On Physical Lines of Force/Part II/Induced currents
On Physical Lines of Force → Part II → Induced currents
The propositions give the equations. This page gives Maxwell's physical narration of what the machine is doing — which is where the model earns its keep, because the story it tells is vivid and, in its qualitative content, correct.
The sequence, told at the figure
Return to the plate. A current runs along AB; rows of vortices lie above and below.
Now let an electric current from left to right commence in AB. The row of vortices above AB will be set in motion in the opposite direction to that of a watch.
The particles along AB begin to move. Rolling against the cells above them, they set those cells spinning. So far, so simple. But the cells have mass, and mass resists being started:
If this current is checked by the electrical resistance of the medium, the rotating particles will act upon the row of vortices, and make them revolve …
The first row of vortices, being spun up, now presses on the next layer of particles above it — and because those particles are being asked to start a second row of vortices which is not yet moving, they are pushed backwards. A backward movement of particles is a current in the reverse direction. That is the induced current.
It appears therefore that the phenomena of induced currents are part of the process of communicating the rotatory velocity of the vortices from one part of the field to another.
Once the whole field has reached its final state — every vortex turning at its proper speed — nothing more needs to be communicated. The particles stop drifting and the induced current dies away.
This is why induction happens only while things are changing. Not as a rule imposed from outside, but because the induced current is the process of communication, and the process ends when the message has arrived.
Force without current
We may now perceive that induced currents are produced when the electricity yields to the electromotive force, — this force, however, still existing when the formation of a sensible current is prevented by the resistance of the circuit.
A distinction Maxwell is careful about, and one that his mechanical picture makes obvious: the force on the particles exists whether or not the particles are free to move. Open the circuit and no current flows, but the push is still there. It is the difference between an electromotive force and a current, and on this model it is the difference between pressing on something and having it give way.
The anchor ring
Maxwell then offers an experiment which, on the action-at-a-distance view, is close to paradoxical, and which his medium explains without effort.
As an example of the action of the vortices in producing induced currents, let us take the following case:—Let B, Pl. V. fig. 3, be a circular ring, of uniform section, lapped uniformly with covered wire. It may be shown that if an electric current is passed through this wire, a magnet placed within the coil of wire will be strongly affected, but no magnetic effect will be produced on any external point. The effect will be that of a magnet bent round till its two poles are in contact.
If the coil is properly made, no effect on a magnet placed outside it can be discovered, whether the current is kept constant or made to vary in strength; but if a conducting wire C be made to embrace the ring any number of times, an electromotive force will act on that wire whenever the current in the coil is made to vary; and if the circuit be closed, there will be an actual current in the wire C.
This is a toroid — a doughnut wound evenly with wire. The magnetic lines close entirely within the ring, and outside it there is, so far as any magnet can tell, nothing at all.
And yet:
This experiment shows that, in order to produce the electromotive force, it is not necessary that the conducting wire should be placed in a field of magnetic force, or that lines of magnetic force should pass through the substance of the wire or near it. All that is required is that lines of force should pass through the circuit of the conductor, and that these lines of force should vary in quantity during the experiment.
Read that once more. The wire C sits in a region of no magnetic field, and it does not need to be near one. What matters is that it encircles a region where the field is changing.
Why this passage is remarkable
Maxwell's own explanation:
In this case the vortices, of which we suppose the lines of magnetic force to consist, are all within the hollow of the ring, and outside the ring all is at rest. If there is no conducting circuit embracing the ring, then, when the primary current is made or broken, there is no action outside the ring, except an instantaneous pressure between the particles and the vortices which they separate. If there is a continuous conducting circuit embracing the ring, then, when the primary current is made, there will be a current in the opposite direction through C; and when it is broken, there will be a current through C in the same direction as the primary current.
The something-outside-the-ring that carries the action is, in the machinery of Part II, the electrotonic state — the quantity of equation (55). The magnetic force genuinely vanishes outside a perfect toroid. The vector potential does not.
Modern physics has an exact successor to this observation. In the Aharonov–Bohm effect (1959), an electron beam passing on either side of a perfectly shielded solenoid — through a region of strictly zero magnetic field — shows an interference shift that depends on the flux enclosed. The vector potential is not merely a computational convenience; the encircled flux is physically detectable from outside.
Maxwell would not have put it that way, and the quantum context is a century beyond him. But the shape of the observation is the same, made in the same apparatus, and offered for the same reason: to show that the action is in the space, not at a distance.
Next: Part III · Previous: Prop. XI
Plain-language version: Why a changing magnet makes a current