Faraday’s Law of Induction describes how an electric current produces a magnetic field and, conversely, how a changing magnetic field generates an electric current in a conductor. English physicist Michael Faraday gets the credit for discovering magnetic induction in 1830; however, an American physicist, Joseph Henry, independently made the same discovery about the same time, according to the University of Texas

It is impossible to overstate the significance of Faraday’s discovery. Magnetic induction makes possible the electric motors, generators and transformers that form the foundation of modern technology. By understanding and using induction, we have an electric power grid and many of the things we plug into it.

Faraday's law was later incorporated into the more comprehensive Maxwell’s equations, according to Michael Dubson, a professor of physics at the University of Colorado Boulder. Maxwell’s equations were developed by Scottish physicist James Clerk Maxwell to explain the relationship between electricity and magnetism, essentially uniting them into a single electromagnet force and describing electromagnetic waves that make up radio waves, visible light, and X-rays. 

Electric charge is a fundamental property of matter, according to the Rochester Institute of Technology. Although it is difficult to describe what it actually is, we are quite familiar with how it behaves and interacts with other charges and fields. The electric field from a localized point charge is relatively simple, according to Serif Uran, a professor of physics at Pittsburg State University. He describes it as radiating out equally in all directions, like light from a bare light bulb, and decreasing in strength as the inverse square of the distance (1/r2), in accordance with Coulomb’s Law. When you move twice as far away, the field strength decreases to one-fourth, and when you move three times farther away, it decreases to one-ninth. 

Protons have positive charge, while electrons have negative charge. However, protons are mostly immobilized inside atomic nuclei, so the job of carrying charge from one place to another is handled by electrons. Electrons in a conducting material such as a metal are largely free to move from one atom to another along their conduction bands, which are the highest electron orbits. A sufficient electromotive force (emf), or voltage, produces a charge imbalance that can cause electrons move through a conductor from a region of more negative charge to a region of more positive charge. This movement is what we recognize as an electric current. 

In order to understand Faraday’s Law of Induction, it is important to have a basic understanding of magnetic fields. Compared to the electric field, the magnetic field is more complex. While positive and negative electric charges can exist separately, magnetic poles always come in pairs — one north and one south, according to San Jose State University. Typically, magnets of all sizes — from sub-atomic particles to industrial-size magnets to planets and stars — are dipoles, meaning they each have two poles. We call these poles north and south after the direction in which compass needles point. Interestingly, since opposite poles attract, and like poles repel, the magnetic north pole of the Earth is actually a south magnetic pole because it attracts the north poles of compass needles. 

A magnetic field is often depicted as lines of magnetic flux. In the case of a bar magnet, the flux lines exit from the north pole and curve around to reenter at the south pole. In this model, the number of flux lines passing through a given surface in space represents the flux density, or the strength of the field. However, it should be noted that this is only a model. A magnetic field is smooth and continuous and does not actually consist of discrete lines. 

Magnetic field lines from a bar magnet.
Magnetic field lines from a bar magnet.
Credit: snapgalleria Shutterstock


Earth’s magnetic field produces a tremendous amount of magnetic flux, but it is dispersed over a huge volume of space. Therefore, only a small amount of flux passes through a given area, resulting in a relatively weak field. By comparison, the flux from a refrigerator magnet is tiny compared to that of the Earth, but its field strength is many times stronger at close range where its flux lines are much more densely packed. However, the field quickly becomes much weaker as you move away. 

If we run an electric current through a wire, it will produce a magnetic field around the wire. The direction of this magnetic field can be determined by the right-hand rule. According to the physics department at Buffalo State University of New York, if you extend your thumb and curl the fingers of your right hand, your thumb points in the positive direction of the current, and your fingers curl in the north direction of the magnetic field. 

Left-hand and right-hand rule for a magnetic field due to a current in a straight wire.
Left-hand and right-hand rule for a magnetic field due to a current in a straight wire.
Credit: Fouad A. Saad Shutterstock

If you bend the wire into a loop, the magnetic field lines will bend with it, forming a toroid, or doughnut shape. In this case, your thumb points in the north direction of the magnetic field coming out of the center of the loop, while your fingers will point in the positive direction of the current in the loop. 

In a current-carrying circular loop, (a) the right-hand rule gives the direction of the magnetic field inside and outside the loop. (b) More detailed mapping of the field, which is similar to that of a bar magnet.
In a current-carrying circular loop, (a) the right-hand rule gives the direction of the magnetic field inside and outside the loop. (b) More detailed mapping of the field, which is similar to that of a bar magnet.
Credit: OpenStax

If we run a current through a wire loop in a magnetic field, the interaction of these magnetic fields will exert a twisting force, or torque, on the loop causing it to rotate, according to the Rochester Institute of Technology. However, it will only rotate so far until the magnetic fields are aligned. If we want the loop to continue rotating, we have to reverse the direction of the current, which will reverse the direction of the magnetic field from the loop. The loop will then rotate 180 degrees until its field is aligned in the other direction. This is the basis for the electric motor. 

