The concept of electromagnetic induction was discovered simultaneously in 1831 by Faraday in London and Joseph Henry, an American scientist working in New York that same year. Faraday’s law describes electromagnetic induction, whereby an electric field is induced, or generated by a changing magnetic field.. but Faraday is credited for the law since he published his work first An emf can be induced in many ways-for instance, by moving a closed loop of wire into a region where a magnetic field exists. The results of these experiments led to a very basic and important law of lectromagnetism known as Faraday’s law of induction. This law states that the magnitude of the emf induced in a circuit equals to the time rate of change of the magnetic flux through the circuit. With the treatment of Faraday’s law, we complete our introduction to the fundamental laws of electromagnetism. These laws can be explained in a set of four equations known as Maxwell’s equations. Together with the Lorentz force law, they represent a complete theory for describing the interaction of charged objects. Maxwell’s equations relate electric and magnetic fields to each other and to their ultimate source, namely, electric charges.

- To see how an emf can be induced by a changing magnetic field, let us consider a loop of wire connected to a galvanometer.
- When a magnet is moved toward the loop, the galvanometer needle deflects in one direction,arbitrarily.
- When we take magnet away from the loop, the needle deflects in the direction .
- When the magnet is held stationary relative to the loop, no deflection take place.

Finally, if the magnet is held stationary and the loop is moved either toward or away from it, the needle deflects. From these observations, we observe that the loop “knows” that the magnet is moving relative to it because it experiences a change in magnetic field. Thus, it seems that a relationship exists between current and changing magnetic field.

Faraday’s Law: an Explanation

Listed below are the two mathematical forms of Faraday’s Law: the point or differential form, and the integral form. Although the two forms appear highly distinct, they mean exactly the same thing and can be used interchangeably in calculations. The point form equation can be transformed to the integral form equation and vice versa by the application of a single vector calculus theorem 1. Although synonymous, the two forms of the law lend themselves to different conceptual understanding depending on the physical context. Physicists and electrical engineers often like to state Faraday’s Law in the more compact point form, but prefer using the integral form for calculations since it is more physically intuitive.

Avoiding the drudgery imposed by attempting to understand the sundry mathematical symbols, Faraday’s law says that a time-varying magnetic field induces an electric field. More formally, here is the essence of Faraday’s Law:

“The sum of all electric field components tangent to a closed spatial path, or “loop,” is equal to the negative time-rate of change of the magnetic flux through the surface bounded by that path.”

First, let’s understand what is meant by “flux.” Imagine water flowing through a pipe in which a screen spans the cross-section . The flow of water across the screen can be considered “flux.” Similarly, magnetic flux refers to a magnetic field intersecting a surface.

Now imagine that, as the water flows through the creen in the pipe, its rate of flow increases, i.e. it accelerates. This means that the time-rate of change of the water flow is positive relative to the direction of flow. On the other hand, if the flow rate decreases, then this time-rate of change is negative with respect to the direction of flow. The same applies to the magnetic flux through a surface: if its magnitude is increasing with respect to the field’s direction, then the time-rate of change is positive; otherwise, it is negative.

In this figure, there is a changing magnetic field, represented by the red arrow “coming out of” the page. Surrounding this changing magnetic field (and flux) is an arbitrary closed path along which are marked several tangential electric field components.

The sum of these components, relatively speaking, is what is indicated by the left sides of the equations in table 1.

Faraday’s Law equates the two last concepts: the total electric field summed around a closed path (the left side of the equation) is equal to the time-rate of change of the magnetic flux through the surface bounded by that path (the right side of the equation). Physically, this means a time-changing magnetic flux gives rise to an electric field in its neighbourhood. Recall from our earlier discussion that there must be an electric potential, or voltage, associated with every electric field. Thus our understanding of Faraday’s law can be extended to say that a time-variant magnetic field induces an electric potential or voltage.

Faraday’s Law: Consequences

Faraday’s Law is so fundamental to the workings of our universe that if the truths it conveys were not so, it is difficult to imagine how the universe as we know it would be different. One could say that electromagnetic waves wouldn’t exist, and without these, perhaps, the universe wouldn’t either. Or, perhaps, life would continue, but in a dramatically different way than what we experience. But this is a discussion best left for philosophers. What we do know for certain is that mankind’s understanding of these laws has had a colossal impact on how we live in our world today: various inventions and technologies that incorporate Faraday’s Law have revolutionised mankind’s living for well more than a century.

Faraday law describe how electromagnetic (EM) waves are generated and, with the help of two other electromagnetics equations, propagated through various media. EM waves are essential to our existence and to our quality of life. EM waves of many different frequencies are responsible for myriads of different phenomena: low frequency EM waves are used for radio transmissions and television broadcasts; low- to mid frequency microwaves are used in satellite and mobile communications and in microwave ovens; mid-frequency infrared radiation from the sun heats our planet; mid-frequency visible light waves allow us to see and makes plant and animal life on earth possible; mid-frequency ultraviolet radiation is enjoyed by tanning sunbathers; high frequency x-rays are used in medical diagnostic equipment and in materials analysis; and ultra-high frequency gamma radiation is involved in subatomic phenomena

Now let us describe an experiment conducted by Faraday.

