ELECTROMAGNETIC FIELD

KONGUNADU COLLEGE OF ENGINEERING AND TECHNOLOGY
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
1
Prepared by Mr.K.KarthiK -AP/ EEE

 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

 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

 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.

 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).

 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.

 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.

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.

 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.

 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

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.

We will never be able to experience this peaceful
world again

 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 .

◦ Magnetic fields from current flow
◦ Electric fields from energized potential

The closer to source the higher the BV
BV ranges from 1000 mV to 50,000 mV

 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.

 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.

 Rectangular or Cartesian Coordinate System –
(x,y,z)
 Circular Cylindrical Coordinate System –
(ρ,φ,z)
 Spherical Coordinate System – (r,θ,φ)

 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)

 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

 Divergence : div F =
 Curl : Curl F =
0
1
lim .
V
s
F nds
V 
0
1
lim
V
s
nxFds
V 

 Divergence theorem :
Stokes Theorem :

 Electrostatics is the branch of
electromagnetics dealing with the effects
of electric charges at rest.
 The fundamental law of electrostatics is
Coulomb’s law.

 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.”

 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.

2
120
21
12
4
ˆ 12
r
QQ
aF R


Q1
Q2
12r
12F
Force due to Q1
acting on Q2
Unit vector in
direction of R12

 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 

 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

 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



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

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 
 mjoulecoulVacuum:
11212
1 10876.8 
 mjoulecoulAir:
Ratio:
003.1
0
1




The Electric Displacement Vector, D, is used to draw lines of
force.
2
mcoulUnits of D:

 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



 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

 Charge can occur as
◦ point charges (C)
◦ volume charges (C/m3)
◦ surface charges (C/m2)
◦ line charges (C/m)
 most general

 Volume charge density
Qencl
r DV’

 Electric field due to volume charge density
Qenclr
dV’
V’
Pr

 Surface charge density
Qencl
r DS’

 Line charge density
Qenclr DL’

 Electric field due to line charge density
Qenclr DL’
r P

 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.

 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

 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

 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.
0C
ldE
C

 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.

 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

 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

 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

 The work done in moving a point charge from
point a to point b can be written as
    
 

b
a
abba
ldEQ
aVbVQVQW

 Along a short path of length Dl we have
lEV
lEQVQW
DD
DDD
or

 Along an incremental path of length dl we
have
 Recall from the definition of directional
derivative:
ldEdV 
ldVdV 

 Thus:
VE 
the “del” or “nabla” operator

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
o4
1

W=qV

 Electric field lines for two
charges of opposite sign
 Electric field lines for two
equal positive charges

 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

 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.

 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 = 0rS
d
F

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

 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

 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.

 Energy Stored by the Capacitor is
 W = ½ CV2
 Energy Density w = W/V
 w = ½ ɛ E2

 1. Et1 = Et2
 2. Dn1 = Dn2
 Based on the Boundary Conditions,

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

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

ELECTROMAGNETIC FIELD

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