Fundamental Physics II

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Fundamental Physics II

PETROVIETNAM UNIVERSITY

FACULTY OF FUNDAMENTAL SCIENCES

Vungtau
, 2013

Pham Hong
Quang

E
-
mail:
quangph@pvu.edu.vn

Chapter 4

Pham Hong
Quang

Faculty of Fundamental Sciences

2

Electromagnetic Induction

and Electromagnetic Wave


4.1 Faraday law


Pham Hong Quang

Faculty of Fundamental Sciences

3

Almost 200 years ago, Faraday looked for evidence that a magnetic
field would induce an electric current with this apparatus:

He found no evidence when the current was steady, but did
see a current induced when the switch was turned on or off.

4.1 Faraday law


Pham Hong Quang

Faculty of Fundamental Sciences

4

A changing magnetic field induces an
emf
.

4.1 Faraday law


Pham Hong Quang

Faculty of Fundamental Sciences

5

Faraday’s Law of Induction; Lenz’s Law

The induced
emf

in a wire loop is
proportional to the rate of change of
magnetic flux through the loop.

Magnetic flux:

Unit of magnetic flux:
weber
,
Wb
.

1
Wb

= 1
T
∙m
2

The magnetic flux is analogous to the electric flux


it is
proportional to the total number of lines passing through the loop.

4.1 Faraday law


Pham Hong Quang

Faculty of Fundamental Sciences

6

Faraday’s law of induction:

The minus sign gives the direction of the induced
emf
:

A current produced by an induced
emf

moves in a direction so
that the magnetic field it produces tends to restore the changed
field.

4.1 Faraday law


Pham Hong Quang

Faculty of Fundamental Sciences

7

Magnetic flux will change if the area of the loop
changes:

4.1 Faraday law


Pham Hong Quang

Faculty of Fundamental Sciences

8

Magnetic flux will change if the angle between
the loop and the field changes:

4.1 Faraday law


Pham Hong Quang

Faculty of Fundamental Sciences

9

This image shows another way the
magnetic flux can change:

4.2 Application of Faraday’s law


Pham Hong Quang

Faculty of Fundamental Sciences

10

Electric Generators

A generator is the opposite of a motor


it
transforms mechanical energy into electrical
energy. This is an ac generator:

The axle is rotated by an
external force such as
falling water or steam. The
brushes are in constant
electrical contact with the
slip rings.

4.2 Application of Faraday’s law


Pham Hong Quang

Faculty of Fundamental Sciences

11

A sinusoidal
emf

is induced in the rotating
loop (
N

is the number of turns, and
A

the area
of the loop):

4.2 Application of Faraday’s law


Pham Hong Quang

Faculty of Fundamental Sciences

12

Transformers and Transmission of Power

A transformer consists of two coils, either interwoven or linked
by an iron core. A changing
emf

in one induces an
emf

in the
other.

The ratio of the
emfs

is equal to the ratio of the number of
turns in each coil:

4.2 Application of Faraday’s law

Pham Hong
Quang

Faculty of Fundamental Sciences

13

This is a step
-
up
transformer


the
emf

in
the secondary coil is
larger than the
emf

in the
primary:

Energy must be conserved;
therefore, in the absence of
losses, the ratio of the
currents must be the inverse
of the ratio of turns:

4.2 Application of Faraday’s law

Pham Hong
Quang

Faculty of Fundamental Sciences

14

Transformers work only if the current is
changing; this is one reason why electricity is
transmitted as ac.

4.2 Application of Faraday’s law

Pham Hong
Quang

Faculty of Fundamental Sciences

15

This microphone works by induction; the
vibrating membrane induces an
emf

in the coil

4.2 Application of Faraday’s law

Pham Hong
Quang

Faculty of Fundamental Sciences

16

Differently magnetized
areas on an audio tape or
disk induce signals in the
read/write heads.

4.3 Inductance

Pham Hong
Quang

Faculty of Fundamental Sciences

17

Mutual inductance: a changing current in one coil
will induce a current in a second coil.

And vice versa; note that the constant M, known as
the mutual inductance, is the same:

4.3 Inductance

Pham Hong
Quang

Faculty of Fundamental Sciences

18

Unit of inductance: the
henry
, H.

1 H = 1
V
∙s
/A = 1
Ω·s
.

A transformer is an
example of mutual
inductance.

