6 The Electrical Displacement Current

"Suppose the poles of a galvanic cell to be connected with the plates of a condenser by means of two wires, one of them containing a switch (Fig. 93). If the switch is pressed down , a current flows..."

Fig. 93  When the condenser is charged by a convection current Jc, the electric field inside the condensers changes and gives rise to a displacement current of the same amount as Jc

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"...which charges the two plates of the condenser; an electric field E is thereby introduced between them. Before Maxwell's time, this phenomenon was regarde as an "open circuit." Maxwell how-ever realized that during the growth of the field E a displacement current flows between the condenser plates, and thus the circuit becomes closed. As soon as the condenser plates are completely charged, both currents, the conduction and displacement current cease..."

Fig 94  Both the convection current Jc and the displacement current Jd produce a surrounding magnetic field.

    "...Now the essential point is Maxwell's affirmation that the displace-ment current just like the conduction current, produces a magnetic field according to Biot and Savart's law. That this is actually so has not only been proved by the success of Maxwell's theory in predicting numerous phenomena but was also later confirmed directly by experiment
    The magnitude of the displacement current can easily be computed...."
     "... Therefore, following Maxwell, the whole current density is the sum j = jc + jd where jc is the current density of the free moveable charges and jd is the displacement current. Both kinds of current are surrounded by a magnetic field in the usual way (

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7 Magnetic Induction

"After Oersted had discovered that a conduction current produces a magnetic field and Biot and Savart had formulated this fact as an action at a distance, Ampere discovered (1820) that two voltaic currents exert forces on each other, and he succeeded in expressing the law underlying this phenomenon again in terms of an action at a distance. This discovery had far- reaching consequences, for it made it possible to regard magnetism as an effect of moving elec-tricity. According to Ampere small closed currents are supposed to flow in the molecules of magnetized bodies. He showed that such currents behaved exactly like elementary magnets. This idea has stood the test of thorough examination; from his time on magnetic fluids became superfluous. Only electricity was left, which, when at rest, produced the electrostatic field, and when flowing, produced the magnetic field besides. Ampere's discovery may also be expressed in the following way: According to Oersted a wire in which the current J 1 is flowing produces a magnetic field in its neighborhood. A second wire in which the current
J 2 is flowing  is then pulled by forces due to this magnetic field. In other words, a field produced by one current  tends to deflect or accelerate flowing electricity.
     Hence the following question suggests itself: Can the magnetic field also set electricity that is at rest into motion? Can it produce or "induce" a current in the second wire which is initially without a current?
     Faraday found the answer to this question (1831)  He discovered that a static magnetic field is not able to produce an electric current  

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but that a field which varies in time is able to. For example, when he quickly brought a magnet close to a loop of wire made of conduct-ing material, a current flowed in the wire as long as the magnet moved. In particular, when he produced the magnetic field by means of a primary current, a short impulse of current occurred in the secondary wire whenever the first current was started or stopped.
     From this it is clear that the induced electric force depends on the velocity of alteration of the magnetic field in time. Faraday succeeded in formulating the quantitive law of this phenomenon with the help of his concept of lines of force. Using Maxwell's ideas we shall give it such a form that its analogy with Biot and Savert's law comes out clearly


Fig. 95 A changing magnetic field which represents a magnetic cur-rent 1 is surrounded by an electric field.

     Fig. 96 Direction of the electric field E induced by a magnetic current 1 (compare with Fig. 84).

We imagine a bundle of parallel lines of magnetic force that con-stitute a magnetic field H. We suppose a circular conducting wire placed around this sheath (Fig 95). If the intensity of field H changes in the small interval of time..." "...by the amount H we call..."  "...its velocity of change or the change in the number of lines of force. If in analogy to the electrical displacement we represent the lines of force as chains of magnetic dipoles ( which, however, according to Amphere  

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then with the change of H a displacement of the magnetic quantities will occur in every ether molecule, or a magnetic displacement current" will flow whose current strength per unit of area or current density is given by I =..."

