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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 Description: 36746.png in which the charges are moving under the influence of an electric field with an average velocity Description: 24953.png
∴ current density, Description: 30292.png
But, Description: 150181.png
Description: 39341.png
Flow of convection current
Description: 28771.png

In vector form,
Description: 39362.png

This is the convection current density.
If there are positive as well as negative charges with charge densities Description: 32621.png and Description: 27929.png moving with average velocities Description: 29389.png and Description: 35064.png respectively then the total convection current density will be,
Description: 39380.png

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 Description: 29626.png is applied, the force on an electron with charge Description: 32013.png is Description: 29983.png
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.
m = Mass of moving electron,

Description: 25526.png= Average drift velocity

By Newton’s law,
Description: 25953.png (τ is the average time interval between successive collisions)
∴    Description: 22513.png

where Description: 34170.png 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,
Description: 36878.png

where Description: 35976.png is the conductivity of the conductor.
Description: 39502.png
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).
R(t) conduction current
iC(t) displacement current

From circuit theory,
Description: 29128.png
RC parallel circuit representing a lossy capacitor
In the resistor, the conduction current model is valid Description: 26964.png The ideal resistor electric field Description: 32049.png and current density Description: 21641.png 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 Description: 28520.png so that no charge actually passes through out from the dielectric Description: 35893.png 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,
Description: 23952.png
So, the displacement current density is given as,
Description: 32644.png
As Description: 22562.png may vary with space, the displacement current density is written as,
Description: 23904.png
Thus, displacement current for a closed surface is,
Description: 21398.png
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.

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