Displacement Current - and how to get rid of it
By I. Catt and M. F. Davidson and D. S. Walton, in Wireless World dec78.
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.
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. "Crosstalk (noise) in digital computers", I. Catt, IEEE Trans. EC-16, Dec. 1967, pp.743-763.
[Note 1. 7oct02. The article discusses a capacitor as it is always drawn in circuit diagrams, for instance the Harmsworth 1905 Encyclopaedia p1541. It has two circular plates, and the connecting wires enter each plate at its centre. See Figure 64 at http://www.ivorcatt.com/6_5.htm . This idea of the capacitor, which is for example a Leyden Jar, led Maxwell to propose "the extra current", later called "Displacement Current". The truth is different, a practical capacitor being as shown in Figure 65 of http://www.ivorcatt.com/6_5.htm . A true diagram, with electric current travelling along the capacitor plate from one end to the other, could have prevented Maxwell from proposing "Displacement Current" in the first place, except that Maxwell was impartial [his treatise, art. 62.] over the possibility of instantaneous action at a distance, so that electric charge (which was not particulate during Maxwell's time, and had no mass,) might be able to jump from one end of the capacitor plate to the other instantaneously.
[This article follows inexorably from the realisation that a capacitor is made up of two parallel plates, entered at one end, exactly like a transmission line. The realisation that classical electromagnetic theory treats displacement current in a capacitor and in a transmission line in contradictory ways has been ignored over the succeeding twenty years by every Reader in Electromagnetism in every university in the world. They keep their heads down. They take their salaries, but evade their duties. Ask your favourite Reader in Electromagnetism, even from the University of North-West Redbourn, to make a written comment on this. Or ask the author of a book on electromagnetic theory. One hundred and fifty pounds to the first man who is successful! However, my money is safe. Not one of them will want to lose his job, or have to modify his book, by commenting in writing, and so betraying their and their colleagues' threadbare, inconsistent dogma. They continue to pump the dogma down the throats of bemused students. - Ivor Catt, jan99.]
Second paper; "History of Displacement Current"
Scandals in Electromagnetic Theory; http://www.ivorcatt.com/28scan.htm
Professor D. A. Bell, (HoD), M.A., B.Sc., Ph.D., F.Inst.P., F.I.E.E., saves the day, using all his gongs. Then, silence for 15 years, which continues. No more cracked chimes from Bell. May he R.I.P.
The intrepid D.A. Bell, Professor of Electrical Engineering at Hull University, F.Inst.P., F.I.E.E., tried to shore up a shaky structure with a dumb article in Wireless World in aug79.;
16dec86. Dear Mr. Catt, I am sorry, but I am unable to agree to the reprinting of any of my Wireless World contributions in your proposed book; and in particular this applies to "No Radio without Displacement Current" [Wireless World, August 1979.] Yours sincerely, [signed] D. A. Bell.
[Comment by I.C. " . and in particular ." presumably indicates that he refers to a particularly fine example of his writing. No throwing pearls before swine! IC 12feb99]
19.12.86. Dear Professor Bell, Thank you for your letter dated 16Dec86. Is your reason for refusal that you consider that you should benefit financially from the re-publication of your contributions? Yours sincerely, Ivor Catt.
No it is not. D. A. Bell, 24.12.86.
Dear Professor Bell, Thank you for your letter dated 16Dec86, in which you refused permission to reprint your part in the debate on electromagnetic theory which has appeared in nearly every issue of Wireless World from 1978 to 1986.
I formally request that you reconsider your decision of 16Dec86.
When the new revolutionary theory of electromagnetism was first put forward by Catt-Walton-Davidson in 1978-79 etc., you took it upon yourself to carry the flag for the traditionalists opposing our new theory. What you wrote in your article "NO RADIO WITHOUT DISPLACEMENT CURRENT" was damaging to us and to the advance of science, because your very senior position in the academic hierarchy in ways particularly relevant to electromagnetic theory (you were ex-Reader in Electromagnetism in Birmingham University) tended to mask the crass ignorance you and your Establishment colleagues (e.g. Prof. Brown [past President of IEE] of Imperial College, now Marconi) showed about the subject that was generating your salaries.
[I heard of a particularly dirty trick by Brown. He went around saying Catt was a genius - for instance to Professor Clarricoat. This was perfect cover for his organisation, the I.E.E., of which he was then President, totally suppressing Catt then and for the next few decades. Catt had to be suppressed or his theoretical advances would show up their ignorance. It was difficult enough for them to keep up appearances in a stable environment. IC 12feb99.]
