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ELECTROMAGNETIC FIELD
1. KONGUNADU COLLEGE OF ENGINEERING AND TECHNOLOGY
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
1
Prepared by Mr.K.KarthiK -AP/ EEE
2. 1. Introduction about EMF
2. Sources and Effects of EMF
3. Coordinate Systems and Types
4. Divergence & Curl
5. Divergence Theorem and Stokes Theorem
2Prepared by Mr.K.KarthiK -AP/ EEE
3. Static Electric Field
Coulomb’s Law
Electric field Intensity
Electric Flux Density
Potential difference
P D in Sphere, isolated sphere and cable
Capacitance
C for parallel plate capacitor
C for Sphere, isolated sphere and cable
Energy Stored and Energy Density
Boundary Conditions
3Prepared by Mr.K.KarthiK -AP/ EEE
5. When an event in one place has an effect on
something at a different location, we talk
about the events as being connected by a
“field”.
A field is a spatial distribution of a quantity; in
general, it can be either scalar or vector in
nature.
5Prepared by Mr.K.KarthiK -AP/ EEE
6. What are Electromagnetic Fields?
EMF always consists of both an electrical
field and a magnetic field.
The transmission of electrical energy
through wires, the broadcasting of radio
signals and the phenomenon of visible light
are examples of electromagnetic fields (EMF).
6Prepared by Mr.K.KarthiK -AP/ EEE
7. What are the Common Sources of EMF?
Electricity is the most common source of
power throughout the world
because it is easily generated and transmitted
to where it is needed.
As electricity moves through wires and
machines, it produces EMF.
Once electricity is delivered to the user, it
continues to produce EMF throughout the
wiring systems of offices, homes, schools,
factories and other structures.
7Prepared by Mr.K.KarthiK -AP/ EEE
8. In the workplace the generators of EMF
include
computers, cell phones, fax machines,
copy machines, fluorescent lights, printers,
scanners, telephone switching systems,
electrical instruments, motors and other
electrical devices.
8Prepared by Mr.K.KarthiK -AP/ EEE
9. In homes, the immediate sources of EMF
include
Electric blankets, electric water bed
heaters, hairdryers, electric shavers,
television sets, stereo systems, air
conditioners, fluorescent lights, telephone
answering machines, cell and portable
phones, refrigerators, blenders, portable
heaters, clothes washers and dryers, coffee
makers, vacuum cleaners, toasters, and
microwave ovens.
9Prepared by Mr.K.KarthiK -AP/ EEE
10. EMF is not only produced by electricity
moving through wires or machines, but it is
the nature of all television and satellite
transmissions, as well as radio and
microwave communication systems,
including cell phones.
Transportation methods such as
automobiles, trucks, airplanes, electrical and
magnetic trains and subway systems are
significant sources of EMF.
10Prepared by Mr.K.KarthiK -AP/ EEE
11. Children are at a GREATER RISK when comparing
with adults.
Radiation Penetration
in head of adult.
Radiation Penetration in
head of 10 year old child.
Radiation Penetration in
head of 5 year old child
11Prepared by Mr.K.KarthiK -AP/ EEE
12. Now, all living things are subject to million of times
more radiation than 50 years ago.
Most of the changes have happened in the last 30
years.
12Prepared by Mr.K.KarthiK -AP/ EEE
13. We will never be able to experience this peaceful
world again
13Prepared by Mr.K.KarthiK -AP/ EEE
14. EMF & Cell Phone Radiation could be the cause
of your headaches.
Your lack of energy is not through doing too
much – it’s EMF.
EMF & Cell Phone Radiation causes depression.
The stress in your life is more likely to be EMF
than lifestyle!
EMF & Cell Phone Radiation causes minor and
major illnesses including cancer.
EMF & Cell Phone Radiation IS THE MAIN CAUSE
OF INSOMNIA!
EMF & Cell Phone Radiation causes birth defects
and abortions .
14Prepared by Mr.K.KarthiK -AP/ EEE
18. The closer to source the higher the BV
BV ranges from 1000 mV to 50,000 mV
18Prepared by Mr.K.KarthiK -AP/ EEE
19. Genetic Effects
Cancer
Cellular/Molecular
Effects
Electrophysiology
Behavior
Nervous System
Blood-brain barrier
Calcium
Cardiovascular
Warm sensation
Hormones
Immunology
Metabolic rate/effects
Reproduction/growth
Subjective symptoms
Stress
Source: Dr. Henry Lai, Research Professor, Department of Bioengineering,
University of Washington. Presentation March 21, 2008 at Council on Wireless
Technology Impacts EMF Panel, San Francisco, CA.
