Mobility of Charge CarrierPublished on 24/2/2012 & updated on 25/8/2018
In other words no one electron can be said associated with any particular atom instead each free electron moves atom to atom in random manner. That means the metal can be visualized as a three-dimensional array of tightly bounded ions along with swarm of electrons move freely inside it. This conception is bitterly described as there is as such an electron gas inside a metal. According to the electron gas theory, electrons are in the metal in continuous motion, and the direction of the motion continuously being changed with each collision with heavy ions. The mean distance between two successive collisions is known as mean free path. As the directions of the motion of electrons inside the metal are completely randomized, there will be no resultant drifts of electrons in any particular direction in a given time hence the average current of the metal is zero in absence of any externally applied electric field.
Now let us assume that one electric field of Ε volt/metre is applied across the piece of metal. Due to influence of this electric field the free electrons will be accelerated. But due to collisions with much heavier ions, the velocity of electrons cannot be increased infinitely. At each collision the electron losses its kinetic energy and then regains its acceleration due to presence of external electric field. In this way the electrons reach to their finite steady Drift velocity after certain time of applied electric field. Let us assume this drift velocity is v metre/sec. It is needless to say the magnitude of this drift velocity of electrons is directly proportional to the intensity of the applied electric field Ε. Where, μ is the constant of proportionality and here it is called as mobility of electrons. This μ is generally known as Mobility of Charge Carrier and here the charge carriers are electrons. Now if the steady-state drift velocity is superimposed on the randomized thermal motion of the electrons, there will be a steady drift of electrons just in opposite to the direction of applied electric field.
This phenomenon constitutes an electric current. The current density J would be defined as, uniformly distributed current passing through a conductor per unit perpendicular cross-sectional area the conductor. J = current density = current per unit area of conductor. More precisely current density can be defined as the uniformly distributed current passing through a conductor of unit cross-sectional area. If the concentration of electrons per cubic metre is n, nv = number of electrons crosses per unit time per unit cross-section of the conductor. Therefore total charge crosses the unit cross-section of the conductor per unit time is env Coulombs. This is nothing but the current density of the conductor. Again for the conductor of unit dimension, cross-sectional area A = 1 m2, length L = 1 m, applied electric field E = V/L = V/1 = V (V is applied voltage across the conductor). Current I = J and resistance R = ρ = 1/σ, where, ρ is resistivity and σ is conductivity of the conductor.
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