If you do not change your position, I shall say in my book that you refused to have your article published. Yours faithfully, Ivor Catt 20 12 86
Professor D. A. Bell, 87 East End,
North Humberside HU17 8RX
Dear Professor Bell, Your refusal to allow me to reprint your Wireless World article NO RADIO WITHOUT DISPLACEMENT CURRENT was unexpected, and I enclose an example of the pages which have already been printed containing your article, on the assumption that you would present no difficulty. Unless you withdraw your refusal, these pages will have to be reprinted, which will be expensive. This will leave a space in the book, because it is far too late to renumber all the pages and reprint the whole book. You are very welcome to write something new to replace your article. I calculate that with my typing it should run to either less than 1600 words (small, orthodox type) or less than 1200 words (this print size).
I am offering space in the book I am making, which book contains all my articles in Wireless World on e-m theory from 1978 to 1986. The space would be that caused by your refusal to allow me to insert your article NO RADIO WITHOUT DISPLACEMENT CURRENT. You would also be welcome to write less than the 1200 words mentioned above.
Should you be concerned that I might in the end refuse you space in my book after you had made the effort to produce the thousand words or so, I plan to defer to the Editor of Wireless World as the arbiter over fair play. I am therefore sending him a copy of this letter plus my previous letter to you.
You will appreciate that membership of the I.E.E. binds you to the Rules of Conduct for a member, which include doing everything within your power to enable discussion of the fundamentals of the subject.
You will also be welcome to the usual author royalty on books sold pro-rated in proportion to the pages you contribute divided by the total pages in the book. I offer the usual higher limit of royalty, which is 15% of retail.
Yours sincerely, Ivor Catt 29.12.86
Dear Mr. Catt,
Thank you for your letter of 18 March. I will arrange for an Investigating Panel to consider your complaint against Professor Bell.
So that there shall be no confusion could you please confirm to me that the cause of your complaint is Professor Bell's refusal to permit you to republish the article which he wrote on "No Radio without Displacement Current" and which appeared in Wireless World in August 1979 in a book which you are preparing.
Yours sincerely F G Helps Chairmen of the Investigating Panel, Institution of Electrical Engineers, Savoy Place, London WC2R 0BL 23mar87
Dear Dr. F G Helps,
Thank you for your letter dated 23 3 87.
You correctly state the cause of my complaint.
I enclose copies of Bell's letter to me dated 15 3 87 and my reply dated 22 3 87.
Should Bell agree to option [c] in my 22Mar letter [You will allow reprint of your Aug79 article in future editions of the book], I would have to consider withdrawing my complaint. However, in view of his item (3) in his 15Mar letter [My decision not to comment is final and I will not enter into any further correspondence], we can dismiss that possibility.
Should Bell assert that his Aug79 article is not a response to my Dec78 and Mar79 articles, I plan to produce;
1 Copies of letters in Wireless World in which the debate between Bell and me (or my co-authors) was continued.
2 Signed confirmation from editor(s) of Wireless World and other experts that Bell entered into a published dialogue with me on the question of the validity of my theories, and that he represented the traditional Establishment position.
The cause of my complaint is narrowly stated in your letter dated 23Mar. However, further documentation will help the Panel to understand the Intent behind his professional misconduct, his Intention to persist in misconduct, and the extent of the damage which has already resulted from his misconduct and the future damage which will accrue unless he changes his behaviour.
My 18Feb letter shows in the narrow sense that Bell is in breach of IEE Rules of Conduct. However, the Rules of Conduct themselves point to a broader approach to such a situation;
"A code of professional conduct designed to cover all eventualities must necessarily be written in general terms expressing broad ethical principles .."
Broadly, it is necessary to show that in the narrow sense, Bell has breached the Rules of Conduct if he is to be disciplined. Once that is so decided, then his punishment should be commensurate with the broader, ethical issues raised by his behaviour. I find it difficult to conjure up behaviour by someone placed as he is, with major resonsibility for furthering the Art and enabling open communication towards that end, that could be more damaging to advance in Science and Engineering, and in breach of the discipline which is central to the interests and responsibilities of the Institution of which he is a Fellow. From his position, he could not have behaved in a manner more damaging to advance in electromagnetic theory.
Yours sincerely, Ivor Catt 26 3 87 cc D A Bell
The I.E.E. Disciplinary Committee later reported to me that their decision was unanimous in favour of D A Bell. - Ivor Catt, 6feb99.
