A metal conductor has large number of free electrons or conduction electrons, whose number density (no of electrons per unit volume) is about 1029m-3 these electrons at room temperature move at random within the body of the conductor like the molecules of a gas. The average thermal speed of the free electrons in random motion at room temperature is of the order of 105ms-1, the directions of motion of these free electrons are so randomly distributed that the average thermal velocity of the electrons is zero. if u1, u2, u3,…..u are random thermal velocities of n free electrons in the metal conductor, then the average thermal velocity of electrons is
as a result of which there will be not net flow of electrons or charge in one particular direct in a metal conductor.
When some potential difference is applied across the two ends of a metal conductor say a copper wire; an electric field is set up inside the conductor. As a result of which the free electrons in the conductor experience a grocers in a direction opposite to that of electric field and are accelerated.
Form negative end to positive end of the conductor on their way the accelerated free electrons suffer frequent collision against the copper ions/atoms and lose their gained kinetic energy. After each collision the free electrons are aging accelerated due to electric field towards the positive end of conductor and lose their gained kinetic energy in the next collision with the ions/atoms of the conductor. It means the extra velocity gained by free electron is lost in subsequent collision. The process conti9nues till the electrons reach the positive end of the conductor.
Thus under the effect of electric field applied the free electors are having random thermal velocities and acquired small velocities by virtue of acceleration due to electric field with which they move towards the positive and of the conductor. There velocities are in different direction. Due to it each free electron describes a curved path between ends of the conductor with some average velocity called drift velocity. Thus drift velocity id defined as the average velocity with which the free electrons get deified towards the positive end of the conductor under the influence of an external electric filed applied; the direct velocity of electrons is of the order of 10-4ms-1.
If V is the potential difference applied across the ends of the conductor of length t the magnitude of electric field set up is
E = potential difference / length = V / T
Average drift speed vd = eE/m τ
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