Superphysics
Chapter 10b

# FitzGerald's system

##### 3 minutes  • 630 words

Despite the advances in the theory of electric oscillations, the gulf between the classical electrodynamics and the theory of light was not yet completely bridged.

• In classical electrodynamics, energy is merely exchanged between one body and another, remaining within the limits of a given system.
• In optics, the energy travels freely through space, unattached to any material body.

The first discovery of a more complete connexion between the two theories was made by FitzGerald, who argued that if the unification which had been indicated by Maxwell is valid, it ought to be possible to generate radiant energy by purely electrical means.

In 1883[29] he described how this could be done. FitzGerald’s system became the magnetic oscillator.

It consists of a small circuit, in which the strength of the current is varied according to the simple periodic law.

The circuit is a circle of small area S. Its centre is the origin and whose plane is the plane of xy.

The surrounding medium will be supposed to be free aether. The current may be taken to be of strength A cos (2πt/T), so that the moment of the equivalent magnet is SA cos (2πt/T).

In the older electrodynamics, the vector-potential due to a magnetic molecule of (vector) moment M at the origin is (1/4π) curl (M/r), where r denotes distance from the origin.

The vector-potential due to FitzGerald’s magnetic oscillator would therefore be (1/4π) curl K, where Kdenotes a vector parallel to the axis of z, and of magnitude (1/r) SA cos (2πt/T).

The change which is involved in replacing the assumptions of the older electrodynamics by those of Maxwell’s theory is in the present case equivalent[30] to retarding the potential; so that the vector-potential a due to the oscillator is (1/4π) curl K where K is still directed parallel to the axis of z, and is of magnitude

The electric force E at any point of space is

˙{\displaystyle -\mathbf {\dot {a}} }, and the magnetic force H is curl a: so that these quantities may be calculated without difficulty. The electric energy per unit volume is E2/8πc2: performing the calculations, it is found that the value of this quantity averaged over a period of the oscillation and also averaged over the surface of a sphere of radius r is

The part of this which is radiated is evidently that which is proportional to the inverse square of the distance,[31] so the average value of the radiant energy of electric type at distance r from the oscillator is

per unit volume. The radiant energy of magnetic type may be calculated in a similar way, and is found to have the same value; so the total radiant energy at distance r is 4

per unit volume; and therefore the energy radiated in unit time is

This is small, unless the frequency is very high; so that ordinary alternating currents would give no appreciable radiation.

FitzGerald, however, in the same year[32] indicated a method by which the difficulty of obtaining currents of sufficiently high frequency might be overcome: this was, to employ the alternating currents which are produced when a condenser is discharged.

The FitzGerald radiator constructed on this principle is closely akin to the radiator afterwards developed with such success by Hertz: the only difference is that in FitzGerald’s arrangement the condenser is used merely as the store of energy (its plates being so close together that the electrostatic field due to the charges is practically confined to the space between them).

The actual source of radiation is the alternating magnetic field due to the circular loop of wire: while in Hertz’s arrangement the loop of wire is abolished, the condenser plates are at some distance apart, and the source of radiation is the alternating electrostatic field due to their charges.

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