A changing magnetic field and an electric current are described in the law of induction. According to the University of Texas at Austin, American physicist Joseph Henry made the same discovery as English physicist Michael Faraday in the same year.

It is impossible to overstate the significance of the discovery. Modern technology is formed by the electric motors, generators and transformers. We have an electric power grid and a lot of things we plug into it.

According to Sacred Heart University, the law was later incorporated into the more comprehensive equations. James Clerk Maxwell, a Scottish physicist, developed equations to explain the relationship between electricity and magnetism, and to describe the waves that make up radio waves, visible light and X-rays.

There are equations that changed the world.

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Electricity

The electric charge is a fundamental property of matter that governs how some particles in that matter are affected by an electric or magnetic field. A professor of physics at Pittsburg State University in Kansas told Live Science that a hypothetical electric charge located at a single point in space is relatively simple. He describes it as being the same in all directions as light from a bare light bulb, and decreasing in strength as the square inverse of the distance, according to Georgia State University. 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.

electrons have a negative charge. Most of the electric currents we are familiar with come from electrons. Austin Community College says that electrons in a metal are mostly free to move from one atom to another along their conduction bands. electrons can move through a conductor from a region of more negative charge to a region of more positive charge if there is a sufficient electrical force. This movement is an electric current.

Magnetism

It is important to have a basic understanding of magnetic fields to understand the law of induction. The electric field is simpler than the magnetic field. Positive and negative electric charges can be separated, but magnetic poles always come in pairs, according to Boston University. Magnets of all sizes are usually dipoles, meaning they have two poles. After the direction in which the compass needles point, the poles are called north and south. The magnetic North Pole is actually a south magnetic pole because it attracts the north poles of compass needles.

According to Florida State University, a magnetic field is often depicted as lines of magnetic flux. In a bar magnet, the lines exit from the north pole and curve around to the south pole. The strength of the field is represented by the number of lines passing through a surface. This is only a model. A magnetic field is not made of lines.

Magnetic field lines from a bar magnet.

Magnetic field lines from a bar magnet. (Image credit: snapgalleria Shutterstock
)

The magnetic field on Earth has a huge amount of magnetic flux, but it is dispersed over a lot of space. A weak field is caused by a small amount of flux passing through the area. The field strength of a refrigerator magnet is much stronger at close range than it is on Earth, according to a lecture by a physicist. As you move away, the field becomes weaker.

Induction

A magnetic field can be created if you run an electric current through a wire. The right-hand rule can be used to determine the direction of the magnetic field. 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 opposite 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. (Image credit: Fouad A. Saad Shutterstock)

If you bend the wire into a loop, the magnetic-field lines will form a toroid. Your thumb points at the magnetic field coming out of the center of the loop, while your fingers point at 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. (Image credit: OpenStax)

If you run a current through a wire loop in a magnetic field, the interaction of these magnetic fields will exert a twisting force on the loop, causing it to spin. It will wobble back and forth until the magnetic fields are aligned. You have to reverse the direction of the current to keep the loop rotating. The field of the loop will be aligned in the other direction after 180 degrees. The electric motor is based on this.

The electric current in the wire will be caused by the magnetic field. The direction of the current will change every half turn, according to the University of Texas at Austin. The electric generator is based on this. The opening and closing of the loop with respect to the direction of the field is what causes the current. The maximum amount of flux can be passed through the loop when it is face-on to the field. When the loop is turned edge-on to the field, no lines pass through it. The change in the amount of flux passing through the loop causes the current.

A wire is formed into a loop and connected to a galvanometer. The needle in the galvanometer will move if you push a bar magnet through the loop. The current returns to zero once you stop the motion of the magnet. The field from the magnet can only be used when the current is increasing or decreasing. According to the University of Florida, if you pull the magnet out, it will cause 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. (Image credit: Fouad A. Saad Shutterstock)

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

In an experiment, you could connect the ends of two wire loops to a galvanometer and a battery with a switch. If you place the two loops close to each other in a face-to-face orientation and turn on the power to the first loop, the galvanometer connected to the second loop will tell you if there's a current.

