Up to the chapter on electrostatics we took it for granted that the electric field was conservative: the circulation of along any closed path was zero, and this allowed us to define a unique electric potential. Faraday’s law overturns this certainty: as soon as the magnetic flux changes in time, can be non-zero. In other words, the induced electric field does not derive from a potential; its field lines close on themselves, like those of a stationary magnetic field.
The significance of this discovery is enormous. It means there exists an electric field “without charges”, not generated by an accumulation of positive or negative charge, but by a change in magnetic flux through the path along which it is measured. It is this field that drives electrons inside the loop of a dynamo, inside the winding of a transformer, inside the aerial of a car radio. Without it we would have neither industrial generators nor radio waves.
The conceptual price to pay is equally large. From Faraday onwards, the “electric potential” we measure in circuits is no longer, in general, the old electrostatic potential: it is a combination of it and a new term linked to the change in the magnetic field. When you connect a voltmeter between two points of a circuit through which a varying flux passes, the reading depends also on the path followed by the voltmeter’s leads: an unsettling result that features among the “thought experiments” of twentieth-century teaching. In about two chapters’ time, with Maxwell’s equations, we shall see that it is precisely this non-conservative term that allows the electromagnetic field to self-sustain and propagate through the vacuum: light.
Links
Topics: Electromagnetic induction Concepts: Faraday-Neumann-Lenz law · Electric field · Electric potential
Related exercises: True or false on field and potential · Cloud-to-ground potential difference · Field lines never cross