4.3 Inductance

Pham Hong
Quang

Faculty of Fundamental Sciences

19

A changing current in a coil will also
induce an
emf

in itself:

Here,
L

is called the
self
-
inductance.

i
L



4.3 Inductance


Pham Hong
Quang

Faculty of Fundamental Sciences

20

S

i

B

l

N turns

The self
-
inductance of a coil

Magnetic field inside the coil

l
Ni
B
/
0


Magnetic flux through one turn

l
NiS
S
B
/
.
0
1




Magnetic flux through N turns

l
iS
N
S
B
/
.
2
0
1




V
n
l
S
N
i
L
.
/
2
0
0
2
0







4.3 Inductance


Pham Hong
Quang

Faculty of Fundamental Sciences

21

Close the switch to a.

What happens? Write down the loop
rule.

Loop Rule: Sum of potentials =0

0



L
R
V
V




iR

L
di
dt

0
Solve this equation for the
current
i
.


RL

Circuits

4.3 Inductance

Pham Hong
Quang

Faculty of Fundamental Sciences

22

)
1
(
L
Rt
R
e
V




L
Rt
L
e
V



4.4 Energy Stored in a Magnetic Field

Pham Hong
Quang

Faculty of Fundamental Sciences

23

Just as we saw that energy can be stored in an electric field,
energy can be stored in a magnetic field as well, in an
inductor, for example.




iR

L
di
dt

0



iR

L
di
dt


i

i
2
R

Li
di
dt
Rate at which energy


is delivered to circuit


from the battery

Rate at which
energy


is lost in resistor

Rate at which energy is

stored in the magnetic
field of the coil

Start with Loop rule or

Kirchoff’s

Law I

Solve it for


Multiply by
i


dU
B
dt

Li
di
dt
4.4 Energy Stored in a Magnetic Field

Pham Hong
Quang

Faculty of Fundamental Sciences

24


dU
B
dt

Li
di
dt

dU
B

Lidi

dU
B
0
U
B


Lidi
0
i


U
B

Lidi
0
i


1
2
Li
2

U
B

1
2
Li
2
4.4 Energy Stored in a Magnetic Field

Pham Hong
Quang

Faculty of Fundamental Sciences

25

Now define the energy per unit volume


u
B

U
B
Al

u
B

1
2
Li
2
Al

L
l
i
2
2
A

u
B

1
2
Li
2
Al

1
2

0
n
2
i
2

B


0
ni

u
B

B
2
2

0
The energy density
formula is valid in
general

4.5 The Production of Electromagnetic

Waves

Pham Hong
Quang

Faculty of Fundamental Sciences

26

Electromagnetic fields are produced by

oscillating charges.

4.5 The Production of Electromagnetic

Waves

Pham Hong
Quang

Faculty of Fundamental Sciences

27

The previous image showed the electric field; a

magnetic field is also generated, perpendicular

both to the electric field and to the direction of

propagation.


The electric field produced by an antenna

connected to an ac generator propagates away

from the antenna, analogous to a wave on a string

moving away from your hand as you wiggle it up

and down.

4.5 The Production of Electromagnetic

Waves

Pham Hong
Quang

Faculty of Fundamental Sciences

28

An electromagnetic wave propagating in the positive
x direction,
showing the electric and
magnetic fiel
ds:

The direction of propagation and the directions of the electric and
magnetic fields in an electromagnetic wave can be determined
using a right
-
hand rule:

Point the fingers of your right hand in the direction of E, curl your
fingers toward B, and your thumb will point in the direction of
propagation.

4.6 The Propagation of Electromagnetic

Waves

Pham Hong
Quang

Faculty of Fundamental Sciences

29

All electromagnetic waves propagate through a

vacuum at the same rate:


c=3.00 x 10
8
m/s


In materials, such as air and water, light slows

down, but at most to about half the above

speed.

4.6 The Propagation of Electromagnetic

Waves

Pham Hong
Quang

Faculty of Fundamental Sciences

30

The value of the speed of light is given by

electromagnetic theory; it is:

0
0
1



c
This is a very large speed, but on an astronomical
scale, it can take light a long time to travel from one
star to another.

Astronomical distances are often measured in light
-
years


the distance light travels in a year.

4.6 The Propagation of Electromagnetic

Waves

Pham Hong
Quang

Faculty of Fundamental Sciences

31

The Doppler effect applies to electromagnetic waves as well
as to sound waves.

The speed of the waves in vacuum does not change, but as
the observer and source move with respect to one another,
the frequency does change.

