Drift velocity refers to the average velocity of charged particles (such as electrons) as they move through a material under the influence of an electric field. When an electric field is applied to a material, it exerts a force on the charged particles, causing them to accelerate in the direction of the field.

The drift velocity depends on the strength of the electric field, the density of the charged particles, and the properties of the material they are moving through (such as its resistivity and temperature).

Drift Velocity

Drift velocity refers to the average velocity of charged particles, such as electrons or ions, in a material when subjected to an electric field.

When an electric field is applied to a conductor, the free electrons within the material are accelerated in the direction of the electric field. Due to the scattering of the electrons by the atoms and other imperfections within the material, the electrons do not move in a straight line, but rather move in a zigzag path with an average velocity in the direction of the electric field. This average velocity is called drift velocity.

The drift velocity can be calculated as-

V_d = μE

Where V_d is the drift velocity, μ is the electron mobility of the material, and E is the electric field strength.

Derivation of Drift Velocity

Consider a conductor in which electric field E is produced. Let a free electron experience a force (-eE) in this field then the acceleration of the free electron is given as –

a = F/m = -eE/m

The final velocity of free electron in time t₁ is given as –

V₁ = u₁ + at₁

For n free electrons the final velocity is v₂, v₃, v₄, ………….v_n.

The Average velocity of a free electron or drift velocity is given as

V_d = ( v₁+v₂+v₃+………..+v_n) / n

V_d = (u₁ + at₁ + u₂ + at₂ +………..+u_n + at_n) /n

V_d = ( u₁+u₂+u₃+……..u_n) + a(t₁+t₂+t₃+…….+t_n ) /n

But ( u₁+u₂+u₃+……..u_n) /n = Average initial velocity of free electron = 0

And (t₁+t₂+t₃+…….+t_n ) /n = Average time taken between two collision =

= Relaxation time

So , V_d = a

V_d = (-eE/m) /

This is the derivation of Drift velocity.

Relation Between Drift Velocity And Electric Current

The relation between drift velocity and electric current is given as –

I = neAV_d

V_d = I / (nAe)

where I is the electric current, n is the number of charge carriers per unit volume (e.g., electrons) in the conductor, A is the cross-sectional area of the conductor, e is the charge of the carrier, and V_dis the drift velocity.

This equation shows that the electric current is directly proportional to the number of charge carriers, the cross-sectional area of the conductor, and the drift velocity of the charge carriers.

Relation Between Drift Velocity and Current Density

Drift velocity is the average velocity of charge carriers (usually electrons) in a material in the presence of an electric field. It is related to the current density, which is the amount of current flowing through a unit area of a material, by the following equation:

J = I/A = neV_d

where J is the current density, n is the number of charge carriers per unit volume, e is the charge of an electron, V_d is the drift velocity.

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