Learn about Faraday’s Law of Induction: it explains how electricity creates magnetism and how changing magnetism creates electricity.

Faraday’s law of induction explains how electricity creates a magnetic field and how a changing magnetic field generates electric current in a conductor. Michael Faraday, an English physicist, is credited with discovering magnetic induction in 1831. Interestingly, American physicist Joseph Henry also independently made the same discovery around the same time, as noted by the University of Texas at Austin.

Faraday’s discovery of magnetic induction holds immense importance. It’s the driving force behind electric motors, generators, and transformers, which are the backbone of modern technology. Thanks to our grasp of induction, we have the electric power grid and the myriad devices that connect to it.

Faraday’s law, which talks about how electricity and magnetism work together, became part of Maxwell’s equations. These equations were made by James Clerk Maxwell, a scientist from Scotland. He made them to show how electricity and magnetism are related. Maxwell’s equations help us understand electromagnetic waves, like radio waves, light we can see, and X-rays.

ELECTRICITY

Electric charge is a basic part of stuff, and it decides how some tiny bits inside that stuff respond to an electric or magnetic field, says Britannica. If you imagine a single point in space with a pretend electric charge sitting there, the electric field around it is quite simple, explains Serif Uran, a physics professor at Pittsburg State University in Kansas.

He says it spreads out evenly in all directions, a bit like light from a bare light bulb, and gets weaker as you move away according to Coulomb’s law, mentioned by Georgia State University. When you go twice as far away, the field strength drops to one-fourth, and when you go three times farther, it’s just one-ninth as strong.

Protons have a plus charge, while electrons have a minus charge. But protons stay mostly stuck inside an atom’s center, so the electric currents we see usually come from electrons. In materials like metals, electrons can move freely from one atom to another along their highest orbits, called conduction bands, as explained by Austin Community College.

When there’s enough electromotive force, or voltage, it creates an imbalance in charge that makes electrons move through a conductor from where there’s more negative charge to where there’s more positive charge, says Iowa State University. This moving around is what we call an electric current.

MAGNETISM

Understanding Faraday’s law of induction requires grasping the basics of magnetic fields. Magnetic fields are more intricate compared to electric fields. While positive and negative electric charges can exist independently, magnetic poles always appear in pairs: one north and one south, according to Boston University.

Most magnets, whether they’re tiny particles or large celestial bodies like planets, have two poles known as dipoles. These poles, named north and south after compass needle directions, exhibit an interesting behavior: opposite poles attract while like poles repel. Thus, Earth’s magnetic North Pole is actually a south magnetic pole because it attracts the north poles of compass needles.

According to Florida State University, people often show a magnetic field as lines of magnetic flux. For example, with a bar magnet, the lines of flux go out from the north pole and bend around to come back in at the south pole. In this way, the number of flux lines going through a certain space shows how strong the magnetic field is. It’s important to remember, though, that this is just a way to understand it. A magnetic field is actually smooth and never breaks into separate lines.

The Earth’s magnetic field creates a lot of magnetic flux, but it spreads out over a huge area. So, only a bit of flux goes through any specific area, making the field relatively weak. Compared to Earth, a fridge magnet has much less flux, but its field is stronger up close because its flux lines are packed tightly together, explains UMass Lowell physicist Jean-François Millithaler. However, as you move away, the field weakens quickly.

INDUCTION

When electricity flows through a wire, it creates a magnetic field around the wire. To figure out the direction of this magnetic field, you can use the right-hand rule. According to the physics department at Buffalo State University of New York, if you stick out your thumb and curl your fingers around the wire, your thumb shows the direction of the current, and your curled fingers show the direction of the magnetic field.

When you shape the wire into a loop, the magnetic field lines follow along, creating a toroid, which looks like a doughnut. Here, if you use the right-hand rule, your thumb points in the direction of the magnetic field coming out from the center of the loop, while your fingers show the direction of the current flowing through the loop.

When you pass a current through a wire loop in a magnetic field, the magnetic fields interact, creating a twisting force called torque, as explained by the Rochester Institute of Technology. This torque makes the loop rotate, but it only turns until the magnetic fields align. Then, it wobbles instead of spinning. To keep it rotating, you need to change the current’s direction, which flips the loop’s magnetic field. As a result, the loop rotates 180 degrees until its field faces the other way. This process forms the foundation of the electric motor.

