Physics : Current Electricity : Microscopic model of current

Microscopic model of current

Consider a conductor with area of cross section A and an electric field applied from right to left. Suppose there are *n* electrons per unit volume in the conductor and assume that all the electrons move with the same drift velocity *d* as shown in Figure 2.5.

The drift velocity of the electrons = *vd* The electrons move through a distance *dx *within a small interval of* dt*

Since A is the area of cross section of the conductor, the electrons available in the volume of length *dx* is = volume × number per unit volume

Substituting for *dx* from equation (2.7) in (2.8)

= (A vd dt ) n

Total charge in volume element *dQ* = (charge) × (number of electrons in the volume element)

The current density ( *J* ) is defined as the current per unit area of cross section of the conductor.

J = I/A

The above expression is valid only when the direction of the current is perpendicular to the area A. In general, the current density is a vector quantity and it is given by

But conventionally, we take the direction of (conventional) current density as the direction of electric field. So the above equation becomes

where σ = *ne*2τ /*m* is called conductivity. The equation 2.12 is called microscopic form of ohm’s law.

The inverse of conductivity is called resistivity (ρ) [Refer section 2.2.1].

A copper wire of cross-sectional area 0.5 mm2 carries a current of 0.2 A. If the free electron density of copper is 8.4 × 1028 m-3 then compute the drift velocity of free electrons.

The relation between drift velocity of electrons and current in a wire of cross-sectional area A is

vd = I/ ne A

vd = 0.03 x 10-3 m s-1

Determine the number of electrons flowing per second through a conductor, when a current of 32 A flows through it.

I = 32 A , t = 1 s

Charge of an electron, e = 1.6 × 10-19 C

The number of electrons flowing per second, n =?

I = q/t = *ne*/*t*

n = It/e

n = 32×1 / 1 .6×10−19 C

n = 20 × 1019 = 2 × 1020 electrons

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