Conduction in Metals-Mobility and Conductivity

CONDUCTION IN METALS-MOBILITY AND CONDUCTIVITY

We know in metals the electrical conductivity depends on the number of charge carriers (free electrons) present in the material.

Let us consider a solid material (S) (metal) of length '7' and area of cross-section 'A' as shown in Fig. 1.3. Let 'n' number of charge carriers (free electrons) be present in it. Then,

Total number of electrons in the solid (metal) N = nAl ….(1)

We know, Total charge Q = Total number of electrons × Charge of one electron

Total charge present in the solid Q = N (-e) …..(2)

The negative sign indicates that the charge of the electron is negative.

Substituting equation (1) in (2) we get

Total charge present in the solid Q = n Al (-e) …..(3)

Now, when the solid is applied an voltage 'V', then the electrons starts moving with an average velocity called drift velocity (v) from one end to the other i.e., along a length 'Ɩ' (or) through a distance 'l', giving rise to conduction of current in the solid.

Substituting equation (3) in (4) we get

......(5)

The current density i.e., the current, flowing through the solid per unit area is given by

......(6)

Substituting equation (5) in equation (6) we can write.

.......(7)

We can write equation (7) as

Current density J = n v_d (-e) ……..(8)

Current density from Ohms Law

We know that the conduction in solids (metals) obeys Ohms law,

......(9)

where R is the electrical resistance i.e., opposition offered by the solid (metal) for the movement of electrons, given by

......(10)

where p is the resistivity of the solid (metal).

Substituting equation (10) in (9) we get

......(11)

Since the conductivity is the reciprocal of the resistivity (i.e) σ =

and Electric field 

we can write equation (11) as

J=σ E….(12)

Comparing equations (8) and (12) we can write

σ E = n v_d (-e)

σ = n μ (-e) …..(13)

where ' μ ' is the mobility of the electron..

Mobility: Mobility of the electron is defined as the drift velocity acquired by the electron per unit electric field applied to it.