Understanding Displacement Current: The Physical Explanation Behind the Concept

[Apteronotus]

When Maxwell first described the displacement current, he rationalized it with imagining space filled with ether. We now know that ether does not exist. So the question remains what is the rationalization behind displacement current?

Wikipedia states "... It is now believed that displacement current does not exist as a real current (movement of charge)... The present day concept of displacement current therefore simply refers to the fact that a changing electric field has an associated magnetic field..."

I have a hard time accepting the term on the basis that it makes the equations work. I guess I need to know what the physical reasoning is behind the term. What physical phenomenon is it describing?
Can anyone help me understand this?

Thanks,

ps. the best explanation I have been able to come up with follows. Please feel free to correct or confirm this.

When an electric field E is applied to a dielectric (any non conducting substance), the actual field that is present inside the dielectric is given by the equation D = εoE+P.

The applied field E causes the atoms of the dielectric to polarize. The polarized atoms form an internal electric field P. Of course the value of this field is determined by the particular media and its electric susceptibility χ. The direction of P would generally be opposite that of E.

The idea is that the displacement field in regions of matter is composed of the "matter-free" field εoE, and an additional contribution from the matter, P.

 

[Peeter]

Physically, this is really a consequence of conservation of charge

[tex]
\frac{\partial \rho}{\partial t} + \nabla \cdot \vec{J} = 0
[/tex]

If you start with the pre-Maxwell Ampere law

[tex]
\nabla \times \vec{B} = \mu_0 \vec{J}
[/tex]

and Gauss's law

[tex]
\nabla \cdot \vec{E} = \rho/\epsilon_0
[/tex]

some manipulation will show that the conservation of charge does not hold. The book "Relativity Demystified", by McMahon on pages 2-3 has a nice walk through of the arithmetic to demonstrate this.

Note that the book above is actually a GR book, but happens to start off with a very clear motivation of this fix-up of Ampere's law by Maxwell.

 

[astrokreng]

it is important to constantly question and seek understanding of concepts, even ones that have been widely accepted and used in equations. The concept of displacement current is no exception.

The term "displacement current" was first introduced by James Clerk Maxwell in his famous set of equations known as Maxwell's equations. At the time, it was believed that space was filled with a medium called ether, and displacement current was used to explain the propagation of electromagnetic waves through this medium.

However, as our understanding of the universe has evolved, we now know that ether does not exist. This raises the question of what the physical reasoning is behind displacement current.

As stated by Wikipedia, the modern understanding of displacement current is that it does not refer to the movement of charge, but rather to the fact that a changing electric field produces a magnetic field. This is known as the Maxwell-Faraday equation, which states that a changing magnetic field induces an electric field, and a changing electric field induces a magnetic field.

In simpler terms, displacement current describes the phenomenon of electromagnetic waves propagating through space. When an electric field changes, it creates a changing magnetic field, which in turn creates a changing electric field, and so on. This cycle allows electromagnetic waves to travel through space without the need for a medium like ether.

In regards to the explanation provided by the individual, it is a valid way to understand the concept of displacement current. The equation D = εoE + P shows the relationship between the electric displacement field (D), the applied electric field (E), and the polarization of the dielectric material (P). This equation helps to illustrate how displacement current is a combination of the "matter-free" electric field and the contribution from the polarization of the material.

In summary, displacement current is a physical phenomenon that describes the relationship between electric and magnetic fields and allows for the propagation of electromagnetic waves through space. While the term may have originated from a now-disproven concept of ether, its modern understanding is rooted in the fundamental principles of electromagnetism.