On Physical Lines of Force/Part III/Conduction and induction

On Physical Lines of Force → Part III → Conduction and induction

The distinction

Bodies which do not permit a current of electricity to flow through them are called insulators. But though electricity does not flow through them, electrical effects are propagated through them, and the amount of these effects differs according to the nature of the body; so that equally good insulators may act differently as dielectrics.

Here then we have two independent qualities of bodies, one by which they allow of the passage of electricity through them, and the other by which they allow of electrical action being transmitted through them without any electricity being allowed to pass.

The footnote here is to Faraday, Experimental Researches, Series XI — Faraday had discovered specific inductive capacity, and this is Maxwell picking it up.

The two qualities are conductivity and permittivity, and they are logically independent. Two substances can insulate equally well and yet transmit electrical action to very different degrees.

The two membranes

Conductor and dielectric compared

A conducting body may be compared to a porous membrane which opposes more or less resistance to the passage of a fluid, while a dielectric is like an elastic membrane which may be impervious to the fluid, but transmits the pressure of the fluid on one side to that on the other.

This is the best analogy in the paper, and it does two jobs at once.

• The porous membrane dissipates. Fluid gets through, and the resistance turns work into heat, irreversibly.
• The elastic membrane stores. Nothing gets through, but pressure is transmitted, and the membrane gives back what was put in when the pressure is released.

Maxwell makes the thermodynamic point explicitly:

As long as electromotive force acts on a conductor, it produces a current which, as it meets with resistance, occasions a continual transformation of electrical energy into heat, which is incapable of being restored again as electrical energy by any reversion of the process.

Polarization

Electromotive force acting on a dielectric produces a state of polarization of its parts similar in distribution to the polarity of the particles of iron under the influence of a magnet and, like the magnetic polarization, capable of being described as a state in which every particle has its poles in opposite conditions.

In a dielectric under induction, we may conceive that the electricity in each molecule is so displaced that one side is rendered positively, and the other negatively electrical, but that the electricity remains entirely connected with the molecule, and does not pass from one molecule to another.

The footnote credits Mossotti's Discussione Analitica, in the Memorie della Società Italiana (Modena), vol. xxiv part 2, p. 49.

The definition of displacement

Here is the passage that matters, and it deserves reading twice.

The effect of this action on the whole dielectric mass is to produce a general displacement of the electricity in a certain direction. This displacement does not amount to a current, because when it has attained a certain value it remains constant, but it is the commencement of a current, and its variations constitute currents in the positive or negative direction, according as the displacement is increasing or diminishing. The amount of the displacement depends on the nature of the body, and on the electromotive force; so that if h is the displacement, R the electromotive force, and E a coefficient depending on the nature of the dielectric,

[the relation between them follows] and if r is the value of the electric current due to displacement, [the current is the rate of change of the displacement].

Three claims, in one sentence, in the right order:

1. the displacement is not a current, because it stops;
2. it is the commencement of a current;
3. its variations are currents, positively or negatively as the displacement grows or shrinks.

That third clause is the displacement current. It is stated here, informally, before the propositions that will justify it, and it is added to the equations of electric currents in Prop. XIV.

Maxwell insists the relation is not model-dependent

These relations are independent of any theory about the internal mechanism of dielectrics; but when we find electromotive force producing electric displacement in a dielectric, and when we find the dielectric recovering from its state of electric displacement with an equal electromotive force, we cannot help regarding the phenomena as those of an elastic body, yielding to a pressure, and recovering its form when the pressure is removed.

This is exactly the move he made in Part I with the stress: state the result in a form that survives the model, then offer the model as the explanation. The relation between displacement and force is an experimental fact about dielectrics. The elasticity of the cells is the proposed reason for it.

And then the mechanism

According to our hypothesis, the magnetic medium is divided into cells, separated by partitions formed of a stratum of particles which play the part of electricity. When the electric particles are urged in any direction, they will, by their tangential action on the elastic substance of the cells, distort each cell, and call into play an equal and opposite force arising from the elasticity of the cells. When the force is removed, the cells will recover their form, and the electricity will return to its former position.

The cell yields, and pushes back

The particles are pushed; they lean on the cells; the cells deform and push back; the particles come to rest a little way from where they started. Remove the push and everything springs back. A charged capacitor, on this picture, is a room full of twisted springs.

A prediction about turpentine

It appears also from Prop. XV. that the attraction between two electrified bodies depends on the value of E², and that therefore it would be less in turpentine than in air, if the quantity of electricity in each body remains the same. If, however, the potentials of the two bodies were given, the attraction between them would vary inversely as E², and would be greater in turpentine than in air.

The same pattern as the Part I predictions: the medium's properties change the observed force, and the direction of the change depends on what you hold fixed. Hold the charges fixed and immersion weakens the attraction; hold the potentials fixed and it strengthens it. Both are correct, and both are still taught.

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Next: Prop. XII · Previous: Part III

Plain-language version: Why the cells had to be springy