Establish Relation Between Drift Velicity and Current Density

Due to Drift Velocity ,current are flowing in a conductor. In metal ,conduction of electricity is due to randomly moving electrons.In the absence of electric field,the average velocity of electron is zero. so ,there is no electric current in a conductor.

When electric field in applied across the conductor,those electrons acquire a constant velocity of opposite direction of applied field.

Definition of Drift Velocity

The average velocity with which Free electrons can get drifted toward the positive end of conductor under the influence of electric field is called Drift velocity. it is denoted by V.

Consider a cylinderical metallic conductor of length l and crosssectional area A.

Then, Volume of conductor is

i.e V = A*l. …….(1)

let n be the no. of electrons per unit volume of conductor.

i.e. n = N/V

or. N = nAl ……(2) [From equation 1]

Total charge (q) in a conductor is

q=Ne

or. q=nAle …..(3)

Consider(I) be current flowing through the conductor,free electron get drifted towards the positive end of the conductor with drift velocity V.

Now, I = q/t

or, I = nAle/t

or, I = nAVe ,where V=l/t is drift velocity of electron.

I= VenA

This is required expression for a current in terms of drift velocity.

Current Density

The current flowing per unit cross sectionalarea is called Current density. it is denoted by I. it is a vector quantity.

i.e Current density= currrnt/crosssectional area

or J = VenA/A

so, J=ven

This is the required expression for current density in terms of drift velocity.

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