On the other hand, when you spin a wire loop within a magnetic field, the field triggers an electric current in the wire. The current’s direction flips every half turn, resulting in an alternating current, notes the University of Texas at Austin. This process forms the foundation of the electric generator.

What’s important to understand is that it’s not the wire’s motion itself, but rather the loop’s opening and closing concerning the field’s direction, that causes the current. When the loop faces the field directly, the maximum flux passes through it. However, when the loop turns sideways to the field, no flux lines pass through it. This change in the flux passing through the loop induces the current.

Another experiment involves shaping a wire into a loop and linking its ends to a sensitive current meter, like a galvanometer. When you push a bar magnet through the loop, the galvanometer’s needle moves, showing an induced current. However, once you halt the magnet’s movement, the current goes back to zero.

The magnet’s field induces a current solely when it’s either increasing or decreasing. If you pull the magnet out, it induces a current in the wire again, but this time, in the opposite direction, explains the University of Florida.

If you were to include a light bulb in the circuit, it would convert electrical energy into both light and heat. As you move the magnet in and out of the loop, you’d notice resistance, feeling like you’re working against something. This resistance occurs because to move the magnet, you need to exert energy, which is comparable to the energy being used up by the light bulb.

In another experiment, you could set up two wire loops: connect one loop’s ends to a battery with a switch, and connect the other loop’s ends to a galvanometer. When you position the two loops close together facing each other and activate the power to the first loop, the galvanometer linked to the second loop will show an induced current briefly before returning to zero, as described by the University of California, Santa Barbara.

Here, the current flowing through the first loop generates a magnetic field. This changing magnetic field, in turn, induces a current in the second loop, but only while the magnetic field is in flux. When you switch off the current, the meter briefly deflects in the opposite direction. This shows that it’s the alteration in the magnetic field’s intensity, rather than its strength or movement, that causes the current to be induced.

The reason behind this phenomenon is that a magnetic field prompts electrons in a conductor to move, resulting in electric current. However, over time, these electrons reach a state of balance with the field, ceasing their movement. Subsequently, when the field is either eliminated or switched off, the electrons return to their initial position, generating a current in the opposite direction.

Unlike gravitational or electric fields, a magnetic dipole field is a more intricate 3D structure, with variations in strength and direction depending on the measurement location, requiring calculus for full description. However, we can simplify it by considering a uniform magnetic field, like a tiny portion of a large field.

In this case, as per Eastern Illinois University, we can express the magnetic flux as ΦB = BA, where ΦB is the magnetic flux’s absolute value, B is the field strength, and A is the defined area the field passes through. Conversely, in this scenario, the field’s strength is the flux per unit area, expressed as B = ΦB/A.

FARADAY’S LAW

Now that we have a foundational grasp of the magnetic field, we can define Faraday’s law of induction. As stated by Rensselaer Polytechnic Institute, it asserts that the induced voltage in a circuit correlates with the rate of change of magnetic flux through that circuit over time. Put simply, the faster the magnetic field changes, the higher the voltage in the circuit. Moreover, the direction of the magnetic field’s change dictates the current’s direction.

To boost the voltage, we can incorporate more loops into the circuit. Adding coils amplifies the induced voltage: with two loops, it doubles compared to one loop, and with three loops, it triples. That’s why practical motors and generators usually feature numerous coils.

In theory, motors and generators function similarly. If you rotate a motor, it can generate electricity, and if you apply that voltage to a generator, it will turn. However, in practice, most motors and generators are optimized for specific functions.

TRANSFORMERS

Another significant application of Faraday’s law of induction is the transformer, credited to Nikola Tesla. In this apparatus, alternating current, which switches direction multiple times per second, flows through a coil wound around a magnetic core. This process generates a fluctuating magnetic field within the core.

Consequently, a current is induced in a second coil wound around another section of the same magnetic core, as explained by Milwaukee Area Technical College.

The ratio of turns in the coils determines the voltage ratio between input and output currents in a transformer. For instance, if a transformer has 100 turns on the input side and 50 turns on the output side, and you input an alternating current at 220 volts, the output will be 110 volts. As per Georgia State University, a transformer cannot amplify power, which is the voltage-current product.

