by
a force, which is always directed toward the
equilibrium position of the body and directly
proportional to the displacement x.
This force is called a linear restoring force or
simply restoring force because it is linearly
proportional to the displacement x and is always
directed toward the equilibrium position and
therefore opposite to the displacement


F kx The inertia of a body is essential to
its harmonious motion. The restoring force in the
equilibrium position is zero (F kx 0 for x
0). Nevertheless, the body does not stop there.
Inertia causes it to pass through this position
so that the restoring force appears again.
100
Simple oscillating system
If an oscillation is caused by a restoring force,
due to the interaction between the different
parts of a system the spring and the mass, the
oscillation is called a free oscillation.
k
k
k
m
Different weight are attached to the same spring
and the periods of the pendulums are
measured. The square of the period T is directly
proportional to the mass m of the weight.
T
4m
2T
T2 oc m or T m
9m
3T
101
A pendulum is attached to different springs. The
period of the springs depends on the spring
constant k. If the spring is softer a small
value of k the frequency of the oscillation
will be smaller too (The period T will be
bigger). Experiment shows that the square of the
period T is inversely proportional to the spring
constant k.
T2 oc 1/k or T 1/ k
The period of the spring can be calculated in the
following way
T 2p

period of a spring pendulum

Using the relation between the period and the
frequency f 1/T
For the frequency of a spring pendulum.
102
Simple pendulum
When a simple pendulum is displaced to a small
angel a0 from its equilibrium position it begins
to move harmonically with a period of Where g is
the earths acceleration.
a0
l
103
Elastic potential energy
The elastic potential energy of an object is
equal to the work done for its deformation.
x
Ek
Ep
104
Energy of harmonic motion
Ep max
Ek 0
Ep 0
Ek max
Ep max
Harmonic motions involves the periodic
transformation of potential energy into kinetic
energy and visa versa, so that the mechanical
energy of the vibrating system remains constant.
Ek 0
A 0 A
Ep Ek 0
105
Damped oscillations
Oscillations whose amplitude decreases are called
damped oscillations.
106
Question A spring pendulum performs a harmonic
motion whose amplitude is A 0.01 m. The spring
constant is k 20 N/m. Find the maximum value of
the restoring force.
Answer The formula for restoring force is F
kx F 0.01m x 20 N/m 0.2 N.
107
Question An automobile chassis with a mass of
1,000 kg is attached to four identical springs,
each with a spring constant of 19,299 N/m. There
are three passengers traveling in the automobile
whose total mass is 200 kg. Find the natural
frequency and the period of the oscillations,
which occur when the automobile starts moving
along a bumpy Bulgarian road.The weight is evenly
distributed on the four springs.
Answer Each spring experiences a force of weight
due to a mass m 300 kg. (Driver 3 passengers
car 1,200 kg.) The frequency of oscillations
of the four identical spring pendulums can be
found from the equation
1
k
1
19,200 N/m
f


