Chapter 5 The Fields of Moving Charges

5.1 From Oersted Einstein

In the winter of 1819-1820 Hans Christian Oersted was lecturing on Electricity ,Galvanism,and Magnetism to advanced students at the University of Copenhagen.

Electricity meant electrostatics;galvanism referred to the effects produced by continuous currents from batteries,a subject opened up by Galvani's chance discovery and the subsequent experiments of Volta;magnetism dealt with the already ancient lore of lodestones,compass needles,and the terrestrial magnetic field.

It seemed clear to some that there must be a relation between galvanic currents and electric charge,although there was little more direct evidence than the fact that bothcould cause shcks.

On the other hand,magnetism and electricity appeared to have nothing whatever to do with one another.

Still,Oersted had a notion,vague perhaps,but tenaciously pursued,that magnetism like the galvanic current might be a sort of "hidden form" of electricity.

Grouping for some manifestation of this,he tried before his classthe experiment of passing a galvanic current through a wire which ran above and at right angles to a compass needle.

It had no effect with a wire running parallel to the compass needle.

The needle swung wide -and when the galvanic current was reversed it swung the other way!

The scientific world was more than ready for this revelation.

A ferment of experimentation and discovery followed as soon as the word reached other laboratories.

Before long Ampere,Faraday,and others had worked out an essentially complete and exact description of the magnetic action of electric currents.

Faraday's crowning discovery of electromagnetic induction came less than 12 years after Oersted's experiment.

In the previous two centuries since the publication in 1600 of William Gilvert's great work De Magnetete,man's understanding of magnetism had advanced not at all.

out of these experimental dicoveries there grew the complete classical theory of electromagnetism.

Formulated mathematically by Maxwell,it was triumphantly corroborated by Heartz's demonstration of electromagnetic waves in 1888.

Special relativity has its histrical roots in electromagnetism.

Lorentz,exploring the electrodynamics of moving charges,was led very close to the final formulation of Einstein.

And Einstein's great paper of 1905 was entitled not "Theory of Relativity",but rahter "On the Electrodynamics of Moving Bodies."

Today we see in the postulates of relativity and their implications a wide frame work,one that embraces all physical laws and not solely those of electromagnetism.

We expect any complete physical theory to be relativistically invarient.

It ought to tell the same story in all inertial frames of reference.

As it happened,physics already had one relativistically invant theory- Maxwell's electromagnetic theory - long before the significance of relativistic invariance was recognized.

Whether the ideas of special relativity could have evolved in the absence of a complete theory of the electromagnetic field is a question for the historian of science to speculate about;probabry it can't be answered.

We can only say that the actual history shows rather plainly a path running from Oested's compass needle to Einstein's postulates.

In this chapter and Chap.6 we are going to follow that path almost in reverse.

This implies no disrespect for history.

Indeed,we think a student of the history of those magnificent discoveries will not be handicapped by a clear view of the essential relation between electricity and magnetism.

That relation can be exposed very directly and simply by looking,in the light of special relativity,at what we have already learned about electric charge and the electric field.

Before we do tha,let's review some ofo the phenomena we shall be trying to example.

5.2 Magnetic Forces

Two wires running parallel to one another and carrying currents in the same direction are drawn together.

The force on one of the wires,per unit length of wire,proves to be proportional to the product of the two current and inversely proportional to the distance between the wires (Fig.5.1a).

Reversing the direction of one of the currents changes the force to one of repulsion.

Thus the two sections of wire in Fig.5.1b which are part of the same circuit tend to fly apart.

There is some sort of "action-at -a-distance"between the two filaments of steady electric current.

It seemes to have nothing to do with any static electric charge on the surface of the wire.

There may be some such charge and the wires may be at different potentials,but the force we are concerned with depends only on the charge movement in the wires,that is,on the two currents.

You can put a sheet of metal between the two wires without affecting this force at all(Fig.5.1c).

These new forces that come into play when charges are moving are called magnetic.
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