)
1
(
,
c
u
f
f


4.7 The Electromagnetic Spectrum

Pham Hong
Quang

Faculty of Fundamental Sciences

32

Because all electromagnetic waves have the

same speed in vacuum, the relationship between the
wavelength and the frequency is simple:


f
c

The full range of frequencies of electromagnetic
waves is called the electromagnetic spectrum.

4.7 The Electromagnetic Spectrum

Pham Hong
Quang

Faculty of Fundamental Sciences

33

Radio waves are the lowest
-
frequency
electromagnetic waves that we find useful.

Radio and television broadcasts are in the range
of 10
6

Hz to 10
9

Hz.

Microwaves are used for cooking and also for

telecommunications. Microwave frequencies

are from 10
9

Hz to 10
12

Hz, with wavelengths

from 1 mm to 30 cm.

4.7 The Electromagnetic Spectrum

Pham Hong
Quang

Faculty of Fundamental Sciences

34

Infrared waves are felt as heat by humans.

Remote controls operate using infrared radiation.
The frequencies are from 10
12

Hz to 4.3 x 10
14

Hz.

Visible light has a fairly narrow frequency range,

from 4.3 x 10
14

Hz (red) to 7.5 x 10
14

Hz (violet).

Ultraviolet light starts with frequencies just above

those of visible light, from 7.5 x 10
14

Hz to 10
17

Hz.

X
-
rays have higher frequencies still, from 10
17

Hz

to 10
20

Hz. They are used for medical imaging.

4.7 The Electromagnetic Spectrum

Pham Hong
Quang

Faculty of Fundamental Sciences

35

Gamma rays have the highest frequencies of all,

above 1020 Hz. These rays are extremely

energetic, and are produced in nuclear reactions.

They are destructive to living cells and are therefore
used to destroy cancer cells and to sterilize food.

4.8 Energy in Electromagnetic Waves

Pham Hong
Quang

Faculty of Fundamental Sciences

36

The energy density in an electric field is:

And in a magnetic field:

Therefore, the total energy density
of an electromagnetic wave is:

2
0
2
1
E
u
E


2
0
2
1
B
u
B


2
0
2
0
2
1
2
1
B
E
u
u
u
B
E






4.8 Energy in Electromagnetic Waves

Pham Hong
Quang

Faculty of Fundamental Sciences

37

It can be shown that the energy densities in
the electric and magnetic fields are equal:

2
0
2
0
2
1
2
1
B
E



B
E
0
0
1



B
c
E
.

4.8 Energy in Electromagnetic Waves

Pham Hong
Quang

Faculty of Fundamental Sciences

38

The energy a wave delivers to a unit area in a unit

time is called the intensity.

u
c
t
A
t
c
A
u
t
A
U
I
.
)
.
.
(







4.9 Polarization


Pham Hong
Quang

Faculty of Fundamental Sciences

39

The polarization of an electromagnetic wave

refers to the direction of its electric field.

4.9 Polarization

Pham Hong
Quang

Faculty of Fundamental Sciences

40

Polarized light has its

electric fields all in the

same direction.



Unpolarized

light has its

electric fields in random

directions.

4.9 Polarization

Pham Hong
Quang

Faculty of Fundamental Sciences

41

A beam of
unpolarized

light can be polarized
by passing it through a

polarizer, which allows

only a particular

component of the

electric field to pass

through. Here is a

mechanical analog:

4.9 Polarization

Pham Hong
Quang

Faculty of Fundamental Sciences

42

A polarizer will transmit the component of
light in the polarization direction:

4.9 Polarization

Pham Hong
Quang

Faculty of Fundamental Sciences

43

Since the intensity of light is proportional to the
square of the field, the intensity of the

transmitted beam is given by the Law of
Malus
:


2
0
cos
I
I

The light exiting from a polarizer is polarized
in the direction of the polarizer.

4.9 Polarization

Pham Hong
Quang

Faculty of Fundamental Sciences

44

If an
unpolarized

beam is passed through a

polarizer, the transmitted intensity is half the

initial intensity.

0
2
1
I
I

4.9 Polarization

Pham Hong
Quang

Faculty of Fundamental Sciences

45

A polarizer and an analyzer can be combined

4.9 Polarization

Pham Hong
Quang

Faculty of Fundamental Sciences

46

LCDs

use liquid

crystals, whose

direction of

polarization can be

rotated depending

on the voltage

across them

47

Nguyen Van A


47



PetroVietnam

University

Thank you!