1.27 Hz
2p
m
2p
300 kg
The period of the oscillations is T 1/f 0.79
s.
108
12
The pendulum clock is an example of forced
oscillations.
9
3
The frequency of forced oscillations equals the
frequency f with which the external periodic
driving force changes.
6
109
Pendulum III which has the same length as
pendulum I, and therefore the same frequency fo,
oscillates with the greatest amplitude while the
other pendulums scarcely move.
II
I
III
IV
Conclusion Pendulums whose natural frequency fo
coincides with the frequency fo of the external
force, has a maximum amplitude of forced
oscillations.
110
The spring pendulum with a natural frequency fo
is suspended from the knee D of a rotating axis.
The knee acts on the pendulum with a force, which
changes with the same frequency v with which the
axis rotates. Changing the the frequency of the
rotation, the amplitude of the forced
oscillations of the pendulum is a maximum when
the frequency v of the external force becomes
equal to the natural frequency fo of the spring
pendulum
D
The abrupt increase in the amplitude of forced
oscillations when the frequency v of the external
force approaches the natural frequency of the
vibrating system is referred to as resonance.
111
If particles of a medium oscillate in a direction
perpendicular to the wave motion, the wave is
called transverse wave. Here the transverse wave
is traveling along a stretched cord. This wave is
called a longitudinal wave as the particles move
parallel to the direction of the wave motion.
P
A wave traveling along a stretched card at
different moments of time. The wavelength l is
equal to the distance the wave has traveled with
a velocity v for a time interval t T l vT
T 0
v
P
f T/4
v
f T
P
l
112
v1
v2
1
2
2
1
v1
v2
1
2
Two wave pulses traveling a stretched string in
opposite directions pass through each other. When
the pulse overlap, the net displacement of the
string equals the sum of the displacements
produced by each pulse.
113
v2
2
v1
1
2
1
v2
2
1
v1
114
The combination of two or more waves in the same
region of space to produce a resultant wave with
a large amplitude is some points and a small (or
zero) amplitude in others, is called interference.
115
At some points on the water surface, the crest of
a wave due to one source always arrives together
with the crest of a wave due to another source.
As a result the two waves become mutually
amplified. This phenomenon is called constructive
interference.
At other points the crest of one wave invariable
arrives together with the trough of another wave
so that the two waves are mutually cancelled. The
phenomenon is known as a destructive interference.
116
v
v
Incident pulse
Reflected pulse
Reflection of a wave pulse at the fixes end of a
stretched string. The reflected pulse is
inverted, but its shape remains the same.
v
v
117
Antinode
l/2
Node
Standing waves on a stretched string
118
Antinode
Node
Standing waves on an elastic circular wire.
119
Types of Mechanical waves
Water waves
Sound waves
Spherical and plane waves
Seismic waves
120
Sound waves
The relation between the speed of sound and
temperature is given by this formulary
v (331 m/s) 1 t/273
If the temperature of the air is 200 C, the
velocity is
v (331 m/s) 1 20/273 343 m/s
121
A vibrating tuning fork disturbs the around
giving it energy, which is carried by the
traveling sound wave.
122
The intensity of a wave is defined as the energy
transported by the wave per unit time (t 1 s)
through the area (A 1 m2) perpendicular to the
direction in which the wave travels The
intensity e/At The SI unit of intensity is
defined in terms of the unit of energy, area and
time J/(m2 x s) watt/ m2
123
Intensity level decibels (dB)
H a r m f u l
dB
Nearby jet airplane
140
Rock concert
120
D a n g e r
100
Subway
Heavy traffic Vacuum cleaner
80
L o u d
Normal conversation
60
Quiet radio
40
Q u i e t
20
Whisper
0
Silence
124
v
Doppler effect
125
1. Electric fields originate on positive charges
and terminate on negative charges. The electric
field due to a point can be determined at a
location by applying Coulomb's force law to a
test charge placed at a location.
The statement is an consequence of the nature of
the electrostatic force between charged
particles, given by Coulombs law. It embodies a
recognition of the fact that free charges
(electric monopoles) exist in nature.
2. Magnetic field lines always form closed loops
that is, they do not begin or end anywhere.
That magnetic fields form continuous loops is
exemplified by the magnetic field lines around
a long, straight wire, which are closed circles,
and the magnetic field lines of a bar magnet,
which forms closed loops.
3. A varying magnetic field induces an emf and
hence an electric field.
This is equivalent to Faradays law of induction.
4. Magnetic fields are generated by moving
charges (current), as summarized in Amperes law.
This is equivalent to Amperes law .
126
In the circuit a charged capacitor is connected
to an inductor. When the switch is closed,
oscillations occur in the current in the circuit
and in the charge on the capacitor. If the
resistance of the circuit is neglected, no energy
is lost to heat, and the oscillation continue
C