Conversely, if we rotate a wire loop in a magnetic field, the field will induce an electric current in the wire. The direction of the current will reverse every half turn, producing an alternating current. This is the basis for the electric generator. It should be noted here that it is not the motion of the wire but rather the opening and closing of the loop with respect to the direction of the field that induces the current. When the loop is face-on to the field, the maximum amount of flux passes through the loop. However, when the loop is turned edge-on to the field, no flux lines pass through the loop. It is this change in the amount of flux passing through the loop that induces the current.

Another experiment we can perform is to form a wire into a loop and connect the ends to a sensitive current meter, or galvanometer. If we then push a bar magnet through the loop, the needle in the galvanometer will move, indicating an induced current. However, once we stop the motion of the magnet, the current returns to zero. The field from the magnet will only induce a current when it is increasing or decreasing. If we pull the magnet back out, it will again induce a current in the wire, but this time it will be in the opposite direction. 

Magnet in a wire loop connected to a galvanometer.
Magnet in a wire loop connected to a galvanometer.
Credit: Fouad A. Saad Shutterstock

If we were to put a light bulb in the circuit, it would dissipate electrical energy in the form of light and heat, and we would feel resistance to the motion of the magnet as we moved it in and out of the loop. In order to move the magnet, we have to do work that is equivalent to the energy being used by the light bulb. 

In yet another experiment, we might construct two wire loops, connect the ends of one to a battery with a switch, and connect the ends of the other loop to a galvanometer. If we place the two loops close to each other in a face-to-face orientation, and we turn on the power to the first loop, the galvanometer connected to the second loop will indicate an induced current and then quickly return to zero. 

What is happening here is that the current in the first loop produces a magnetic field, which in turn induces a current in the second loop, but only for an instant when the magnetic field is changing. When you turn off the switch, the meter will deflect momentarily in the opposite direction. This is further indication that it is the change in the intensity of the magnetic field, and not its strength or motion that induces the current. 

The explanation for this is that a magnetic field causes electrons in a conductor to move. This motion is what we know as electric current. Eventually, though, the electrons reach a point where they are in equilibrium with the field, at which point they will stop moving. Then when the field is removed or turned off, the electrons will flow back to their original location, producing a current in the opposite direction. 

Unlike a gravitational or electric field, a magnetic dipole field is a more complex 3-dimensional structure that varies in strength and direction according to the location where it is measured, so it requires calculus to describe it fully. However, we can describe a simplified case of a uniform magnetic field — for example, a very small section of a very large field — as ΦB = BA, where ΦB is the absolute value of the magnetic flux, B is the strength of the field, and A is a defined area through which the field passes. Conversely, in this case the strength of a magnetic field is the flux per unit area, or B = ΦB/A

Now that we have a basic understanding of the magnetic field, we are ready to define Faraday’s Law of Induction. It states that the induced voltage in a circuit is proportional to the rate of change over time of the magnetic flux through that circuit. In other words, the faster the magnetic field changes, the greater will be the voltage in the circuit. The direction of the change in the magnetic field determines the direction of the current. 

We can increase the voltage by increasing the number of loops in the circuit. The induced voltage in a coil with two loops will be twice that with one loop, and with three loops it will be triple. This is why real motors and generators typically have large numbers of coils. 

In theory, motors and generators are the same. If you turn a motor, it will generate electricity, and applying voltage to a generator, it will cause it to turn. However, most real motors and generators are optimized for only one function. 

Another important application of Faraday’s Law of Induction is the transformer, invented by Nikola Tesla. In this device, alternating current, which changes direction many times per second, is sent through a coil wrapped around a magnetic core. This produces a changing magnetic field in the core, which in turn induces a current in second coil wrapped around a different part of the same magnetic core. 

Transformer diagram
Transformer diagram
Credit: photoiconix Shutterstock


The ratio of the number of turns in the coils determines the ratio of the voltage between the input and output current. For instance, if we take a transformer with 100 turns on the input side and 50 turns on the output side, and we input an alternating current at 220 volts, the output will be 110 volts. According to Hyperphysics, a transformer cannot increase power, which is the product of voltage and current, so if the voltage is raised, the current is proportionally lowered and vice versa. In our example, an input of 220 volts at 10 amps, or 2,200 watts, would produce an output of 110 volts at 20 amps, again, 2,200 watts. In practice, transformers are never perfectly efficient, but a well-designed transformer typically has a power loss of only a few percent, according to the University of Texas.

Transformers make possible the electric grid we depend on for our industrial and technological society. Cross-country transmission lines operate at hundreds of thousands of volts in order to transmit more power within the current-carrying limits of the wires. This voltage is stepped down repeatedly using transformers at distribution substations until it reaches your house, where it is finally stepped down to 220 and 110 volts that can run your electric stove and computer. 

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