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By I Catt, Walton and
Davidson. Wireless World, December 1978. |
Displacement Current - and how to get rid of it |
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[Figures missing.] 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. …. …. 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. |
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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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