Drift Velocity

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Drift Velocity

The average velocity gained by the free electrons of a conductor in the opposite direction of the externally applied electric field is called Drift Velocity. The parameter drift-velocity symbol is called drift velocity of electrons.

drift-velocity

The relation between Electric current and Drift velocity:

Derivation of OHM’S Law:

Current in terms of drift velocity (vd) is I = enAvd

Number of electrons in length l of the conductor = n × volume of the conductor = n Al

Total charge contained in length l of the conductor is q = en Al

All the electrons which enter the conductor at the right end will pass through the conductor at the left end in time,

current-formula

This equation relates the current I with the drift velocity vd

Current density ‘j’ is given by

current density formula

In vector form,

current density in vector form

The above equation is valid for both positive and negative values of q.

Deduction of Ohm’s Law:

when a potential difference V is applied across a conductor of length l, the drift velocity in terms of V is given by

deduction of ohm law

If the area of cross section of the conductor is A and the number of electrons per unit volume of the electron density of the conductor is n, then the current through the conductor will be

ohm law

At a fixed temperature, the quantities m, l, n, e, τ and A, all have constant values for a given conductor.

Therefore,

ohm law

This prove Ohm’s law for a conductor and here

resistivity

is the resistance of the conductor.

Resistivity in terms of electron density and relaxation time:

The resistance R of a conductor of length l, the area of cross-section A and resistivity ρ is given by

resistivity-relation

where τ is the relaxation time. Comparing the above two equations, we get

resistivity-relation

Constant value e = 1.6 × 10-19C.

Obviously, ρ is independent of the dimension of the conductor but depends on its two parameters:

  1. The number of free electrons per unit volume or electron density of the conductor.
  2. The relaxation time τ, the average time between two successive collisions of an electron.

Units:

Drift velocity vd is in ms-1 , free-electron density in m3, cross-sectional area A in m2, current density j in Am-2. All resistance in Ω.

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