# Electromagnetic Induction

## Fundamentals

The phenomenon of electromagnetic induction was discovered by the British physicist Michael Faraday in 1831 and independently observed soon thereafter by the American physicist Joseph Henry. Prior to that time, it was known that the presence of an electric charge would cause other charges on nearby conductors to redistribute themselves. Furthermore, in 1820 the Danish physicist Hans Christian Oersted demonstrated that an electric current produces a magnetic field. It seemed reasonable, then, to ask whether or not a magnetic field might cause some kind of electrical effect, such as a current.

An electric charge that is stationary in a magnetic field will not interact with the field in any way. Nor will a moving charge interact with the field if it travels parallel to the field's direction. However, a moving charge that crosses the field will experience a force that is perpendicular both to the field and to the direction of motion of the charge (Figure 1). Now, instead of a single charge, consider a rectangular loop of wire moving Figure 1. Illustration by Hans & Cassidy. Courtesy of Gale Group.

through the field. Two sides of the loop will be subjected to forces that are perpendicular to the wire itself so that no charges will be moved. Along the other two sides charge will flow, but because the forces are equal the charges will simply bunch up on the same side, building up an internal electric field to counteract the imposed force, and there will be no net current (Figure 2).

How can a magnetic field cause current to flow through the loop? Faraday discovered that it was not simply the presence of a magnetic field that was required. In order to generate current, the magnetic flux through the loop must change with time. The term flux refers to the flow of the magnetic field lines through the area enclosed by the loop. The flux of the magnetic field lines is like the flow of water through a pipe and may increase or decrease with time.

To understand how the change in flux generates a current, consider a circuit made of many rectangular loops connected to a light bulb. Under what conditions will current flow and the light bulb shine? If the circuit is pulled through a uniform magnetic field there will be no current because the flux will be constant. But, if the field is non-uniform, the charges on one side of the loop will continually experience a force greater than that on the other side. This difference in forces will cause the charges to circulate around the loop in a current that Figure 2. Illustration by Hans & Cassidy. Courtesy of Gale Group.

Figure 3. Illustration by Hans & Cassidy. Courtesy of Gale Group. Figure 4. Illustration by Hans & Cassidy. Courtesy of Gale Group.
lights the bulb. The work done in moving each charge through the circuit is called the electromotive force or EMF. The units of electromotive force are volts just like the voltage of a battery that also causes current to flow through a circuit. It makes no difference to the circuit whether the changing flux is caused by the loop's own motion or that of the magnetic field, so the case of a stationary circuit and a moving non-uniform field is equivalent to the previous situation and again the bulb will light (Figure 3).

Yet a current can be induced in the circuit without moving either the loop or the field. While a stationary loop in a constant magnetic field will not cause the bulb to light, that same stationary loop in a field that is changing in time (such as when the field is being turned on or off) will experience an electromotive force. This comes about because a changing magnetic field generates an electric field whose direction is given by the right-hand rule—with the thumb of your right hand pointing in the direction of the change of the magnetic flux, your fingers can be wrapped around in the direction of the induced electric field. With an EMF directed around the circuit, current will flow and the bulb will light (Figure 3).

The different conditions by which a magnetic field can cause current to flow through a circuit are summarized by Faraday's law of induction. The variation in time of the flux of a magnetic field through a surface bounded by an electrical circuit generates an electromotive force in that circuit.

What is the direction of the induced current? A magnetic field will be generated by the induced current. If the flux of that field were to add to the initial magnetic flux through the circuit, then there would be more current, which would create more flux, which would create more current, and so on without limit. Such a situation would violate the conservation of energy and the tendency of physical systems to resist change. So the induced current will be generated in the direction that will create magnetic flux which opposes the variation of the inducing flux. This fact is known as Lenz's law.

The relation between the change in the current through a circuit and the electromotive force it induces in itself is called the self-inductance of the circuit. If the current is given in amperes and the EMF is given in volts, the unit of self-inductance is the henry. A changing current in one circuit can also induce an electromotive force in a nearby circuit. The ratio of the induced electromotive force to the rate of change of current in the inducing circuit is called the mutual inductance and is also measured in henrys.