Download Active and Passive Dielectrics The dielectric materials can be

MAHATMA GANDHI INSTITUTE OF
TECHNICAL EDUCATION & RESEARCH CENTRE
Sub:Engineering Electromagnetic
BE 3rd year sem v
Electronics &communication
Guided by:Sapna garde
Anita patel
Prepaired by:Pokia Fenil 130330111035
Tiwari shiva 130330111049
Vaghasiya Suraj 130330111051
TOPIC: Nature of dielectric material and
boundary condition for perfect dielectric and
boundary condition for conductor-free space
Dielectric Materials

Dielectric materials are also called as insulators.

In dielectric materials, all the electrons are tightly bound to
their parent molecules and there are no free charges. In addition, the
forbidden energy band gap (e.g.) for dielectric materials is more than
3eV.

Not possible for the electrons in the valence band to excite to
the conduction band, by crossing the energy gap, even with normal
voltage or thermal energy.

Dielectrics are non-metallic materials of high specific
resistance and negative temperature coefficient of resistance
 Active and Passive Dielectrics

The dielectric materials can be classified into active and
passive dielectric materials.
i.
Active dielectrics

When a dielectric material is kept in an external electric
field, if it actively accepts the electricity, then it is known as
active dielectric material. Thus, active dielectrics are the
dielectrics, which can easily adapt themselves to store the
electrical energy in it.
 ii.

Passive dielectrics
Passive dielectrics are the dielectrics, which restrict the flow
of electrical energy in them. So, these dielectrics act as insulators.

Examples: All insulating materials such as glass, mica, rubber
etc.,

Basic Definitions in Dielectrics
Electric Field
The region around the charge within which its
effect is felt or experienced is known as electric field.
The electric field is assumed to consist of imaginary
electric lines of force. These lines of force originate from
the positive charges and terminate to the negative charges
.
Electric field strength or electric field intensity (E)
Electric field strength at any point is defined as the force experienced
by an unit positive charge placed at the point. It is denoted by ‘E’.
‘q’ - magnitude of the charge in coulombs
‘f’ - force experienced by that charge in Newton,
electric field strength (E)
. Its unit is Newton / Coulomb (or) volt / metre.
Electric flux
It is defined as the total number of electric lines of force passing
through a given area in the electric field. (Emanated from the positive
charge). Unit: Coulomb
Electric flux density or electric
displacement vector (D)
It is defined as the number of electric lines of force passing
normally through an unit area of cross section in the field.
Its unit is Coulomb / m2
Permittivity
Permittivity is defined as the ratio of electric displacement vector
(D) in a dielectric medium to the applied electric field strength (E).
Mathematically the permittivity is, .Its unit is Farad /metre
The permittivity indicates the degree to which the medium can
resist the flow of electric charge and is always greater than unity.
Dielectric Constant
The dielectric constant or relative permittivity of a material determines
its dielectric characteristics. It is the ratio of the permittivity of the medium
and the permittivity of free space
Electric Polarization
 Consider an atom. We know that it is electrically neutral. Furthermore,
the centre of the negative charge of the electrons coincides with the
positive nuclear charge, which means that the atom has no net dipole
moment.
 However, when this atom is placed in an external electric field, the
centre of the positive charge is displaced along the field direction while
the centre of the negative charge is displaced in the opposite direction.
 When a dielectric material is placed inside an electric field, such
dipoles are created in all the atoms inside.
Polarizability ()
When the electric field strength ‘E’ is increased, the
strength of the induced dipole is also increased. Thus, the
induced dipole moment is proportional to the intensity of the
electric field.
Polarization vector
The dipole moment per unit volume of the dielectric material is
called polarization vector.
 ’ - average dswdipole moment per molecule and
‘N’ - number of molecules per unit volume
Unit: Coulomb / m2
Polarization vector is given by,
CONDUCTOR
CONDITIONS
–
FREE
+ + + + + + +
SPACE
BOUNDARY
free space
conductor
-
-
- -
- -
-
GRAPHICAL ILLUSTRATION
E1t
E1n
E1
Medium # 1
Medium # 2
E2n
E2
E2t
E1
E
2
E1t + E1n
Normal component
Tangential component
E2n +
E2t
NORMAL COMPONENTS
E1n
1
E1n
S
Maxwell’s equation (Gauss’s law)
rs
#1
+
E2n
+
+
#2
2
+
h
3
E2n
 
 D  ds  Qen
D 1 n ẑ
s
0
 
 
 
 D  ds1   D  ds 2   D  ds 3
ds 1 ẑ
D 2 n ẑ
 r ds
s
ds3  ẑ
Assume h → 0
Boundary condition for normal components
D1n S  D2 n S  rs S
D1n  D2 n  rs
s
TANGENTIAL COMPONENTS
E1t
#1
1
E1t
2
Maxwell’s equation (Conservation of energy)
h
#2
4
E2t
 
 E  d  0
3
ℓ
E2t
0
0
 3  4  1 
2
 E  d   E  d   E  d   E  d
1
2
3
4
Assume again h → 0
Boundary
condition
for tangential
components
E1t  E2 t
E1t   E2 t   0
CONDUCTOR – FREE SPACE
BOUNDARY CONDITION
#1
Free space
e0
#2
Conductor
e0
Boundary condition for normal components
0
D1n  D2 n  rs
Boundary condition for tangential components
0
E1t  E2 t
D1n  rs
Boundary conditions
for conductor – free
space/dielectric
E1 t  E 2 t  0
GRAPHICAL ILLUSTRATION
Conductor
Free space
+
+
+
Unit vector
normal to the
surface
+
+
+

D  rsân
+
+
rs
 rs
E  â n
e0
SUMMARIZED THE PRINCIPLES WHICH APPLY
TO CONDUCTORS IN ELECTROSTATIC FIELDS
 The static electric field intensity inside a conductor is
zero.
 The static electric field at the surface of a conductor is
everywhere directed normal to that surface.
 The conductor surface is an equipotential surface.