19Prepared by Mr.K.KarthiK -AP/ EEE
20. In Electromagnetics, all quantities are the
functions of space and time.
Types:
◦ 1. Rectangular Coordinate System – 3 distances
◦ 2. Circular Cylindrical Coordinate System – 2
distance with 1 angle.
◦ 3. Spherical Coordinate System – 1 distance with 2
angle.
20Prepared by Mr.K.KarthiK -AP/ EEE
21. Rectangular or Cartesian Coordinate System –
(x,y,z)
Circular Cylindrical Coordinate System –
(ρ,φ,z)
Spherical Coordinate System – (r,θ,φ)
21Prepared by Mr.K.KarthiK -AP/ EEE
22. Cartesian into cylindrical coordinate systems
Cartesian into spherical coordinate systems
Cartesian System Cylindrical System
x
y
z
ρ=√(x2+y2)
Ф = tan-1(y/x)
z=z
Cartesian System Spherical System
x
y
z
r=√(x2+y2 +z2)
Ф = tan-1(y/x)
θ = cos-1(z/r)
22Prepared by Mr.K.KarthiK -AP/ EEE
23. Cylindrical system into Cartesian system
Spherical system into Cartesian system
Cylindrical System Cartesian System
ρ
Ф
z
x= ρ cos Ф
y= ρ sin Ф
z= z
Spherical System Cartesian System
r
θ
Ф
x=r sin θ cos Ф
y= r sin θ sin Ф
z= r cos θ
23Prepared by Mr.K.KarthiK -AP/ EEE
24. Divergence : div F =
Curl : Curl F =
0
1
lim .
V
s
F nds
V
0
1
lim
V
s
nxFds
V
24Prepared by Mr.K.KarthiK -AP/ EEE
28. Electrostatics is the branch of
electromagnetics dealing with the effects
of electric charges at rest.
The fundamental law of electrostatics is
Coulomb’s law.
28Prepared by Mr.K.KarthiK -AP/ EEE
29. Electrical phenomena caused by friction are part of
our everyday lives, and can be understood in terms
of electrical charge.
The effects of electrical charge can be observed in the
attraction/repulsion of various objects when
“charged.”
Charge comes in two varieties called “positive” and
“negative.”
29Prepared by Mr.K.KarthiK -AP/ EEE
30. Coulomb’s law is the “law of action” between
charged bodies.
Coulomb’s law gives the electric force between
two point charges in an otherwise empty
universe.
A point charge is a charge that occupies a region
of space which is negligibly small compared to
the distance between the point charge and any
other object.
30Prepared by Mr.K.KarthiK -AP/ EEE
32. The force on Q1 due to Q2 is equal in
magnitude but opposite in direction to the
force on Q2 due to Q1.
1221 FF
32Prepared by Mr.K.KarthiK -AP/ EEE
33. Consider a point
charge Q placed at
the origin of a
coordinate system
in an otherwise
empty universe.
A test charge Qt
brought near Q
experiences a force: 2
04
ˆ
r
QQ
aF t
rQt
Q
Qt
r
33Prepared by Mr.K.KarthiK -AP/ EEE
34. The existence of the force on Qt can
be attributed to an electric field
produced by Q.
The electric field produced by Q at a
point in space can be defined as the
force per unit charge acting on a test
charge Qt placed at that point.
t
Q
Q Q
F
E t
t 0
lim
34Prepared by Mr.K.KarthiK -AP/ EEE
35. ELECTRIC FIELD
An Electric field exists in the presence of a charged body
ELECTRIC FIELD INTENSITY (E)
A vector quantity: magnitude and direction (Volts/meter)
MAGNITUDE OF E: Proportional to the force acting on a unit
positive charge at a point in the field
DIRECTION OF E: The direction that the force acts
35Prepared by Mr.K.KarthiK -AP/ EEE
36. The Electric Field (E) is represented by drawing the Electric
Displacement Vector (D), which takes into account the characteristics of
the medium within which the Electric Field exists.
EmcoulD 2
, the Electric Conductive Capacity or Permittivity, is related to the
ability of a medium, such as air to store electrical potential energy.
11212
0 10850.8
mjoulecoulVacuum:
11212
1 10876.8
mjoulecoulAir:
Ratio:
003.1
0
1
36Prepared by Mr.K.KarthiK -AP/ EEE
37. The Electric Displacement Vector, D, is used to draw lines of
force.
