Displacement Current

By I Catt, Walton and Davidson.

Wireless World, December 1978.

 

Displacement Current - and how to get rid of it

[Figures missing.]

Also at article ; article

Scandals in Electromagnetic Theory

To enable the continuity of electric current to be retained across a capacitor Maxwell proposed a "displacement current". By treating the capacitor as a special kind of transmission line this mathematical convenience is no longer required.

Conventional electromagnetic theory proposes that when an electric current flows down a wire into a capacitor it spreads out across the plate, producing an electric charge which in turn leads to an electric field between the capacitor plates. The valuable concept of continuity of electric current is then retained by postulating (after Maxwell) [reference 1] a "displacement current", which is a mathematical manipulation of the electric field E between the capacitor plates which has the dimensions of electric current and completes the flow of "electricity". This approach permits us to retain Kirchhoff's Laws and other valuable concepts, even though superficially it appears that at the capacitor there is a break in the otherwise continuous flow of electric current.

The flaw in this model is revealed when we notice that the electric current entered the capacitor at one point only on the capacitor plate. We must then explain how the electric charge flowing down the wire suddenly distributes itself uniformly across the whole capacitor plate. We know that this cannot happen since the charge cannot flow out across the plate at a velocity in excess of the velocity of light. This paradoxical situation is brought about by a fundamental flaw in the basic model. Work on high speed logic design [reference 2] has shown that the model of a lumped capacitance is faulty, and "displacement current" is an artefact of this faulty model.

The true model is quite different. Electric current enters the capacitor [Note 1] through a wire and then spreads out across the plate of the capacitor in the same way as ripples flow out from a stone dropped into a pond. If we consider only one pie-shaped wedge of the capacitor, see Figure 64 in http://www.ivorcatt.com/6_5.htm or Fig. 1c in WW dec78, we can recognise it as a parallel plate transmission line whose only unusual feature is that the line width is increasing (and hence the impedance is decreasing). The capacitor is made up of a number of these pie-shaped transmission lines in parallel, so the proper model for a capacitor is a transmission line.

Equivalent series resistance for a capacitor is the initial characteristic impedance of this transmission line at a radius equal to the radius of the input wires. Series inductance does not exist. Pace the many documented values for series inductance in a capacitor, this confirms experience that when the so-called series inductance of a capacitor is measured it turns out to be no more than the series inductance of the wires connected to the capacitor. No mechanism has ever been proposed for an internal series inductance in a capacitor.

Since any capacitor has now become a transmission line, it is no more necessary to postulate "displacement current" in a capacitor than it is necessary to do so for a transmission line. The excision of "displacement current" from Electromagnetic Theory has been based on arguments which are independent of the classic dispute over whether the electric current causes the electromagnetic field or vice versa.

Appendix.

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References.

1.      1.      1.      "History of displacement current", by Catt, Davidson and Walton, Physics Education, to be published early 1979. [jan99. The Inst. Phys. broke their contract with me to publish this article. It was eventually published in Wireless World in March 1979. (Essen F.R.S. told me Inst. Phys broke their contract with him to publish another article.)]

2.     2.     2.     "Crosstalk (noise) in digital computers", I. Catt, IEEE Trans. EC-16, Dec. 1967, pp.743-763.

 

Catt Question

http://www.ivorcatt.com/28anom.htm

http://www.electromagnetism.demon.co.uk/catanoi.htm

 

Maxwell's Equations

http://www.ivorcatt.org/ic3804.htm

http://www.ivorcatt.com/2804.htm

 

Moving Backwards.

http://www.ivorcatt.com/2607.htm

 

TEM Wave.

http://www.electromagnetism.demon.co.uk/17136.htm

http://www.electromagnetism.demon.co.uk/20136.htm

The Heaviside Signal http://www.ivorcatt.com/2604.htm

http://www.ivorcatt.com/1_1.htm figures 4, 5.

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