Physics for Information Science: Unit I: Electrical Properties of Materials
Expression for Electrical Conductivity
Definition, Unit, Formula
We know in the absence of external electric field, the motion of electrons in a metal moves randomly in all directions.
EXPRESSION FOR ELECTRICAL CONDUCTIVITY
We
know in the absence of external electric field, the motion of electrons in a
metal moves randomly in all directions. When an electric field (i.e.,)
potential difference is maintained between the two ends of a metallic rod, as
shown in Fig. 1.4 the electrons will move towards the positive field direction
and produces the current in the metallic rod.
If
'n' is the free electron density and ‘e' is the charge of electron then the
current density (i.e.,) the current flowing through unit area is given by
J
= n vd (-e) ….(1)
The
- ve sign implies that the charge of the electron is negative and it also
indicates that the conventional direction of current is in the opposite
direction to the electron movement.
Due
to the electric field applied, the electron gains the acceleration 'a'
(or) vd =aτ ….(2)
If
E is the electric field intensity and 'm' is the mass of the electron, Then,
The
force experienced by the electron is F =- eE ...(3)
From
Newton's Second law of motion,
The
force on the electron F = ma ...(4)
Equating
equation (3) and equation (4) we have
- eE= ma
...(5)
Substituting
equation (5) in equation (2) we have
….(6)
Substituting
equation (6) in equation (1) we have
….(7)
Here
the number of electrons flowing per second through unit area (i.e.,) the
current density, depends on the field applied. Thus if the field (E) applied is
more, current density (J) will also be more
We
can write J α E (or) J = σ E ….(8)
If
A = 1; E = 1 then
σ
= 1.
Definition: Coefficient of
electrical conductivity (o) which is defined as the quantity of electricity
flowing per unit area per unit time maintained at unit potential gradient. Unit: Ω -1m-1
Comparing
equation (7) and equation (8) we can write
….(9)
Physics for Information Science: Unit I: Electrical Properties of Materials : Tag: : Definition, Unit, Formula - Expression for Electrical Conductivity
Physics for Information Science: Unit I: Electrical Properties of Materials
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Physics for Information Science
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