Electromagnetic Induction

The video lesson for this topic is coming soon.

Essential Question

How can a magnet make electricity?

Electricity can make a magnet, so can a magnet make electricity? Yes, as long as the magnetic field is changing. By the end of this lesson, you should be able to predict when a current is induced and which way it flows, and use Faraday’s law to calculate the induced voltage.

Faraday’s Discovery

Changing field in a coil: current
This is called induction
No battery needed

A bar magnet with its N pole facing a coil of copper wire moves toward the coil, shown by an arrow labeled v. The coil's ends connect to a meter below it, and the meter's needle swings to the right. Caption: moving magnet makes a current.

In 1831, Michael Faraday discovered that moving a magnet into a coil of wire makes a current flow in the coil, even though there is no battery anywhere in the circuit. Making a current this way is called electromagnetic induction, and the current is called an induced current. The key is change: the magnetic field passing through the coil has to be changing.

Direction Depends on Motion

Magnet in: needle one way
Magnet out: needle the other way
Flip the magnet: current flips too

Two rows. Top: a magnet with its N pole facing a coil is pushed in, and the meter needle swings right. Bottom: the same magnet is pulled out, and the meter needle swings left.

The direction of the induced current depends on how the field changes. Pushing the N pole into the coil makes the meter swing one way. Pulling it back out makes the meter swing the opposite way, because now the field through the coil is decreasing instead of increasing. Turning the magnet around so the S pole leads also reverses the current.

No Change, No Current

Magnet held still: no current
Even when it sits inside the coil
Only a changing field counts

A bar magnet sits still inside a coil, labeled v = 0. The coil is connected to a meter whose needle points straight up at zero. Caption: still magnet, no current.

A magnet sitting still produces no induced current, even if it rests right inside the coil where the field is strongest. The field through the coil is strong, but it is not changing, so nothing is induced. Induction depends on the change in the field, not on how strong the field is.

Making More Current

More turns in the coil
A stronger magnet
Faster motion

Three cards. More turns: each loop adds its own push. Stronger magnet: a bigger change in the field. Faster motion: the same change in less time.

Three things increase the induced current. A coil with more turns gives a bigger current, because every loop has its own voltage induced in it, and the loops add up like batteries in series. A stronger magnet makes a bigger change in the field. And moving the magnet faster makes the same change happen in less time. Slowly sliding a weak magnet into one loop of wire barely moves the meter, but quickly plunging a strong magnet into a big coil makes a large current.

Magnetic Flux

Φ = BA

Φ (Greek letter phi) = magnetic flux, in webers (Wb)
B = magnetic field, in teslas (T)
A = area of the loop, in square meters (m²)

A rectangular red loop of wire with a field of blue dots, meaning the field points out of the page, passing through it. The loop's area is labeled A. A yellow equation box below reads flux equals B times A.

Magnetic flux measures how much magnetic field passes through a loop. Picture the field lines as arrows poking through the loop: more lines through the loop means more flux. When the field points straight through the loop, the flux is the field times the area. Flux changes if the field gets stronger or weaker, if the loop’s area changes, or if the loop turns so fewer field lines pass through it.

Faraday’s Law

ε = N ΔΦ / Δt

ε (Greek letter epsilon) = induced voltage, called the induced emf, in volts (V)
N = number of turns in the coil
ΔΦ = change in magnetic flux, in webers (Wb)
Δt = time for the change, in seconds (s)

The equation epsilon equals N times delta phi over delta t in a yellow box. Below it, four cards: epsilon is the induced voltage in volts, N is the number of turns, delta phi is the change in flux in webers, and delta t is the time for the change in seconds. A note says the induced current is I equals epsilon over R.

Faraday’s law says the induced voltage equals the number of turns times how fast the flux changes. A bigger change in flux, a shorter time, or more turns all make a bigger voltage. Once you know the voltage, Ohm’s law gives the induced current: I = ε/R. (The full law has a minus sign that tells the direction of the induced current. In this course we find the size with this equation and the direction from the motion.)

Motion Becomes Electricity

The coil pushes back on the magnet
You do work to move it
Your work becomes electrical energy

An energy flow chart with three cards connected by downward arrows: kinetic energy from your push on the magnet, then electrical energy in the induced current, then light and heat from a bulb.

Induction does not make energy out of nothing. When a current is induced, the coil becomes an electromagnet that pushes back against the moving magnet, so you have to do work to keep the magnet moving. That work, which starts as the kinetic energy of the moving magnet, is transformed into electrical energy in the coil, and then into light and heat in a bulb. Energy is conserved the whole way.

Worked Examples

Try each problem on your own first, then check your work against the solution.

Example 1: Reading the Meter

When a magnet’s N pole is pushed into a coil, the meter swings right. The magnet is turned around, and its S pole is pulled out of the coil. Which way does the meter swing?

A magnet with its S pole facing a coil is pulled away from the coil, shown by an arrow pointing away. The coil connects to a meter marked with a question mark.

Start: N pole pushed in: the meter swings right.
Change 1: flip the pole: Using the S pole instead of the N pole reverses the current: the meter would swing left.
Change 2: reverse the motion: Pulling out instead of pushing in reverses the current again.
Answer: Two reversals cancel, so the meter swings right.

Example 2: Magnetic Flux

A rectangular loop of wire measures 0.20 m by 0.25 m. A 0.40 T magnetic field points straight through it. What is the magnetic flux through the loop?

A red rectangular loop 0.25 meters wide and 0.20 meters tall with blue dots inside, showing a 0.40 tesla field pointing out of the page through it.

Knowns: B = 0.40 T, loop is 0.20 m × 0.25 m, field points straight through the loop
Area: A = (0.20 m)(0.25 m) = 0.050 m²
Equation: Φ = BA
Substitute: Φ = (0.40 T)(0.050 m²)
Answer: Φ = 0.020 Wb

Example 3: Induced Voltage

A coil has 50 turns, each with an area of 0.020 m². The field through it increases steadily from 0 T to 0.30 T in 0.10 s. What voltage is induced in the coil?

A graph of magnetic field versus time. A straight line rises from 0 tesla at 0 seconds to 0.30 tesla at 0.10 seconds.

Knowns: N = 50, A = 0.020 m², B changes from 0 T to 0.30 T, Δt = 0.10 s
Change in flux: ΔΦ = ΔB × A = (0.30 T)(0.020 m²) = 0.0060 Wb
Equation: ε = N ΔΦ / Δt
Substitute: ε = (50)(0.0060 Wb) / (0.10 s)
Answer: ε = 3.0 V

Example 4: Induced Current

The flux through a 100-turn coil changes by 0.012 Wb in 0.20 s. The coil is connected to a circuit with a total resistance of 12 Ω. Find the induced current.

A coil labeled N = 100 connected in a loop to a resistor labeled 12 ohms.

Knowns: N = 100, ΔΦ = 0.012 Wb, Δt = 0.20 s, R = 12 Ω
Induced voltage: ε = N ΔΦ / Δt = (100)(0.012 Wb) / (0.20 s) = 6.0 V
Ohm’s law: I = ε / R
Substitute: I = 6.0 V / 12 Ω
Answer: I = 0.50 A

Big Ideas

A changing field through a coil induces current
Reverse the change: reverse the current
No change: no current
Φ = BA and ε = N ΔΦ / Δt

Back to the essential question: a magnet makes electricity when its magnetic field through a coil changes, for example when the magnet moves in or out. The changing field induces a voltage and a current, and the induced voltage is ε = NΔΦ/Δt, so more turns, a stronger magnet, or faster motion means more current. Next up, we’ll see how motors and generators put magnetic forces and induction to work.