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Faraday's Law of Electromagnetic Induction: Equation and Application

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  • 0:01 Michael Faraday
  • 1:48 Faraday's Law
  • 5:03 Applications of Faraday's Law
  • 6:34 Lesson Summary
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Lesson Transcript
Instructor: Sarah Friedl

Sarah has two Master's, one in Zoology and one in GIS, a Bachelor's in Biology, and has taught college level Physical Science and Biology.

Electromagnetic induction allows us to induce voltage with the movement of a magnetic field. Credited to Michael Faraday, this discovery was not only groundbreaking at the time, but it has since led to many applications in everyday life.

Michael Faraday

If you get caught in a thunderstorm, one of the safest places you can seek shelter is in your car. This is because the car provides a protective cage around you, known as a 'Faraday Cage.' Named after Michael Faraday, this type of cage protects whatever is inside the cage from electrical fields outside the cage. Faraday Cages are found everywhere these days because this principle is used to protect electrical equipment, the insides of buildings, and more. The coolest part about Faraday Cages is that they can be reversed too: microwaves and TVs act to keep electrical waves inside the cage, which allows you to cook food and watch your favorite program without electrical interference. Too bad it doesn't work on commercials, though...

The saying, 'Greatness comes from within,' could not be truer than with someone like Michael Faraday. He came from a poor family and had little scientific education, but eventually became one of the greatest scientists of all time. In fact, he is known as the 'father of electricity' and revered as an excellent physicist and chemist. But why is he held in such high regard? It's not just because he invented the modern balloon, though personally I think that alone should have earned him such a title. It's also not because he began a Christmas lecture program to bring science to children that still runs today.

It's because of a major discovery he made about electricity and magnets known as electromagnetic induction. This is when voltage is induced by a changing magnetic field. Faraday discovered that an electric current can be produced in a coil of wire by moving a magnet in or out of the coil or by moving the coil through the magnetic field. In either case, voltage is induced, or created, through that motion. It sounds simple enough, but at the time this was really shocking stuff.

Faraday's Law

This discovery was so fundamental and important, that it is now known as Faraday's Law, which states that the amount of induced voltage is equal to the rate of change of the magnetic flux. This can be represented in equation form as:

farraday

That's quite a mouthful, so let's break it down to see what's going on here.

First we need to brush up on our Greek. For this law, we're going to use the Greek letter epsilon to represent the magnitude of the induced voltage, also known as EMF. This stands for 'electromotive force.' Think of it as the electric current caused by the motion of a force. It might also help to see that epsilon kind of looks like a cursive E for 'EMF'. Next is the letter delta, which means 'change in.' Finally we have phi, which represents the magnetic flux. This is simply the amount of magnetic field passing through a given surface area. In Faraday's case, the surface area was through the coil of wire he moved the magnet in and out of. Finally, the t on the bottom of the equation stands for 'time'.

Now that we know how to read Faraday's law, let's look at exactly what it means. We can tell by just looking at the equation, that the EMF and the magnetic flux are proportional because both are on top in the equation. This means that as one variable increases or decreases, the other variable will change in the same direction by the same amount. The change in time is on the bottom, so this means that it is inversely proportional to the EMF. The change here will be the opposite. As one variable increases or decreases, the other variable will change in the opposite direction by the same amount. As the change in flux increases, so does the EMF. But if the change in time increases, the EMF will decrease. Remember: 'delta' means 'change in,' so it's not the magnitude of the flux or the time, it's the magnitude of the change in either one of those variables that we're interested in.

Take Faraday's coils of wire, for example. If you have a magnet and you put it through a looped coil of wire, you create or induce a certain amount of voltage. But if you put that same magnet through a coil with twice as many loops, you create twice as much voltage because you have doubled the surface area the magnetic field passes through. If you put the magnet through a coil with 20 loops, you would induce 20 times as much voltage. In this way, we can see how magnetic flux and EMF are proportional because they change by the same amount.

We can use Faraday's coil wire to see how time affects the EMF as well. Moving the magnet very slowly through the loops of coil creates a small voltage because the change in time is very large. However, move that magnet through the loop quickly, and you create a large voltage because the change in time is very small. This shows us how these two are inversely proportional - as one goes up, the other goes down by the same amount. A large change in time (slow movement) means a small voltage is created, while a small change in time (fast movement) means a large voltage is induced.

Applications of Faraday's Law

Faraday's Law goes way beyond cool lab experiments with magnets and wires. The real-world applications of this type of voltage induction are numerous and whether you know it or not, they surround you in everyday life.

Generators and motors both make use of Faraday's Law. A generator converts mechanical energy into electrical energy, which is why it's useful during a power outage. A motor does the opposite and converts electrical energy into mechanical energy. This makes them useful for powering vehicles. A generator produces an electric current by rotating a coil in a stationary magnetic field. In a motor, a current is passed through a coil, which forces it to spin. In either case, both employ coils of wire and magnetic fields to induce voltage. Every time you drive to work or school, you are putting Faraday's Law to use!

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