13.2. The Electric Field#
The first field was the Magnetic Field, which, as we’ve seen, was forcefully suggested by iron filing patterns around a permanent magnet or steady current. But for our general introduction, the Electric Field is easier to understand, so that’s where we’ll start.
Faraday believed strongly in a unified nature in which the laws would be related and so given his conclusion about magnetic lines of force and his speculation about electric lines of force, he also imagined a Gravitational field in the same spirit…performing many failed experiments to try to detect a gravitational influence on currents and magnets. He was limited to guessing about electricity since a visual demonstration for charges analogous to the iron filings experiments was beyond his lab’s capability. Nonetheless, he speculated about the existence electric lines of force and Maxwell baked that idea into his theory of both Electric and Magnetic fields. We’ve already dealt with Coulomb’s law, which is the force of attraction or repulsion between two electrically charged objects. It’s so important, let me reprise it here (\(Q_1\) and \(Q_2\), separated by a distance, \(R\)):
Remember that the \(Q\)’s have an algebraic sign, \(+\) for a positively charged object and \(-\) for a negatively charged object – and then the multiplication results in an overall sign for \(F\): if positive (like two positive or two negative \(Q\)’s) then the force is repulsive and if negative (where one \(Q\) is positive and the other is negative), then the force is attractive.
Into the middle 1800s, everyone assumed that whatever effects were felt by charges in Coulomb’s law, masses in Newton’s Gravitational law, and magnets were instantaneous and facilitated through motions in an ether.
Faraday felt otherwise: his fields would propagate between objects at a finite speed and were themselves “a thing” not requiring any intermediate substance. By contrast, Maxwell thought that his theory was a model of the ether – that the propagation of electric and magnetic fields were disturbances in it. It wasn’t until the 20th century that the ether idea was abandoned. This strange substance maybe one of the longest-believed, mathematically sophisticated (lots of still useful mathematics was developed in trying to describe the nature of the ether), and wholly false models in the history of physics! So we’ll describe Maxwell’s theory differently from how he would have. Ours is an ether-free-zone.
The modern idea of the field was conceived by Faraday – who was right! – is shown in the cartoon above which imagines the electrostatic attraction of an electron and a proton. A mathematical metaphor, if you will. In this view there are three aspects to the field:
The source (“cause”). An electric charge, a magnetic pole or current, or mass create a field in its vicinity.
The sink (“effect”). An electric charge, a magnetic pole or a current, or a mass detects a field in its vicinity.
The disturbance (“field”). The intermediate space is filled by the field, which propagates at a finite velocity from source, to sink.
Of course, one person’s source is another persons effect. That is, each acts on the other through the field.