The current in the first loop produces a magnetic field, which in turn causes a current in the second loop to change. The meter will move in the opposite direction when you turn off the switch. The change in the intensity of the magnetic field is what causes the current.

A magnetic field causes electrons in a conductor to move. The electric current is what we know as this motion. The electrons will stop moving at a point where they are in equilibrium with the field. The electrons will flow back to their original location when the field is turned off.

A magnetic dipole field is a more complex 3D structure that varies in strength and direction according to the location where it is measured, so it requires a full description of it. We can describe a simplified case of a uniform magnetic field, where the absolute value of the field is. The strength of a magnetic field is determined by the amount of magnetic field per unit area.

Faraday's law

Now that we have a basic understanding of the magnetic field, we are ready to define the law of induction. It states that the rate of change in the magnetic field of a circuit is related to the rate of change in the induced voltage in that circuit. The faster the magnetic field changes, the higher the voltage in the circuit will be. The direction of the magnetic field affects the direction of the current.

Adding more loops to the circuit can increase the voltage. With one loop and three loops, the induced voltage in the coil will be triple. Large numbers of coils are what real motors and generators have.

In theory, generators and motors are the same. If you turn a motor, it will generate electricity, and if you apply the voltage to a generator, it will turn. Most real generators and motors are only designed for one function.

Transformers

The transformer is an important application of the law. A coil wrapped around a magnetic core is used to send alternating current through the device. This produces a changing magnetic field in the core, which in turn causes a current in a second coil wrapped around a different part of the same magnetic core, according to Milwaukee Area Technical College.

Transformer diagram

Transformer diagram (Image credit: photoiconix Shutterstock
)

The ratio of the number of turns in the coil is used to calculate the voltage between the inputs and outputs. If you take a transformer with 100 turns on the input side and 50 turns on the output side, and you input an alternating current of 220 volts, the output will be 120 volts. Georgia State University says a transformer can't increase power because it's the product of voltage and current. The current is proportionally lowered if the voltage is raised. In our example, an input of 220 volts at 10 Amps, or 2,200 Watts, would produce an output of 220 volts at 20 Amps. The University of Texas at Austin says that a well-designed transformer can have a power loss of only a few percent.

Our industrial and technological society depends on the electric grid being powered by transformers. Cross-country transmission lines are able to transmit more power due to their large capacity. When the voltage reaches your house, it's stepped down to 220 and 110, which can run your electric stove and computer.

The article was updated on Feb. 7, 2022.

Additional resources

Bibliography

The University of Texas at Austin has a lecture by Richard Fitzpatrick.

Lindsay Guilmette wrote "The History Of Maxwell's Equations" at Sacred Heart University.

Georgia State University has Coulomb's Law.

Ben Franklin should have said positive things. Wrong at www.austincc.edu/wkibbe/truth.htm

Iowa State University has a website called "Voltage."

Boston University, Magnetic Fields.

Florida State University has generators and motors.

Chapter 8: Magnetism andElectromagnetism is written by Jean-Francois Millithaler.

Buffalo State University of New York has a guide to finding the direction of the magnetic force.

Magnetic Torques and Amp's Law are written by Michael Richmond.

The University of Texas at Austin has a lecture by Richard Fitzpatrick.

The University of Florida has a course onDirection of Induced Current.

The University of California, Santa Barbara has a lecture aboutMutual Insturment with coils and galvanometer.

"Faraday's Law" was published by Eastern Illinois University on February 15, 2011.

The introduction to Magnetism and Induced Currents was published in 2002.

Georgia State University has a website called "Transformer".

Jim Mihall is a professor at Milwaukee Area Technical College.

The University of Texas at Austin had a lecture by Richard Fitzpatrick.