9: Electromagnetic Induction

*The black strip found on the back of credit cards and driver’s licenses is a very thin layer of magnetic material with information stored on it. Reading and writing the information on the credit card is done with a swiping motion. The physical reason why this is necessary is called electromagnetic induction and is discussed in this chapter. (credit: modification of work by Jane Whitney)*

We have been considering electric fields created by fixed charge distributions and magnetic fields produced by constant currents, but electromagnetic phenomena are not restricted to these stationary situations. Most of the interesting applications of electromagnetism are, in fact, time-dependent. To investigate some of these applications, we now remove the time-independent assumption that we have been making and allow the fields to vary with time. In this and the next several modules, you will see a wonderful symmetry in the behavior exhibited by time-varying electric and magnetic fields. Mathematically, this symmetry is expressed by an additional term in Ampère’s law and by another key equation of electromagnetism called Faraday’s law. We also discuss how moving a wire through a magnetic field produces an emf or voltage. Lastly, we describe applications of these principles, such as the card reader shown above.

So far we’ve learned that electric charges create electric fields. And we know that a steady E-field pushes charges around (the force is F = qE), making currents flow. We’ve used the word “emf” for this occasionally, where an emf is any voltage difference capable of generating electric currents.

Think of emf = ΔV (= E Δx)

(Note: batteries have an emf, but resistors do NOT. Even though an R can have a voltage difference across it, the resistor is not generating the voltage. Resistors don’t make currents spontaneously flow, but batteries do.)

Michael Faraday (*side note: Faraday is my favorite physicist and Faraday’s law is my favorite formula*) a British physicist (at the same time as Joseph Henry, an American, but Faraday published first) about 180 years ago (1831) discovered a remarkable new property of nature:

Changing magnetic fields (not steady ones) can make emf’s.

In other words, a magnetic field that changes in time can make currents flow.

Watch this video of a simulation showing a loop of wire connected to a light bulb. This loop/bulb system is not connected to a battery so the bulb does not light up. But when I move a magnet near the loop, the bulb lights up!

If the B field is steady then there is NO CURRENT, the bulb is dark. But, if the B field changes with time, the bulb lights up, a current flows through that wire! I did this just by moving a big magnet closer, or farther away (yes, weakening the B-field is still a *change*)… or move the coil itself closer (or farther) from the magnet face.

There’s no battery here, no external voltage source, but the bulb still glows! This effect is surprising, it’s something new…

Faraday spent only 10 days of (intensive) work on these experiments, but they changed the world radically. This is how most of **modern society’s electricity is now generated. **Faraday worked out an equation (Faraday’s Law) which quantifies the effect (how much current do you get?). But before we can write it down, we need to first define one relevant quantity: Magnetic Flux and it’s what we will start with in this module. Then we will see all the amazing applications of Faraday’s law and maybe you’ll like it as much as I do.

#### 9.1 Faraday’s Law

- Determine the magnetic flux through a surface, knowing the strength of the magnetic field, the surface area, and the angle between the normal to the surface and the magnetic field
- Use Faraday’s law to determine the magnitude of induced emf in a closed loop due to changing magnetic flux through the loop

#### 9.2 Lenz’s Law

- Use Lenz’s law to determine the direction of induced emf whenever a magnetic flux changes
- Use Faraday’s law with Lenz’s law to determine the induced emf in a coil and in a solenoid

#### 9.3 Motional Emf

- Determine the magnitude of an induced emf in a wire moving at a constant speed through a magnetic field
- Discuss examples that use motional emf, such as a rail gun and a tethered satellite

#### 9.4 Induced Electric Fields

- Connect the relationship between an induced emf from Faraday’s law to an electric field, thereby showing that a changing magnetic flux creates an electric field
- Solve for the electric field based on a changing magnetic flux in time

#### 9.5 Eddy Currents

- Explain how eddy currents are created in metals
- Describe situations where eddy currents are beneficial and where they are not helpful

#### 9.6 Electric Generators and Back Emf

- Explain how an electric generator works
- Determine the induced emf in a loop at any time interval, rotating at a constant rate in a magnetic field
- Show that rotating coils have an induced emf; in motors this is called back emf because it opposes the emf input to the motor

#### 9.7 Applications of Electromagnetic Induction

- Explain how computer hard drives and graphic tablets operate using magnetic induction
- Explain how hybrid/electric vehicles and transcranial magnetic stimulation use magnetic induction to their advantage