# 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.

An example of convection current is the motion of electrons from the cathode towards the anode in a vacuum tube.

A convection current does not require a conductor and does not obey Ohm’s law. It is also not electrostatically neutral.

We consider a region with volume charge density  in which the charges are moving under the influence of an electric field with an average velocity
∴ current density,
But,
Flow of convection current

In vector form,

This is the convection current density.

If there are positive as well as negative charges with charge densities  and  moving with average velocities  and  respectively then the total convection current density will be,

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.

To maintain a steady current within a conductor, a continuous supply of electrons at one end and their removal at the other is necessary. So, a conductor as a whole is electrostatically neutral.

When an electric field  is applied, the force on an electron with charge  is

As the electrons are not free in space, they will not be accelerated by the field; but they will suffer constant collisions with atomic lattice and drift from one atom to another.

Let
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.

If there are N electrons per unit volume, the electron charge density is,
ρv = -Ne

Thus, the conduction current density is,

where  is the conductivity of the conductor.
∴

This is the conduction current density.

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 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).

Here,
i
R(t) conduction current
iC(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 Q(t) be the total capacitor charge on the positive plate.

Hence, the capacitor current, also termed the displacement current, is given as,

So, the 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.