L
-
Qm
S
The has an initial charge of Qm and the switch is
closed at t 0.
When the capacitor is fully charged, the total
energy energy in the circuit is stored in the
electric firld of the capacitor and is equal to
Qm2/2C. The current is zero, so no energy is
stored in the inductor.
As the capacitor discharges, the energy stored in
its electric field decreases and the current
increases and energy equal to LI2/2 is now stored
in the magnetic field of the inductor.
The energy is transferred from the electric field
of the capacitor to the magnetic field of the
inductor.
127
When the capacitor is fully discharged it stores
no energy!
The current reaches its maximum value, and all
the energy is stored in the inductor!
The process then repeats in the reverse
direction. The energy continues to to transfer
between the inductor and the capacitor,
corresponding to oscillations in the current and
charge.
128
Time
I 0
Qmax
k
v 0
L
E

-
t0
m
-Qmax
A
X0
vmax
L
Q 0
m
tT/4
I 0
X0
-Qmax
v 0
L
E
-
m

tT/2
Qmax
A
X0
129
t3/4 T
vmax
L
Q 0
m
I 0
X0
Qmax
v 0
L
E

tT
m
-
-Qmax
A
X0
Stages of energy transfer in an LC circuit with
zero resistance. The capacitor has a charge of Qm
at t 0 when the switch is closed, and a
mechanical analog, then mass-spring system.
130
Input
Induction coil
Transmitter
q
-q
Receiver
131

---
t T/4
t 0
132
---

t T/2
133

---
t T
134
I
Sine the oscillating charges create a current in
the rods, a magnetic field is generated when the
current in the rods is upward. The magnetic field
lines circle the antenna and are perpendicular to
the electric field at all points. As the current
changes with time, the magnetic field lines
spread out from the antenna. At great distance
from the antenna, the strength of the electric
and magnetic fields become very weak.
However, at these distances is it necessary to
take into account that
(1) A changing magnetic field produces a changing
electric field
(2) A changing electric field produces a changing
magnetic field
135
An electromagnetic wave sent out by oscillation
in an antenna. Note that the electric field is
perpendicular to the magnetic field and both are
perpendicular to the direction of wave
propagation.
E
B
An electromagnetic wave is a transverse wave.
Magnetic field
Electric field
c
Direction of wave propagation
136
y
E
E
A plane electromagnetic wave traveling in the
positive, x, direction. The electric field is
along the y direction, and the magnetic field is
Along the z direction.
c
c
x
B
B
z
A plane electromagnetic wave, is a wave in which
the oscillating field associated with the wave
are uniform over a plane in a given time.
In this case, the oscillations of the electric
and magnetic fields take place in planes
perpendicular to the x axis and thus to the
direction of travel for the wave,
137
Electromagnetic waves travels with the speed of
light. It can be shown that the speed of an
electromagnetic wave is related to the
permeability and permittivity of the medium
through which it travels. Maxwell found this
relations for free space to be
1
c
m0e0
c is the speed of the light
m0 4 p x 10-7 N x s2/C2 is the permeability
constant of free space
e0 8.85 x 10-12 C2/N x m2 is the permittivity
constant of free space
c 2.99792 x 108 m/s
138
In summary electromagnetic waves traveling
thorough free space have the following properties
1. Electromagnetic waves travel at the speed of
light.
2. Electromagnetic waves are transverse waves,
since the electric and magnetic fields are
perpendicular to the direction of propagation of
the wave and to each other.
3. The ratio of the electric field to the
magnetic field in an electromagnetic wave equals
the speed of light.
3. Electromagnetic waves carry both energy and
momentum, which can be delivered to a surface.
139
All electromagnetic waves travel through vacuum
with a speed of c, their frequency, f, and
wavelength, l, are related by the expression c
fl .
Frequency, Hz
Wavelength
1022
Gamma ray
1021
1020
1019
1 angstrom, Å
X-ray
1018
1 nanometer, nm
1017
Ultraviolet
1016
1015
Visible light
1 micron, m
1014
1013
Infrared
1012
1011
1 centimeter, cm
1010
Microwaves
109
1 meter, m
108
TV, FM
107
106
Standard broadcast
1 kilometer, km
105
1 micrometer (mm) 10-6 m 1 nanometer (nm)
19-9 m 1 angstrom (Å) 19-10 m
104
Long wave
103