MOBILITY & CONDUCTIVITY ~ ECE

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Thursday, 14 February 2013

MOBILITY & CONDUCTIVITY

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MOBILITY

When an electric field E is applied across a piece of material, the electrons respond by moving with an average velocity called the drift velocity, $\, v_d$ . Then the electron mobility μ is defined as

$\,v_d = \mu E$

where

$\, v_d$ is the drift velocity (m/s)
$\, E$ is the magnitude of the applied electric field (V/m)
$\, \mu$ is the mobility (m²/(V.s))

In other words, the electrical mobility of the particle is defined as the ratio of the drift velocity to the magnitude of the electric field:

$\,\mu = \frac{v_d}{E}$

Electrical mobility is proportional to the net charge of the particle. This was the basis for Robert Millikan's demonstration that electrical charges occur in discrete units, whose magnitude is the charge of the electron.

Electrical mobility of spherical particles much larger than the mean free path of the molecules of the medium is inversely proportional to the diameter of the particles; for spherical particles much smaller than the mean free path, the electrical mobility is inversely proportional to the square of the particle diameter.

Derivation for Electric current and conductivity

Let L be the length of the conductor

A be the area of cross-section

N be number of electrons in the conductor

T be the time taken by electron to travel a distance L
^{V_d be the average drift velocity}

Current ( I )= ^{Total charge Q}

^Time

Total charge = number of electrons in the conductor * charge = Nq

I = ^Nq

Speed = distance / time

Average drift speed = L / T = V

T = L / V