Lecture ( 9 )
Chapter Three : Electric Field in Material Space
Properties of Materials , Convection and Conduction Currents, and Conductors
3.1 Properties of Materials
Just as electric fields can exist in free space, they can exist in material media. Materials are
broadly classified in terms of their electrical properties as conductors, semiconductors and
insulators. Non-conducting materials are usually referred to as insulators or dielectrics.
A conductor is a material which contains movable electric charges. Metals such as copper
aluminium are examples of conductors. In a Conductor the outer electrons of the atoms are
loosely bound and free to move through the material. In conductors, the valence electrons are
essentially free and strongly repel each other. Any external influence which moves one of them
will cause a repulsion of other electrons which propagates through the conductor.
In an insulator the free electric charges are very few in number. Most solid materials are
classified as insulators because they offer very large resistance to the flow of electric current. In
insulators the outermost electrons are so tightly bound that there is essentially zero electron flow
through them with ordinary voltages.
The properties of semiconductors lie in between conductors and insulators. Here we
examine the electric field inside a conductor and an insulator.
Also is Classified in terms of their conductivity
– High conductivity ( >> 1) is referred to as a metal
– Low conductivity (<< 1) is referred to as a dielectrics (or insulators)
– The rest is semiconductor
Note: the major difference between a metal and dielectric lies in the amount of electrons
available for conduction of current
3.2 Convection and Conduction Currents
= = .
The current density ( J )
∆
=
∆
• Current classification:
1. Conduction current is the current flowing through a conductor
2. Convection current is the current flowing through an insulating
medium (doesn’t satisfy Ohm’s law)
3. Displacement current
Convection current , as distinct from conduction current , dose not involve conductors and
consequently does not satisfy Ohm’s law
A flow charge ( , )
The y- direction current density ( Jy ) is given point is the current through a unit normal area at
that point by
Hence , in general ( J Convection current density ( A / m2) )
Conduction current , requires a conductor . A conductor is characterized by a large amount of
free electrons that provide conduction current due an impressed electric field
The force on an electron with charge ( -e ) is
F = -eE
According to Newton’s law , we have
Where ( τ ) is the average time interval between collisions , if there are ( n ) electrons per unit
volume , the electron charge density is given by
= −
Thus the conduction current density is
= = =
The conductivity of the conductor ( σ )
3.3 Conductors
A perfect conductor cannot contain an electrostatic field with it , under static conditions
Surface charge
The induced
Very quickly
A conductor has
An isolated zero electric field
conductor under under static
the influence of a conditions
static electric field
Resistance
As the electrons move , they encounter some damping forces called resistance as shown in
figure
A conductor of uniform cross section under an applied ( E ) field
The electric field applied is uniform and its magnitude is given by
Since the conductor has a uniform cross section
Substituting ( J = σ E ) and use the value of ( E ) we obtain
Hence
or
Where ( = )is the resistivity of the material
The basic definition of resistance ( R ) as the ratio of the potential difference ( V ) between the
two ends of the conductor to the current ( I ) through the conductor still applies
Power ( P )
Power P (in watts) is define as the rate of change of energy W (in joules) or force times
velocity
P = F .u = ∫ . = ∫ .
Or
= ∫ .
For a conductor with uniform cross section , dv = ds dl , so last equation becomes
= =
Or