If the field H is not in the ether but ii a substance of permeability..." "...the density of the magnetic displacement current is i =..." "...Thus the magnetic displacement current is I =..." Thus the magnetic displacement current is I =..." Thus the magnetic current I = fi = f ..." "...passes through the cross section f, that is, through the surface of the circle formed by the conducting wire.
        Now according to Faraday, this magnetic current produces all round it an electric field E, which encircles the magnetic current exactly as the magnetic field H encircles the electric current in Oersted's experiment but in the reverse
direction. It is this electric field E that drives the induced current around in the conducting wire; it is also present even if there is no conducting wire in which the current can form.
     We see that the magnetic induction of Faraday is a perfect parallel to the electromagnetic discovery of Oersted. The quantitative law too, is the same. According to Biot and Savert, the magnetic field H produced by a current element of length l and of strength j (compare fig. 84) in the middle plane perpendicular to the connecting line r and to the current direction, and has the value H = J1 (formula (54)).
Exactly the same holds when electric and magnetic quantities are exchanged and when the sense of rotation is reversed (Fig.96). The induced electric intensity of field in the central plane is given by
       E = I l .
       In it the same constant c, the ratio of the electromagnetic to the electrostatic unit of current, occurs which was found by Weber and Kohlrausch to be equal to the velocity of light. It can easily be seen from considerations about the energy involved that this must be so.
     A great number of the physical and technical applications of electricity and magnetism depend on the law of induction. The transformer, the induction coil, the dynamo and innumerable other  

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apparatus and machines are appliances for inducing electric currents by means of changing magnetic fields. But however interesting these things may be, they do not lie on the road of our investigation, the final goal of which is to examine the relationship of the ether with the space problem. Hence we turn our attention at once to the theory of Maxwell, whose object was to combine all known magnetic phenomena into one uniform theory of contiguous action.
                                                                 8 Maxwell's Theory of Action by Contact
    We have already stated that soon after Coulomb's law had been established, electrostatics and magnetostatics were brought into the form of pseudocontiguous action. Maxwell now under-took to fuse this theory with Faraday's ideas, and to elaborate it so that it also included the newly discovered phenomena of dielectric and magnetic polarization, of electromagnetism and magnetic induction.
Alizzed substituted * and  letter for the symbols used by Brother Born.
Must we said the scribe needs must said Zed Aliz.
Maxwell took as the starting point of his theory the idea already mentioned above that an electric field E is always accompanied by an electric displacement D = *E not only in matter, for which * is different for one, but also in the ether, where *  = 1. We explained how the displacement can be visualized as the separation and flowing of electric fluids in the molecules. And we have found a differential law, which connects the charge density p in every space point with the divergence of D =

*E= 4 pi p


Exactly the same considerations apply to magnetism, but with one important difference:  According to Ampere no real magnets exist, no magnetic quantities, but only electromagnets.  The magnetic field is always to be produced by electric currents, whether they be conduction currents in wires or molecular currents in the molecules. From this it follows that the magnetic lines of force never end, that is they are either closed or stretch to infinity. This is so in the case of an electromagnet, a coil through which a current is flowing (Fig 97a,b); the magnetic lines of force are straight lines in the in-terior of the coil, but outside they are partly closed and partly going off into infinity. If we consider the coil between two planes A and B,  

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Formal agreement of this kind is by no means a matter of indiffer-ence. It exhibits the underlying simplicity  of phenomena in nature, which remains hidden from direct perception because of the limitations of our senses and reveal itself only to our analytical faculty.
     In general a conduction and a displacement current will be present simultaneously. For the former, Ohm's law, jc =
o E,
Holds (52) p162; for the latter, Maxwell's law, jd =
*     E   If both are present simultaneously
pi  t
we thus have  J =
*   E    E  +  o E.
                                 4 pi  t

There is no conduction current for magnetism, so we always have  
                                                                                                         I =
u    H
pi  t

If we insert this in our symbolic equations (58) to (61) we get:      
(a)                 div *E = 4
pi p,
(b)                 div  
u H = O,

(c)                 c curl  H   = * E + 4
pi  o E,

(d)                 c curl E = u H .  

These are Maxwell's laws which have remained the foundation of all electromagnetic and optical theories up to our own time. To the mathematician they are precise differential equations. To us they are precise differential equations. To us they are mnemonics which state:

(a)   Wherever an electric charge occurs an electric field arises of such a kind that in every volume the charge is exactly compensated by the displacement.
(b)   Through every closed surface Just as much magnetic displace-ment passes outwards as comes inwards there are no free magnetic charges).
(c)   Every electric current, be it a conduction or a displacement current is surrounded by a magnetic field.
(d)   A magnetic displacement current is surrounded by an electric field in the reverse sense. " /

The Alizzed reminded those who needed to know, of the needs must, symbol changes that had had to be made.
These yonder scribe had in the main emphasised,.advising consulting the original oracle Brother Born, for missing hieroglyphics and total accuracy of interruption.
Then in a sort of apology the scribe writ. That there wasn't much call for that sort of thing in our part of the world.
Then out of the blue the scribe writ the words Karmic magnet.
You are a caution scribe said Alizzed.
And you Zed Aliz said the scribe, adding, and you.

