# Displacement Current

## Main Question or Discussion Point

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.

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Physically, this is really a consequence of conservation of charge

$$\frac{\partial \rho}{\partial t} + \nabla \cdot \vec{J} = 0$$

$$\nabla \times \vec{B} = \mu_0 \vec{J}$$

and Gauss's law

$$\nabla \cdot \vec{E} = \rho/\epsilon_0$$

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.