Therefore, if the voltage increases, the current decreases proportionally, and vice versa. In our example, an input of 220 volts at 10 amps, or 2,200 watts, would yield an output of 110 volts at 20 amps—again, 2,200 watts. In reality, transformers are not perfectly efficient, but a well-designed transformer typically incurs only a slight power loss, usually just a few percent, according to the University of Texas at Austin.

Transformers play a crucial role in enabling the electric grid that underpins our industrial and technological society. Cross-country transmission lines operate at extremely high voltages—hundreds of thousands of volts—to transmit more power while staying within the current-carrying limits of the wires.

This high voltage is stepped down multiple times using transformers at distribution substations until it reaches your house. Here, it is further reduced to 220 and 110 volts, which are suitable for powering appliances like electric stoves and computers.

ADDITIONAL RESOURCES

• Visual demonstration of Faraday’s law: PhysicsHigh YouTube channel video
• Interactive activity showcasing the right-hand rule: University of Tennessee, Knoxville
• Insights into induction from Richard Feynman’s lecture: Caltech

BIBLIOGRAPHY

Richard Fitzpatrick, “Faraday’s Law,” University of Texas at Austin, July 14, 2007. https://farside.ph.utexas.edu/teaching/302l/lectures/node85.html 

Lindsay Guilmette, “The History Of Maxwell’s Equations,” Sacred Heart University, 2012. https://digitalcommons.sacredheart.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1002&context=wac_prize 

Georgia State University, “Coulomb’s Law.” http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefor.html#c1 

Austin Community College, “Ben Franklin Should Have Said Electrons are Positive? Wrong.” https://www.austincc.edu/wkibbe/truth.htm 

Iowa State University, “Voltage.” https://www.nde-ed.org/Physics/Electricity/electricalcurrent.xhtml 

Boston University, “Magnetic Fields.” http://physics.bu.edu/~duffy/sc526_notes09/B_field.html 

Florida State University, “Generators and Motors,” 2015. https://micro.magnet.fsu.edu/electromag/electricity/generators/ 

Jean-François Millithaler, “Chapter 8: Magnetism & Electromagnetism,” UMass Lowell. https://faculty.uml.edu//JeanFrancois_Millithaler/FunElec/Spring2017/pdf/Ch8%20-%20Magnetism%20n%20Electromagnetism.pdf 

Buffalo State University of New York, “Right-Hand Rules: A Guide to finding the Direction of the Magnetic Force.” http://physicsed.buffalostate.edu/SeatExpts/resource/rhr/rhr.htm 

Michael Richmond, “Magnetic Torques and Amp’s Law,” Rochester Institute of Technology. http://spiff.rit.edu/classes/phys213/lectures/amp/amp_long.html 

Richard Fitzpatrick, “The Alternating Current Generator,” University of Texas at Austin, July 14, 2007. https://farside.ph.utexas.edu/teaching/302l/lectures/node90.html 

University of Florida, “Direction of Induced Current.” http://www.phys.ufl.edu/courses/phy2049/f07/lectures/2049_ch30B.pdf 

University of California, Santa Barbara, “Mutual induction with coils and galvanometer.” https://web.physics.ucsb.edu/~lecturedemonstrations/Composer/Pages/72.48.html 

Eastern Illinois University, “Faraday’s Law,” February 15, 2011. https://ux1.eiu.edu/~cblehman/phy1161/0handouts_sp11/phy1161Lect14_Faraday_law_handout_short.pdf 

Doris Jeanne Wagner, “Introduction to Magnetism and Induced Currents,” Rensselaer Polytechnic Institute, 2002. https://www.rpi.edu/dept/phys/ScIT/InformationStorage/faraday/magnetism_a.html 

Georgia State University, “Transformer.” http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html 

Jim Mihall, “Electromagnetic Induction,” Milwaukee Area Technical College, 2016. https://ecampus.matc.edu/mihalj/scitech/unit3/induction/induction.htm 

Richard Fitzpatrick, “Transformers,” University of Texas at Austin, July 14, 2007. https://farside.ph.utexas.edu/teaching/302l/lectures/node106.html