2
mcoulUnits of D:
37Prepared by Mr.K.KarthiK -AP/ EEE
38. For a point charge at the origin, the
electric field at any point is given by
3
0
2
0 44
ˆ
r
rQ
r
Q
arE r
38Prepared by Mr.K.KarthiK -AP/ EEE
39. For a point charge located at a point
P’ described by a position vector
the electric field at P is given by
rrR
rrR
R
RQ
rE
where
4 3
0
r
Q
P
r R
r
O
39Prepared by Mr.K.KarthiK -AP/ EEE
40. Charge can occur as
◦ point charges (C)
◦ volume charges (C/m3)
◦ surface charges (C/m2)
◦ line charges (C/m)
most general
40Prepared by Mr.K.KarthiK -AP/ EEE
41. Volume charge density
Qencl
r DV’
41Prepared by Mr.K.KarthiK -AP/ EEE
42. Electric field due to volume charge density
Qenclr
dV’
V’
Pr
42Prepared by Mr.K.KarthiK -AP/ EEE
43. Surface charge density
Qencl
r DS’
43Prepared by Mr.K.KarthiK -AP/ EEE
44. Line charge density
Qenclr DL’
44Prepared by Mr.K.KarthiK -AP/ EEE
45. Electric field due to line charge density
Qenclr DL’
r P
45Prepared by Mr.K.KarthiK -AP/ EEE
46. An electric field is a force field.
If a body being acted on by a force is
moved from one point to another, then
work is done.
The concept of scalar electric potential
provides a measure of the work done in
moving charged bodies in an electrostatic
field.
46Prepared by Mr.K.KarthiK -AP/ EEE
47. The work done in moving a test charge from one
point to another in a region of electric field:
b
a
b
a
ba ldEqldFW
a
b
q
F
ld
47Prepared by Mr.K.KarthiK -AP/ EEE
48. In evaluating line integrals, it is customary
to take the dl in the direction of increasing
coordinate value so that the manner in
which the path of integration is traversed is
unambiguously determined by the limits of
integration.
3
5
ˆ dxaEqW xba
x
3 5
b a
48Prepared by Mr.K.KarthiK -AP/ EEE
49. The electrostatic field is conservative:
◦ The value of the line integral depends only on
the end points and is independent of the path
taken.
◦ The value of the line integral around any closed
path is zero.
0C
ldE
C
49Prepared by Mr.K.KarthiK -AP/ EEE
50. The work done per unit charge in
moving a test charge from point a
to point b is the electrostatic potential
difference between the two points:
b
a
ba
ab ldE
q
W
V
electrostatic potential difference
Units are volts.
50Prepared by Mr.K.KarthiK -AP/ EEE
51. Since the electrostatic field is conservative
we can write
aVbV
ldEldE
ldEldEldEV
a
P
b
P
b
P
P
a
b
a
ab
00
0
0
51Prepared by Mr.K.KarthiK -AP/ EEE
52. Thus the electrostatic potential V is a scalar field
that is defined at every point in space.
In particular the value of the electrostatic
potential at any point P is given by
P
P
ldErV
0
reference point
52Prepared by Mr.K.KarthiK -AP/ EEE
53. The reference point (P0) is where the
potential is zero (analogous to ground
in a circuit).
Often the reference is taken to be at
infinity so that the potential of a point
in space is defined as
P
ldErV
53Prepared by Mr.K.KarthiK -AP/ EEE
54. The work done in moving a point charge from
point a to point b can be written as
b
a
abba
ldEQ
aVbVQVQW
54Prepared by Mr.K.KarthiK -AP/ EEE
55. Along a short path of length Dl we have
lEV
lEQVQW
DD
DDD
or
55Prepared by Mr.K.KarthiK -AP/ EEE
56. Along an incremental path of length dl we
have
Recall from the definition of directional
derivative:
ldEdV
ldVdV
56Prepared by Mr.K.KarthiK -AP/ EEE
57. Thus:
VE
the “del” or “nabla” operator
57Prepared by Mr.K.KarthiK -AP/ EEE
58. Electrostatic field
Field strength (unit)
Force
Field strength outside
isolated sphere
Potential outside
isolated sphere
Energy transferred
q
F
E (N C-1)
2
21
4
1
r
qq
F
o
2
4
1
r
Q
E
o
r
Q
V
o4
1
W=qV
58Prepared by Mr.K.KarthiK -AP/ EEE
59. Electric field lines for two
charges of opposite sign
Electric field lines for two
equal positive charges
59Prepared by Mr.K.KarthiK -AP/ EEE
60. Capacitance: the ratio between
charge and potential of a body
Measured in coulombs/volt. This
unit is called the farad [F].