A primary coil is connected to a switch and a battery. The coil is wrapped around a ring, and a current in the coil produces a magnetic field when the switch is closed. A secondary coil also is wrapped around the ring and is connected to a galvanometer. No battery is present in the secondary circuit, and the secondary coil is not connected to the primary coil. Any current detected in the secondary circuit must be induced by some external agent. Initially, we might guess that no current is ever detected in the secondary circuit. However, something quite amazing happens when the switch in the primary circuit is either suddenly closed or suddenly opened. At the instant the switch is closed, the galvanometer needle deflects in one direction and then returns to zero. At the instant the switch is opened, the needle deflects in the opposite direction and again returns to zero. Finally, the galvanometer reads zero when there is either a steady current or no current in the primary circuit. The key to under-standing what happens in this experiment is to first note that when the switch is closed, the current in the primary circuit produces a magnetic field in the region of the circuit, and it is this magnetic field that penetrates the secondary circuit.

Furthermore, when the switch is closed, the magnetic field produced by the current in the primary circuit changes from zero to some value over some finite time, and it is this changing field that induces a current in the secondary circuit.As a result of these observations, Faraday concluded that an electric current can be induced in a circuit (the secondary circuit in our setup) by a changing magnetic field. The induced current exists for only a short time while the magnetic field through the secondary coil is changing. Once the magnetic field reaches a steady value, the current in the secondary coil disappears. In effect, the secondary circuit behaves as though a source of emf were connected to it for a short time. It is customary to say that an induced emf is produced in the secondary circuit by the changing magnetic field.

The experiments shown in Figures 31.1 and 31.2 have one thing in common:

In each case, an emf is induced in the circuit when the magnetic flux through the circuit changes with time.

In general,

“The emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit”.

Where is the magnetic flux through the circuit (see Section 30.5). If the circuit is a coil consisting of N loops all of the same area and if _B is the flux through one loop, an emf is induced in every loop; thus, the total induced emf in the coil is given by the expression.

The negative sign in Equations 1 and 2 is of important physical significance.

Suppose that a loop enclosing an area A lies in a uniform magnetic field B.

From this expression, we see that an emf can be induced in the circuit in several

ways:

- The magnitude of B can vary with time.
- The area covered by the loop can vary with time.
- The angle _ between B and the normal to the loop can vary with time.
- Any combination of the above the three can occur.

Faraday’s law as two different phenomena

Some physicists have remarked that Faraday’s law is a single equation describing two different phenomena: The motional EMF generated by a magnetic force on a moving wire, and the transformer EMF generated by an electric force due to a changing magnetic field. James Clerk Maxwell drew attention to this fact in his 1861 paper On Physical Lines of Force. In the latter half of part II of that paper, Maxwell gives a separate physical explanation for each of the two phenomena.

So the “flux rule” that the emf in a circuit is equal to the rate of change of the magnetic flux passes through the circuit applies whether the flux changes because the field changes or because the circuit moves (or both)…. Yet in our explanation of the rule we have used two completely distinct laws for the two cases.

Applications of Faraday’s Law

The ground fault interrupter (GFI) is an interesting safety device that protects electrical appliances against electric shock. Its operation makes use of

Faraday’s law. In the GFI wire 1 leads from the wall outlet to the appliance to be protected, and wire 2 leads from the appliance back to the wall outlet. An iron ring surrounds the two wires, and a sensing coil is wrapped around part of the ring. Because the currents in the wires are in opposite directions, the net magnetic flux through the sensing coil due to the currents is zero. However, if the return current in wire 2 changes, the net magnetic flux through the sensing coil is no longer zero. (This can happen, for example, if the appliance gets wet, enabling current to leak to ground.) Because household current is alternating (meaning that its direction keeps reversing), the magnetic flux through the sensing coil changes with time, inducing an emf in the coil. This induced emf is used to trigger a circuit breaker, which stops the current before it is able to reach a harmful level.

Another interesting application of Faraday’s law is the producing sound in an electric guitar. The coil in this case, called the pickup coil , is placed near the vibrating guitar string, which is made of a metal that can be magnetized. A permanent magnet inside the coil magnetizes the portion of the string nearest the coil. When the string vibrates at some frequency, its magnetized segment produces a changing magnetic flux through the coil. The changing flux induces an emf in the coil that is fed to an amplifier. The output of the amplifier is sent to the speakers, which produce the sound waves we hear.

(a) In an electric guitar, a vibrating string induces an emf in a pickup coil.

(b) The circles beneath the metallic strings of this electric guitar detect the notes being played and send this information through an amplifier and into speakers.

Applications of electromagnetic induction that has had a tremendous impact on the way the society functions is electric power generation.

The electric generator (figure 7) uses electromagnetic induction by rotating windings (loops of wire) in a magnetic field. As the windings rotate through the field, a time-varying flux is incident across them, resulting in an induced voltage.