PPT No. 10
* Dielectrics
* Polar and Nonpolar Molecules
* Polarization P
* Polarization Charge Density
Introduction
A medium plays a significant role in
determining the response of an electric field.
The phenomena related to electrostatic fields in matter
are discussed using macroscopic model of matter.
Introduction
Depending upon the behavior of different materials
in an electrostatic field,
they are divided in two main categories
Conductors 2. Insulators or dielectrics.
They are described in brief as follows
A) Conductors
Conductors are materials which contain
electrons that are free to move and
an electric field produces a steady drift of charge i.e.
current.
They “conduct” the current or
allow the flow of electric charges like electrons fairly easily.
B) Insulators or Dielectrics
Dielectric is basically an electrically insulating material.
The electrons are strongly bound to the atoms or molecules.
They cannot be separated by the application of
an electric field.
A steady flow of electrons cannot flow through it.
B) Insulators or Dielectrics
Literally, Dielectric is a material
placed across the plates of a capacitor
like a little nonconducting bridge.
(The Greek prefix di or dia means "across").
Insulators or Dielectrics
Dielectric materials traditionally used in industrial applications are
oil-impregnated paper, mica, Elastomers, press-molded resins etc.
Presently materials used are synthetic polymers such as
polyethylene, polypropylene, polystyrene, polyvinyl chloride,
polytetrafluoroethylene, polymethyl methacrylate,
polyamide, polyimide etc.
Dielectric materials are classified into two broad groups:
1. Polar 2. Nonpolar
Polar and Nonpolar Molecules
A) Polar molecules
Polar means having electrical poles (i.e. electrical polarity).
The molecules in which the arrangement or
geometry of the atoms is such that
one end of the molecule has a positive electrical charge and
the other side has a negative charge are called as
polar molecules.
Examples of polar molecules are
Water (H2O)
Ammonia (NH3),
Hydrochloric acid (HCl), Sulfur Dioxide (SO2),
Hydrogen Sulfide (H2S), Carbon Monoxide (CO) etc
Polar molecules
Fig. (a) Polar Molecule - Water and Chemical Bonds in Water
B) Nonpolar molecules:
O=C=O
(b)Chemical Bonds in CO2
Nonpolar molecules
A non-polar molecule is that
in which the electrons are distributed more
symmetrically
It does not have an excess /abundance of charges
at the opposite sides.
The charges all cancel out each other. e.g.
CO2, H2, N2, O2, CH4, CCl4 etc.
A Slab in an Electric Field
Due to difference in the atomic structures of materials
conductors and insulators exhibit different response
when placed in an electric field.
The particular response is studied by placing
in an external electric field E0.
a) a slab of conducting material
b) a slab of insulating material
A) A Slab in an Electric Field- Conductor
•Net charge resides on the surface:
•Electrons move to the positive side of the field.
•As they cannot leave the material,
they accumulate on the surface i.e.
•charges are induced on the surface.
A) A Slab in an Electric Field- Conductor
*The
induced charges produce a field of their own Ei
which is directed opposite to the applied field E0 and
Ei tends to cancel E0.
Charge flow continues till Ei completely cancels E0
Result is Einside = 0 E = 0 inside the conductor
A Slab in an Electric Field- Conductor
•Conductor is an equipotential surface:
As
Potential φ is constant everywhere inside the conductor.
A Slab in an Electric Field- Conductor
ρ = 0:
According to Gauss law
If Einside = 0 => ρ = 0.
•E is normal to the surface:
•The electric lines of force are normal to the surface.
B) Nonpolar Dielectrics in Electric Field
Fig (a1) Nonpolar Molecule-Unpolarized
(a2) Polarization in an applied electric Field
Dielectric molecules in an Electric Field
In nonpolar dielectric molecules,
Permanent electric dipoles are not present.
However, after applying an external electric field
to an insulator or dielectric, positive and negative electric charges
within it undergo slight relative shift In opposite directions
Electric field distorts the negative cloud of electrons around
positive atomic nuclei in a direction opposite to the field.
Dielectric molecules in an Electric Field
The slight separation of charge
(stretching or shift of a fraction of an atomic diameter)
makes one side of the atom somewhat positive and
the opposite side somewhat negative i.e.
dipoles are created in nonpolar dielectric molecules.
Electric field induces dipoles &
Polarization in nonpolar dielectric molecules
Polar Dielectric Molecules in the Electric Field
In polar dielectric molecules,
permanent dipoles are present
however, due to thermal agitation,
they are generally in random orientations
Dielectric is in unpolarizated condition.
Polar Dielectric Molecules in the Electric Field
When an electric field is applied,
the dipoles are oriented by rotation and
aligned in the direction of the electric field so that
one type of bound charges (+ve or -ve) appear on a surface
and the opposite type on opposite surface.
Thus electric field polarizes the material of polar molecules
Polar Molecule in the Electric Field
Fig (b1) Polar Molecule-Unpolarized
(b2) Polarization in an applied electric Field
Effect of an Electric Field on Dielectric Materials
•Thus application of an external electric field creates
polarization in both types of molecules•Nonpolar and Polar
By Two different mechanisms
By inducing dipoles (in Nonpolar Dielectrics) or
By reorienting & aligning already existing dipoles (in Polar).
Effect of an Electric Field on Dielectric Materials
•Polarization reduces the electric field intensity
within the dielectric material
by a factor known as
the dielectric constant
(or relative permittivity) of the material.
Polarization P
Electric polarization
(or simply Polarization) or
the Polarization density is
the vector field
that expresses the density of permanent or
induced Electric Dipole moment in a dielectric material.
Polarization P
The polarization vector P is defined
as the dipole moment per unit volume.
The SI unit of measure of Polarization P is
Coulombs per square meter.
Polarization Density
When a dielectric is placed in a uniform external electric field E,
electric Polarization creates additional bound charges
on the surface of the material as explained above.
The surface Charge density is denoted as
the bound charge density σb.
where
is the unit normal Vector pointing outwards
Surface Charge Density and Volume Charge Density
Fig. Surface charge density of a polarized dielectric
Polarization P
Consider a rectangular block of the polarized dielectric of
length l & each face having uniform cross-sectional area A.
Let surface charge densities of polarization or bound charges
appearing at the end faces be +σp and -σp.
This surface charge is the only bound charge.
Therefore, the total charge induced on each face = σp A
Polarization P
Total induced electric dipole moment = -ql = σp Al
Volume of block = Area x Length = Al
Therefore, Polarization P i.e.
Induced dipole moment per unit volume
Polarization
P = σp
Polarization P
The polarization inside the material is equal to
‘the surface charge density appearing at faces
perpendicular to the direction of applied electric field’.
If P is not uniform inside the material, then there will be
accumulation of bound charges within the volume of
material (in addition to bound charges on the surfaces)
having volume charge density ρb.
Polarization P
If P is not uniform inside the material,
Then it can be proved that
Polarization P is a vector field whose Divergence
depends on the volume charge density ρb due to
bound or polarization charges in the material