The IEE for its own part stood its ground for a further decade, insisting that Ivor Catt's contributions to e-m did not exist, until they published a slamming denigration in an IEE journal of Catt's 1994 book Electromagnetism by one B. Lago, see http://www.ivorcatt.com/9_review.htm . (B Lago's only function in life seems to be to lob a grenade at Catt's theories once every 20 years. Apart from that, he doesn't appear to exist. Nobody seems to have met him.) However, during that period '85-'95, although for another ten years embargoing Catt's e-m theory, they began, shortly after the misconduct by Bell, to publish commentary on the major projects to develop the "Catt Spiral" WSI invention with funding by the Brit. Govt., Unisys, Fujitzu, Tandem, SGS. (All attempts by Catt to publish on the matter have however always been rejected by the IEE.) The IEE's doyen Dr. A. Lynch then broke rank, and the IEE published the joint Lynch-Catt paper on e-m, discussing the Catt Anomaly, in 1998. It is on this website. However, IEE members still are shielded from my dec78 paper; the one attacked by Bell. I predict that the IEE will risk giving it members access to the dec78 ideas in around the year 2015. However, we have to get past a lot more ignorant noise before that happy day.
Ivor Catt feb99.
IC 15feb99. This is not just another run-of-the-mill scandal like the BSE suppression.
I decided that both I.E.E. officials and others should be able to read today's appraisal by my two co-researchers of the significance of the advances we have made, which have been suppressed by individuals like Bell and by institutions like the IEE and the InstPhys. The first reply was David;
"In so far as one can be a competent judge of one's own work - 'very significant'."
Recently I spent three hours talking to two of our senior technicians on em theory. They were spellbound as I went through all the concepts. It reminded me of the power of a coherent theory, which, in reality, is incredibly sound and has a profound impact on those that listen with an open mind. It did me a lot of good.
- Malcolm, feb99.
It is a great privilege to go through the experience that Ivor, Malcolm and David went through. We have experienced something that very few men have in the whole of history. We were at the hinge of history. You will never forget the day when I sat before the window with you at my right, and said "Then electric current goes." The evening before Walton had said to me "Then that's the end of Displacement Current." These are the turning points in the history of mankind. You were there. Dave was there. I was there. We are very privileged. I started calculating the way energy goes from capacitor to inductor and back. Remember the excitement when it turned down again, and so it looked as though it would simluate a sine wave with lots of small steps.
Then I had to phone Dave.
Henry V said; "I was there, on St. Crispin's Day." There were thousands of them. But at the end of displacement current and at the end of electric current, there were only the three of us very privileged adventurers.
"He that outlives this day, and comes safe home,
Will stand a tip-toe when this day is nam'd,
And rouse him at the name of Crispian.
He that shall live this day, and see old age,
Will yearly on the vigil feast his neighbours,
And say 'Tomorrow is St. Crispian'.
Then will he strip his sleeve and show his scars,
And say 'These wounds I had on Crispian's day'.
Old men forget; yet all shall be forgot,
But he'll remember, with advantages,
What feats he did that day. Then shall our names,
Familiar in his mouth as household words -
Harry the King, Bedford and Exeter,
Warwick and Talbot, Salisbury and Gloucester-
Be in their flowing cups freshly rememb'red.
This story shall the good man teach his son;
And Crispin Crispian shall ne'er go by,
From this day to the ending of the world,
But we in it shall be remembered-
We few. we happy few, we band of brothers;
For he today that sheds his blood with me
Shall be my brother; be he ne'er so vile,
This day shall gentle his condition;
And gentlemen of England now a-bed
Shall think themselves accurs'd they were not here,
And hold their manhoods cheap whiles any speaks
That fought with us upon Saint Crispin's day.
The dates are writ big in history.
David moved fast.
On 26may76 David Walton had said to Catt; 'So that gets rid of displacement current.'
Then, on 27may76, Catt said to Davidson; "The electric current goes."
These were truly St. Crispin's Day, but shared by a tiny group of three.
A very favoured few, a happy few.
I have before me a letter from Walton, unnoticed until today; "27may76. Your phone call last night was very exciting. I think I see the transformer now in terms of crosstalk ...."
How could such as we have been more favoured?
I think you should show this to your technicians, who were so much impressed by your talk on e-m. Can we get them to glimpse the grandeur of the experience?
- Ivor, feb99.