Introduction to Displacement Current

Displacement current is the rate of change of electric displacement field. You can understand it well when explained through Maxwell’s Equation.

The Maxwell-Ampere Law

Electricity and magnetism are one of the significant parts of physical science. Electricity and magnetism are intrinsically linked with each other, that's why they are put under a single topic known as electromagnetism. We can see an insight into electromagnetism while dealing with a current-carrying wire. When an electric current passes through a wire, it generates a magnetic field that surrounds the wire or any conductor through which it passes.

This type of current, which passes through a conductor, is known as conduction current and is caused by the actual movement of electrons through the conductor. This type of current is mostly used in our day to day life. There is also another kind of current, which is known as displacement current. Displacement current differs from the conduction current because the displacement current does not involve electrons' movement. The displacement current has enormous importance for the propagation of electromagnetic waves.

James Clerk Maxwell, a famous physicist, was the first to develop a theory about the displacement current. Maxwell is quite well known for his work on Maxwell's equations. He has developed four equations, which form a fundamental way to represent electricity and magnetism. Among all his equations, one of the equations is known as Maxwell-Ampere law.

Before Maxwell developed any equation, a scientist, namely Andre-Marie Ampere, had developed a famous equation called Ampere's law. According to Ampere's law, when conduction current (I) passes through a closed-loop, a magnetic field (B) is generated surrounding the closed-loop.

The Ampere Maxwell equation is given as:

∮B.ds = μₒI

Where μ_{0} is said to be the permeability of free space

Ampere's law holds true in any situation where there is a continuous supply of conduction current. The problem arises when Ampere's law is used to calculate the figures in written format. To understand this, let's take the example of an electric circuit having a capacitor. As per the diagram below, a source of voltage is connected to charge a capacitor. The positive charges (Q+) and the negative charges (Q-) get accumulated on the opposite plates of the capacitor.

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Expression for displacement current

The equation for displacement current is given by,

I_{D} = J_{D}S = S\[\frac{∂D}{∂t}\]

Where,

● S is the area of the plate of the capacitor

● ID is the displacement current

● JD is the density of displacement current

● D is it related to the electric field, D=εE

● ε is the permittivity of the medium that is present between the plates

During the charging and discharging process of the capacitor, the electric current flows through the wires of the circuit. However, no current flow between the plates of the capacitor. According to Ampere's law, the magnetic field should not present between the plates as there is no current, but in reality, the magnetic field exists there. Maxwell formulated this limitation of Ampere's law by adding a term in the equation of Ampere's law to solve the issue.

The conduction current, be it steady or varying, always produces a magnetic field surrounding the conductor through which it passes. In the 91st century, Maxwell predicted that the magnetic field will still exist even in the absence of conduction current, and the magnetic field may be associated with the changing electric field. This theory of Maxwell was experimentally proved in the subsequent years.

Since the magnetic field is associated with the electric field, the general displacement current formula is given by,

∮ B.ds = μ₀(I + ϵ₀ \[\frac{d\phi_{E}}{dt}\])

This equation is the generalized formula of Maxwell-Ampere law.

Displacement Current Definition

The displacement current (ID) is the part which Maxwell has added to the Ampere's law. To understand the concept of displacement current, first, let's take a look at its formula.

\[I_{d}\] = ϵ₀ \[\frac{d\phi_{E}}{dt}\]

The above equation consists of two terms that multiply, the first term is the permittivity of free space (ε0), and the second term is the derivative of electric flux (ΦE) concerning time. Electric flux is the time rate change of flow of the electric field through a surface. If we take the derivative of electric flux, we get the rate of change of the electric field of a given area concerning time.

FAQ (Frequently Asked Questions)

1. What is a Displacement Current in a Capacitor?

Ans. A capacitor is always accompanied by displacement current but not the conduction current under normal conditions. This is when the plates of the capacitor are subjected with potential difference below the maximum voltage of the capacitor. Conduction current is the current, which occurs due to the actual movement of the electrons, but in displacement current, no movement of electrons takes place. Displacement current occurs due to the variations of the electric field, almost equivalent to a flowing current.

When a high voltage is applied across the capacitor, the insulators stop insulating and conduct electricity. Beyond a specified voltage, the dielectrics behave like a conductor. This gives rise to a conduction current. This phenomenon is called the breaking down of a capacitor.

2. What are the Uses of Displacement Current?

Ans. Displacement current plays a prime factor in a range of fields like:

Propagation of electromagnetic radiation like radio waves, light waves and through empty space

A traveling and the varying magnetic field is related to a synchronous change in the electric field that results in displacement current.

The displacement current plays a major role during the propagation of electromagnetic radiations like light waves and radio waves through space.

3. How Does Displacement Current Relate to the Behavior of Electric and Magnetic Fields?

Ans. Displacement current in electric and magnetic fields is a phenomenon that lies analogy to the ordinary electric current. These are produced due to the changing effect of the electric current. As electric charges don’t flow through the insulating material from one plate of a capacitor to another, there is no conduction current. Rather, a displacement current works to account for the continuous flow of magnetic fields.

A varying electric field produces a magnetic field, and a varying magnetic field produces an electric field. That's why electric and magnetic fields are symmetric in nature as they are interlinked with each other.

Hope, you understood the concept behind the displacement current and Maxwell-Ampere formula, and the equations of the displacement current and displacement formula, the significance of displacement current and its uses.