# Electric Current

Electric current is defined as the rate of flow of electric charges or electrons through a cross-sectional area.

# Convection Current

The motion of charged particles in free space (vacuum) is said to constitute convection current.∴ current density,

But,

**Flow of convection current**

In vector form,

This is the convection current density.

where the positive charges will move in the direction of the electric field and the negative charges will move in the opposite direction.

# Conduction Current and Ohm’s Law

The motion of the free electrons present in a conductor by the influence of an electric field constitutes the*conduction current*.

m = Mass of moving electron,

= Average drift velocity

By Newton’s law,

(

*τ*is the average time interval between successive collisions)

where is the mobility of electrons.

From the above Eq. we see that

*drift velocity is directly proportional to the applied field*.

*N*electrons per unit volume, the electron charge density is,

*ρ*= -Ne

_{v}Thus, the conduction current density is,

where is the conductivity of the conductor.

∴

This is the
From Eq., it is seen that the current density is linearly dependent on the external electric field.
This equation is known as the point form of

*conduction current density*.*Ohm’s law which states that the current density at any point in a conducting medium is directly proportional to the electric field*.

# Displacement Current

The concept of displacement current can be illustrated by considering the currents in a simple parallel*RC*network (assume ideal circuit elements, for simplicity).

*i*

*(*

_{R}*t*) conduction current

*i*(

_{C}*t*) displacement current

From circuit theory,

**RC parallel circuit representing a lossy capacitor**

In the resistor, the conduction current model is valid The ideal resistor electric field and current density are assumed to be uniform throughout the volume of the resistor.

The conduction current model does not characterise the capacitor current. The ideal capacitor is characterised by large, closely spaced plates separated by a perfect insulator so that no charge actually passes through out from the dielectric The capacitor current measured in the connecting wires of the capacitor is caused by the charging and discharging of the capacitor plates. Let

Hence, the capacitor current, also termed the

The conduction current model does not characterise the capacitor current. The ideal capacitor is characterised by large, closely spaced plates separated by a perfect insulator so that no charge actually passes through out from the dielectric The capacitor current measured in the connecting wires of the capacitor is caused by the charging and discharging of the capacitor plates. Let

*Q*(*t*) be the total capacitor charge on the positive plate.Hence, the capacitor current, also termed the

*displacement current*, is given as,*displacement current density*is given as,

As may vary with space, the displacement current density is written as,

Thus, displacement current for a closed surface is,

Thus, the displacement current does not represent a current. It is only an

*apparent current*representing the rate at which flow of charge takes place from electrode to electrode in the external circuit. Hence, the term ‘*displacement*’ is justified.