Capacitance is only defined for two
conducting bodies, across which the
potential difference is connected.
C =
Q
V
C
V
60Prepared by Mr.K.KarthiK -AP/ EEE
61. Body B is charged by
the battery to a
positive charge Q and
body A to an equal but
negative charge –Q.
Any two conducting
bodies, regardless of
size and distance
between them have a
capacitance.
61Prepared by Mr.K.KarthiK -AP/ EEE
62. Parallel plate capacitor:
◦ Assumes d is small,
◦ 0 is the permittivity of vacuum,
◦ r the relative permittivity (dielectric constant) of
the medium between plates,
◦ S the area of the plates and
◦ d the distance between the plates.
◦ 0 is a constant equal to 8.854x10 F/m
◦ r is the ratio between the permittivity of the
medium to that of free space.
◦ available as part of the electrical properties of
materials.
C = 0rS
d
F
62Prepared by Mr.K.KarthiK -AP/ EEE
63. Material r Material r Material r
Quartz 3.8-5 Paper 3.0 Silica 3.8
GaAs 13 Bakelite 5.0 Quartz 3.8
Nylon 3.1 Glass 6.0 (4-7) Snow 3.8
Paraffin 3.2 Mica 6.0 Soil (dry) 2.8
Perspex 2.6 Water (distilled) 81 Wood (dry) 1.5-4
Polystyrene foam 1.05 Polyethylene 2.2 Silicon 11.8
Teflon 2.0 Polyvinyl Chloride 6.1 Ethyl alcohol 25
Ba Sr Titanate 10,000.0 Germanium 16 Amber 2.7
Air 1.0006 Glycerin 50 Plexiglas 3.4
Rubber 3.0 Nylon 3.5 Aluminum oxide 8.8
63Prepared by Mr.K.KarthiK -AP/ EEE
64. The work done in moving a test charge from one
point to another in a region of electric field:
b
a
b
a
ba ldEqldFW
a
b
q
F
ld
64Prepared by Mr.K.KarthiK -AP/ EEE
68. If r2 tends to infinity
It is called an isolated sphere.
Otherwise it is called equation for potential
for spherical shells or cylinder.
Capacitance C = q/v
We may find capacitance of an isolated
sphere and spherical shells.
68Prepared by Mr.K.KarthiK -AP/ EEE
69. Energy Stored by the Capacitor is
W = ½ CV2
Energy Density w = W/V
w = ½ ɛ E2
69Prepared by Mr.K.KarthiK -AP/ EEE
70. 1. Et1 = Et2
2. Dn1 = Dn2
Based on the Boundary Conditions,
70Prepared by Mr.K.KarthiK -AP/ EEE
72. Electric Field Magnetic Field
Flux Ψ - Coulomb Flux φ - Weber
Charge Q Pole Strength - m
Coulomb’s Law F = Q1Q2/4πɛr2 F = m1m2/4πμr2
Electric Field Intensity E = F/Q V/m Magnetic Field Intensity H=F/m
A/m
Electric Flux Density D =Ψ/A C/m2 Magnetic Flux Density B = φ /A
Wb/m2 or Tesla
D = ɛE , ɛ = ɛ0ɛr
ɛ0= 8.854x10-12 F/m
B = μH, μ =μ0μr
μ0 =4π x 10-7 H/m
Electric Potential V = W/Q
V =Q/4πɛr2
Magnetic Potential M = m/4πμr2
Energy Stored – Electrostatic Energy
W = ½ CV2
Energy Stored – Electromagnetic
Energy W = ½ LI2
72Prepared by Mr.K.KarthiK -AP/ EEE
73. Electric Field Magnetic Field
Energy Density w = ½ ɛE2 = ½ DE Energy Density w = ½ μH2 = ½ BH
Electrical Dipole Magnetic Dipole
Electrical Dipole Moment (Ql) Magnetic Dipole Moment (ml)
Polarization -Ql/V Magnetization – ml/V
Boundary Conditions – Electric
field
Boundary Conditions – Magnetic
Field
73Prepared by Mr.K.KarthiK -AP/ EEE