18. Electromagnetic Induction

Electromagnetic induction is the phenomenon in which an electromotive force (and, if the circuit is closed, a current) is generated (induced) in a conductor as a result of a change in the magnetic flux linked with it. This is, in a sense, the converse of the magnetic effect of current: whereas a current produces a magnetic field, a changing magnetic field can in turn produce a current. Electromagnetic induction was discovered independently and almost simultaneously by the English scientist Michael Faraday and the American scientist Joseph Henry around 1831, although Faraday is generally credited with first publishing the discovery and with formulating its governing laws, and it is his name that is universally associated with this phenomenon in the exam context ('Who discovered electromagnetic induction?' → Michael Faraday, 1831).

Faraday's Laws of Electromagnetic Induction

Faraday's first law states that whenever the magnetic flux linked with a circuit changes, an EMF is induced in the circuit; this induced EMF lasts only as long as the change in flux is actually occurring — a steady, unchanging magnetic field, however strong, induces no EMF at all. Faraday's second law (the quantitative law) states that the magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linked with the circuit — that is, the faster the flux changes, the greater the induced EMF.

Factors Affecting the Magnitude of Induced EMF

• The rate at which the magnet (or the current producing the field) and the coil move relative to each other — faster relative motion produces a greater rate of change of flux, and hence a larger induced EMF.
• The strength of the magnetic field (or magnet) used — a stronger magnet produces a greater flux and, when moved at a given speed, a greater rate of change of flux.
• The number of turns in the coil — a coil with more turns has a proportionally larger induced EMF for the same rate of change of flux per turn, since the EMFs induced in each turn add up in series.
• The area of the coil — a larger coil area intercepts more magnetic flux for a given field strength.

Lenz's Law

Lenz's law, formulated by the Russian physicist Heinrich Lenz, specifies the direction of the induced current (Faraday's laws give only the magnitude). Lenz's law states that the direction of an induced current is always such that it opposes the very change in magnetic flux that produced it. For example, if a magnet's north pole is being pushed toward a coil (increasing the flux through the coil), the induced current in the coil flows in a direction that makes the near face of the coil itself behave like a north pole, so as to repel the approaching magnet and oppose the increase in flux; conversely, if the magnet is being pulled away (decreasing the flux), the induced current flows in the opposite direction, making the near face a south pole so as to attract the receding magnet and oppose the decrease in flux. Lenz's law is essentially a direct and elegant consequence of the law of conservation of energy: if the induced current instead aided the change in flux rather than opposing it, the system would spontaneously generate ever-increasing energy from nothing, which would violate the conservation of energy. Because work must be done against this opposing induced effect to keep moving the magnet or coil, that mechanical work done is precisely what gets converted into the electrical energy of the induced current.