Mobility of Charge Carrier:

It is a property of a conductor, defined as the ratio of the speed of rise to the electric field in a conductor. The rate at which charge carriers move in a conductor depends on two factors, one is the intensity of the electric field applied to the conductor and the other is a property of the conductor called the mobility of charge carriers. In other words, for the same electric field, the acceleration of electrons on different metallic conductors will be different. This increased speed of electrons depends on a certain property of the conductor called the mobility of charge carriers.
In a metal, the band occupied by the balance electron cannot be completely filled and hence there are no forbidden levels at high energies. Because of this, there are always one or more free electrons available for many atoms that can move freely within the metal. The free electrons in the metal are not bound at all to their parent atoms and lose their individuality and move freely in the metal crystal.
In other words, no single electron can be said to be attached to a particular atom rather each free electron moves randomly from atom to atom. This means that a metal can be thought of as a three-dimensional array of tightly bound ions with a multitude of electrons moving freely within it. This concept is described in a rough way because there is such an electron gas inside the metal. According to the electron gas theory, electrons are in constant motion in a metal, and the direction of motion is constantly changing with each collision with heavy ions. The average is to be distance between two successive collisions is known as the mean free path. Since the directions of motion of the electrons within the metal are completely random, there will be no result of electrons moving in any particular direction at any given time, so in the absence of an externally applied electric field, the metal averages The current is zero.
Now we assume that an electric field of Ε volt/meter is applied to the piece of metal. Free electrons will accelerate due to the influence of this electric field. But due to collisions with very heavy ions, the speed of the electron cannot be increased infinitely. At each collision the electron loses its kinetic energy and then regains its acceleration due to the presence of an external electric field. Thus the electrons reach their fins.
Steady flow velocity after a specified time of applied electric field. Let us assume that this acceleration speed is v m/s. Needless to say, the magnitude of this increased electron velocity is directly proportional to the magnitude of the applied electric field Ε.
where, μ is the proportionality constant and is here called the electron mobility. This μ is commonly known as the mobility of charge carriers and here the charge carriers are electrons. Now if the steady state acceleration is superimposed on the random thermal motion of the electrons, there will be a steady acceleration of the electrons exactly opposite to the direction of the electric field.
This phenomenon creates an electric current. The current density J shall be defined as, the uniformly distributed current passing through the conductor per unit vertical cross-sectional area.
J = current density = current per unit area of the conductor. More precisely current density can be defined as the current uniformly distributed through a conductor of unit cross-sectional area.
If the concentration of electrons per cubic meter is n,
nv = number of electrons per unit cross section of the conductor per unit time.
So the total charge crossing the unit cross-section of the conductor per unit time is env Coulombs. It’s nothing but a tee.

Mobility of Charge Carrier diagram:

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