Heinrich Hertz

Hertz

In 1884, however, the theory was established[44] on a different basis by a pupil of Helmholtz’, Heinrich Hertz (b. 1857, d. 1894).

When Ampère heard of Oersted’s discovery of the magnetic field produced by electric currents, he inferred that electric currents should exert ponderomotive forces on each other.

Ampère argued that a current was competent to originate a magnetic field. The current must be equivalent to a magnet in other respects. Therefore currents, like magnets, should exhibit mutual attraction and repulsion.

Ampère’s reasoning assumes that the magnetic field produced by a current is in all respects of the same nature as that produced by a magnet – only one kind of magnetic force exists.

This is the principle of the “unity of magnetic force”.

Hertz proposed to supplement this by asserting that the electric force generated by a changing magnetic field is identical in nature with the electric force due to electrostatic charges.

This second principle he called the “unity of electric force.”

Suppose, then, that a system of electric currents ι exists in otherwise empty space.

According to the older theory, these currents give rise to a vector-potential a1, equal to Pot ι[45].

The magnetic force H1 is the curl of a1 while the electric force E1, at any point in the field, produced by the variation of the currents, is

…

The electric force so produced is assumed indistinguishable from the electric force which would be set up by electrostatic charges.

Therefore that the system of varying currents exerts ponderomotive forces on electrostatic charges; the principle of action and reaction then requires that electrostatic charges should exert ponderomotive forces on a system of varying currents, and consequently (again appealing to the principle of the unity of electric force) that two systems of varying currents should exert on each other ponderomotive forces due to the variations.

But just as Helmholtz,[46] by aid of the principle of conservation of energy, deduced the existence of an electromotive force of induction from the existence of the ponderomotive forces between electric currents (i.e. variable electric systems), so from the existence of ponderomotive forces between variable systems of currents (i.e. variable magnetic systems) we may infer that variations in the rate of change of a variable magnetic system give rise to induced magnetic forces in the surrounding space.

The analytical formulae which determine these forces will be of the same kind as in the electric case; so that the induced magnetic force H′ is given by an equation of the form

…

where e denotes some constant, and b1, which is analogous to the vector-potential in the electric case, is a circuital vector whose curl is the electric force E1, of the variable magnetic system. The value of b1, is therefore

…

so we have

…

This must be added to H1. Writing H2, for the sum, H + H′, we see that H2 is the curl of a2, where

…

and the electric force E2, will then be

…

This system is not, however, final.

This is because we must now perform the process again with these improved values of the electric and magnetic forces and the vector-potential.

And so, we obtain for the magnetic force the value curl a3, and for the electric force the value

…

This process must again be repeated indefinitely; so finally we obtain for the magnetic force H the value curl a, and for the electric force E the value

…

where

…

The quantity a thus defined satisfies the equation

…

This equation may be written

…

while the equations H = curl a},

…

These are, however, the fundamental equations of Maxwell’s theory in the form given in his memoir of 1868.[47]