In this episode, we will explore how Wilhelm Weber was the first to define
an electron theory and how this shaped how we view diamagnetism and paramagnetism.
While Faraday was engaged in discovering the laws of induced Currents by use of a
conception of lines of force, his contemporary Franz Neumann preferred to take Amperes model.
The main assumptions on which Neumann based his work was a rule which had been formulated,
not long after Faraday's original Discovery, by Emil Lenz.
this rule stated when a conducting circuit is moved in a magnetic field, the induced current
Flows in such a direction that the ponderomotive forces on it tend to oppose the motion.
Having arrived at the formula in this way he noticed a peculiarity that suggested
a totally different method of treating the subject. The electromotive force
induced in a circuit by the motion of other circuits carrying currents
is proportional to the time rate of variation of the potential. The induction of current
is therefore governed by the vector a; this is generally known as the vector potential.
This may be regarded as the analytical measure of Faraday's electrotonic state.
While Neumann was endeavouring to comprehend the laws of induced currents in an extended
form of amperes theory, another investigator was attempting a still more ambitious Project.
No less than that of uniting electrodynamics into a coherent whole with electrostatics.
Wilhelm Weber Was in the earliest part of his scientific career as a friend and colleague of
gauss at Gottingen. Weber theory was Closely connected with the work of another Leipzig
professor Gustav Theodor Fechner. In 1845 he introduced certain assumptions regarding the
nature of electric currents. Fechner supposed every current to consists in a streaming of
electric charges, the vitreous charges travelling in one direction, and the resinous charges,
equal to them in magnitude and number, travelling in the opposite direction with equal velocity.
He further supposed that like charges attract each other when they are moving parallel to the
same direction, while unlike charges attract when they're moving in opposite directions.
Based on these assumptions he succeeded in bringing Faraday's induction effects
into connection with Amperes law of electrodynamics.
Weber’s theory was the first of the electron theories. This is a name given to any theory
which attributes the phenomena of electrodynamics to the agency of moving electric charges,
the forces on which depend not only on the position of the chargers,
as in electrostatics, but also on their velocities.
This last point led its earliest critics to deny that his law of force could be reconciled with the
principle of conservation of energy. They were, however, mistaken on this point. Another more
serious one now presented itself. The occurrence of the negative sign within his formula implies
that a charge behaves somewhat as if its mass were negative, so that in certain circumstances
is velocities might increase indefinitely under the action of a force opposed to the motion.
Leaving this objection unanswered, it can be seen that Weber's law of force between
electrons leads to the formula for the induction of currents. The necessity for induced currents
may be inferred by General reasoning from the first principles of Weber’s theory.
When a circuit s moves in the field due to the currents, the velocity of the vitreous charges
in s is, owing to the motion of s, not equal and opposite to that of the resinous charges.
This gives rise to a difference in the forces acting on the vitreous and resinous charges in s,
and hence the charges of opposite sign separate from each other and move in opposite directions.
The assumption that positive and negative charges move in equal and opposite velocities relative to
the matter of the conductor is an integral part of Weber’s Theory, and cannot be excised from it.
At the time, Weber’s discovery was felt to be a great advance.
It caused an Awakening in the mathematical physicist to a sense of the possibilities
latent in the theory of electricity. Its influence was also felt in general dynamics;
for Weber’s electrokinetic energy, which resembles kinetic energy in some respect
and potential energy in others, could not be precisely classified under either.
Another subject whose development was stimulated by the work of weather
was the theory of gravitation. Under the influence of Weber's ideas, astronomers began to think of
modifying Newton's law by adding a term involving the velocities of bodies. Tisserant in 1872
discussed the motion of planets around the sun on the supposition that the law of gravitation is the
same as Weber's law of electrodynamic action so that the force is as follows. The effect would be
to rotate the major axis of the orbit of mercury in the direct sense 14 seconds in a century.
At the time a difference between the theory and observation was known to exist
in regard to the motion of Mercury's perihelion. The attraction of the Planets might be expected
to turn the perihelion 527 seconds in the direct sense in a century, whereas the motion actually
observed was greater than this by 38 seconds. It is evident that only 3/8 of the excess is
explained by Tisserand’s adoption of Weber's law. It was found later that three quarters of
the excess could be explained by substituting Riemann’s electrodynamic law for Weber's and
that a combination of the laws of Riemann and Weber would give exactly the observed amount!
After the publication of his memoirs on the law of force between electrons,
Weber turned his attention to the question of diamagnetism.
He remarked that if, with Ampere, we assume the existence of molecular circuits
in which there is no ohmic resistance, so that current can flow without dissipation of energy,
it is quite natural to suppose that currents would be induced in these molecular circuits
if they were situated in a varying magnetic field. He pointed out that such induced molecular
currents would confer upon the substance the properties characteristic of diamagnetism.
The problem with this hypothesis is that it infers that all bodies,
without exception, should be diamagnetic. Weber avoided this conclusion by supposing that in
iron and other magnetic substances there exist permanent molecular currents, which do not owe
their origin to induction, and which, under the influence of impressed magnetic force,
set themselves in definitive orientations. Since a magnetic field tends to give such a
direction to a pre-existing current that its course becomes opposed to that of the current
which would be induced by the increase of the magnetic force, it follows that a
substance stored with such pre-existing currents would display the phenomena of paramagnetism.
The radical distinction which Weber postulates between the natures of paramagnetism and
diamagnetism seems to be confirmed by many facts which we discovered subsequently.
In 1852 Weber wrote ‘Through the discovery of diamagnetism the
hypotheses of electric molecular Currents in the interior of bodies is corroborated,
and the hypothesis of magnetic fluids in the interior of bodies is refuted.’
The concept of magnetic fluids was unable to account for the phenomena shown by bodies that
are strongly magnetic like iron. It was discovered that when the magnetizing force is gradually
increased to a very large value, the magnetization induced in such bodies does not increase in
proportion, but tends to a saturation value. This could be explained using Weber's Theory where the
magnetizing force merely oriented existing magnets, and when it has attained such a
value that all of them are oriented in the same direction, there is nothing further to be done.
The form of the hypothesis which ultimately gained acceptance was that the orientation
is resisted by couples that arise from the mutual action of the molecular magnets themselves.
In the unmagnetised condition, the molecules arrange themselves so as to satisfy the mutual
attraction by the shortest path, and thus form a complete closed circuit of attraction.
When an external magnetizing force is applied, the small circuits are broken up.
At any stage of the process, the molecular magnet is an equilibrium under the joint
influence of the external force and the force which is due to the other molecules.
In 1871 whether restated his theory of magnetism in terms of a theory of electric particle charges.
And Amperian molecular current was now supposed to be constituted by an
electric charge moving in an orbit around the fixed electric charge of the opposite sign,
a picture which would reappear 40 years later in the electron orbits of the Rutherford ball atom.
In the 20th century, many theoretical physicists were at first inclined to
doubt whether the magnetic theory of Ampere and
Weber could be successfully expressed in terms of the new electron theory.
These doubts were set to rest by Paul Langevin who gave a complete formulation. In this,
the diamagnetic phenomena is regarded in all cases as the sole initial effect of applying an external
magnetic field. Paramagnetism is attributed to subsequent mutual actions between molecules.