Physics › ⚡ Electricity & Magnetism

Electromagnetic Induction

Drop a magnet through a copper pipe and it falls in slow motion — no batteries required, just change.

AP Physics 2 levelUni Year 1
💡
The big idea: Electricity can be created without touching a single wire to a battery — all it takes is a changing magnetic environment near a loop of wire. Faraday's law tells you how big the resulting push on charges (the EMF) will be, and Lenz's law tells you which way it points. Together they explain everything from bicycle dynamos to the transformers on utility poles.
🎯 By the end, you'll be able to
  • You'll be able to calculate magnetic flux through a loop given field strength, area, and orientation angle.
  • You'll be able to apply Faraday's law to determine the induced EMF from a rate of change of flux.
  • You'll be able to use Lenz's law to predict the direction of an induced current.
  • You'll be able to relate transformer turns ratios to voltage and current changes between primary and secondary coils.
📎 You should already know
  • Magnetic fields and the force on moving charges
  • Basic circuits: current, voltage, and resistance
  • Comfort with rates of change (intro calculus helps but isn't required)

Why does a moving magnet make a light bulb glow?

Drop a magnet through a copper pipe and something strange happens: it falls in slow motion. No batteries, no wires touching the magnet — just motion near a conductor. That's electromagnetic induction, and it's the same physics that turns spinning turbines into the electricity in your wall socket.

The trick isn't the magnet itself. It's change. A stationary magnet sitting near a wire does nothing electrically interesting. It's only when the magnetic environment around a loop of wire is shifting — because the magnet moves, the loop moves, or the field itself grows and shrinks — that nature responds by pushing charges around the loop.

🔑 The core principle: change, not strength

Electromagnetic induction runs on one idea: a changing magnetic flux through a loop induces an electromotive force (EMF) in that loop. It doesn't matter how strong the magnetic field is if it isn't changing — a powerful, steady field induces exactly zero EMF. What matters is how fast the flux is changing.

\[ \Phi_B = B A \cos\theta \]
Magnetic flux measures how much magnetic field passes through a loop of area A, tilted at angle θ from the direction perpendicular to the loop.
\[ \varepsilon = -N \dfrac{d\Phi_B}{dt} \]
Faraday's law: the induced EMF equals the number of turns N times the negative rate of change of flux through each turn. The minus sign encodes Lenz's law.
\[ \dfrac{V_s}{V_p} = \dfrac{N_s}{N_p} = \dfrac{I_p}{I_s} \]
In an ideal transformer, secondary voltage scales with the turns ratio while current scales inversely, keeping input and output power equal.
🎮 Interactive: Induction in a Coil LIVE
Move the magnet or change the field strength and watch the induced EMF and current respond in real time. Notice that current only flows while something is actually changing — freeze the magnet, and the needle drops straight to zero.

Lenz's law: nature is a good accountant

The minus sign in Faraday's law isn't decoration — it's Lenz's law hiding in plain sight. It tells you the induced current always flows in the direction that opposes the change in flux that created it. Push a magnet's north pole into a loop, and the loop fights back by generating its own north pole facing the incoming magnet, resisting the motion.

This isn't the universe being stubborn; it's energy conservation in action. If the induced current helped the change along instead of opposing it, you'd get a magnet accelerating on its own, building energy from nothing. Lenz's law means you always have to do work — push the magnet, spin the turbine, spin the generator shaft — to get induced current out. That's the whole reason power plants need a fuel or water source to turn a generator in the first place.

📝 Worked example: A flat circular coil with 200 turns and a cross-sectional area of 0.050 m² sits with its plane perpendicular to a magnetic field. The field increases uniformly from 0.20 T to 0.80 T over 0.40 s. Find the magnitude of the induced EMF.
  1. Since the coil's plane is perpendicular to \(B\), \(\cos\theta = 1\), so \(\Phi_B = BA\) for each turn.
  2. Find the change in flux per turn: \(\Delta\Phi_B = \Delta B \cdot A = (0.80 - 0.20)\,\text{T} \times 0.050\,\text{m}^2 = 0.030\,\text{Wb}\).
  3. Apply Faraday's law with \(N = 200\) turns: \(\varepsilon = N\dfrac{\Delta\Phi_B}{\Delta t} = 200 \times \dfrac{0.030\,\text{Wb}}{0.40\,\text{s}}\).
  4. Compute: \(\varepsilon = 200 \times 0.075\,\text{V} = 15\,\text{V}\).
✓ 15 V
📝 Worked example: A step-down transformer has 500 turns on its primary coil and 100 turns on its secondary coil. The primary is plugged into a 120 V outlet and draws 2.0 A. Assuming an ideal transformer, find the secondary voltage and the secondary current.
  1. Use the turns ratio for voltage: \(\dfrac{V_s}{V_p} = \dfrac{N_s}{N_p} = \dfrac{100}{500} = 0.20\).
  2. Solve for secondary voltage: \(V_s = 0.20 \times 120\,\text{V} = 24\,\text{V}\).
  3. An ideal transformer conserves power, so \(V_p I_p = V_s I_s\).
  4. Solve for secondary current: \(I_s = \dfrac{V_p I_p}{V_s} = \dfrac{120\,\text{V} \times 2.0\,\text{A}}{24\,\text{V}} = 10\,\text{A}\).
✓ Secondary voltage = 24 V; secondary current = 10 A
⚠️ Common trap: 'strong field' is not the same as 'changing field'

A frequent mix-up is assuming a strong, unchanging magnetic field should induce a large EMF because the field is powerful. It won't — a coil sitting motionless in a huge but constant field induces nothing at all, because \(d\Phi_B/dt = 0\). Another trap: forgetting the number of turns, N. Ten turns of wire experience the same flux change as one turn but multiply the induced EMF by ten — exactly why generators and transformers use tightly wound coils rather than single loops.

Check your understanding

1. What quantity does Faraday's law say induces an EMF in a loop?
Faraday's law states EMF is proportional to the rate of change of flux, \(d\Phi_B/dt\) — not the field strength or area by themselves, and not a static direction.
2. According to Lenz's law, the direction of an induced current is such that it:
Lenz's law says the induced current creates its own magnetic field that opposes the change in flux — a direct consequence of conservation of energy.
3. A single loop of wire (N = 1) with area 0.020 m² sits perpendicular to a magnetic field that increases uniformly from 0.10 T to 0.50 T in 0.20 s. What is the magnitude of the induced EMF?
\(\Delta\Phi_B = \Delta B \cdot A = 0.40\,\text{T} \times 0.020\,\text{m}^2 = 0.008\,\text{Wb}\). Then \(\varepsilon = \Delta\Phi_B/\Delta t = 0.008\,\text{Wb}/0.20\,\text{s} = 0.04\,\text{V}\).
4. A bar magnet is held perfectly still inside a coil of wire. Is there an induced EMF?
Induction requires a changing flux. A stationary magnet produces a constant flux through the coil, so no EMF is induced no matter how strong the field is or how many turns the coil has.
✅ Key takeaways
  • Magnetic flux, \(\Phi_B = BA\cos\theta\), measures how much field 'passes through' a loop — it depends on field strength, area, and orientation.
  • Faraday's law, \(\varepsilon = -N\,d\Phi_B/dt\), says the induced EMF depends only on how fast the flux is changing, never on how strong the field is if it's constant.
  • Lenz's law fixes the direction: induced currents always oppose the change that created them, which is exactly why induction never gives you energy for free.
  • Generators turn mechanical motion into changing flux (and EMF); transformers use two flux-linked coils to step voltage up or down according to their turns ratio.