Einstein's Theory Of Relativity
1924 - 1962
Max Born

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"Maxwell's "field equations," as they are called, constitute a true theory of contiguous action or action by contact, for, as we shall presently see, they give a finite velocity of propagation for electro-magnetic forces
      At the time they were set up, however, faith in direct action at a distance, according to the model of Newtonian attraction, was still so deeply rooted that a considerable interval elapsed before they were accepted, for the theory of action at a distance had also suc-ceeded in mastering the phenomena of induction by means of formulae. This was done by assuming that moving charges exert, in addition to the Coulomb attraction, certain actions at a distance that depend on the amount and direction of the velocity. The first hypo-theses of this kind were due to Neumann (1845). Another famous law is that set up by
Wilhelm Weber (1846); similar formulae were given by Riemann (1858) and Clausius (1877). These theories have in common the idea that all electrical and magnetic actions are to be explained by means of forces between elementary electrical charges, or as we say nowadays, "electrons." They were thus precursors of the present-day theory of electrons, with however an essential factor omitted: the finite velocity of propagation of the forces. These theories of electrodynamics, based on action at a distance, gave a complete explanation of the electromotive forces and induc-tion currents that occur in the case
Of closed conduction currents. But in the case of "open" circuits that is, condenser charges and discharges, they were doomed to failure, for here the displacement currents come into play, of which the theories of action at a distance know nothing. It is to Helmholtz that we are indebted for appro-priate experimental devices allowing us to decide between the theories of action at a distance and action by contact. He succeeded in carrying out the experiment with a certain measure of success, and he himself became one of the most zealous pioneers of Maxwell's theory. But it was his pupil Hertz who secured the victory for Maxwell's theory by discovering electromagnetic waves.


                                                        9 The Electromagnetic Theory of Light
" We have already mentioned (V, 4 p. 163 ) the impression which the
coincidence, established by Weber and Kohlrausch, of the electro  

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magnetic constant c with the velocity of light made upon the physicists of the day. And there were still further indications that there is an intimate relation between light and electromagnetic phenomena. This was shown most strikingly by Faraday's
discovery (
1834 ) that a polarized ray of light which passes through a magnetized transparent substance is influenced by it. When the beam is parallel to the magnetic lines of force, its plane of polarization becomes turned. Faraday concluded from this that the luminiferous ether and the carrier of electromagnetic lines of force must be identical. Although his mathematical powers were not sufficient to allow him to convert his ideas into quantitative laws and formulae, his ideas were of a most abstract type and far surpassed the trivial view which accepted as known what was familiar. Faraday's ether was no elastic medium. He derived its properties, not by analogy from the apparently known material world, but from exact experiments and systematic deductions from them. Maxwell's talents were akin to those of Faraday, but they were supplemented by a complete mastery of the mathematical means available at the time.
       We shall now show how the propagation of electromagnetic forces with finite velocity arises out of Maxwell's field laws (62). In doing so we shall confine ourselves to events that occur in vacuo or in the ether. The latter has no conductivity, that is,  
o = O, and no true charges, that is p = O and its dielectric constant and permeability are equal to 1, that is, * = 1, u = 1. The first two field equations (62) then assert that
                                                                               div E = O,      div H = O
or that all lines of force are either closed or run off to infinity. To obtain a rough picture of the processes we shall imagine individual, closed lines of force.
      The other two field equations are then        
                                                                                 (a)  E = c curl H,            (b)  H = c curl E.
t                                      t
We now assume that, somewhere in a limited space, there is an elec-tric field E which alters by the amount E in the small interval of time T; then E   is its rate of change. According to the first equation, a  /

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magnetic field immediately coils itself around this electric field, and its strength is proportional to  E  
The magnetic field, too, will alter in time, say by H during each successive small interval  
Again, in accordance with the second equation, its rate of change  H  
immediately induces an interwoven electric field. In the following interval of time the latter again induces an encircling magnetic field, according to the first equation, and so this chainlike process con-tinues with finite velocity (Fig.