Electromagnetic Induction

Lesson 2 of 3: Magnetism

In this lesson:

• Faraday's Law:
• Magnetic flux:
• Lenz's Law — direction of induced current

Learning Objectives for This Lesson

1. State Faraday's Law; explain electromagnetic induction
2. Define magnetic flux:
3. Apply Lenz's Law to find induced current direction
4. Explain how EMF depends on rate of flux change
5. Describe conditions required for electromagnetic induction
6. Connect Faraday's Law to generators and transformers

Faraday's 1831 Discovery of Induction

Needle deflects only when the magnet moves — not when it's stationary.

Defining Electromagnetic Induction and EMF

• A changing magnetic flux through a conducting loop induces an EMF
• The induced EMF drives a current in the loop — no battery needed
• Faraday's Law:

Key insight: It is the change in flux — not the flux itself — that induces EMF.

The "Change" is the Key

Generators: The Big Picture Explained

Every power plant uses electromagnetic induction:

• Coal, gas, nuclear → steam → turbine spins coil in B field
• Hydroelectric → water → turbine spins coil in B field
• Wind → blades spin coil in B field

The generator principle is universal.

Quick Check: Predict Induction from Motion

A strong bar magnet sits inside a conducting loop.

The magnet is not moving. Does induction occur? Why or why not?

Magnetic Flux:

• = magnetic field magnitude (T), = area of loop (m²)
• = angle between and the normal to the loop surface
• SI unit: weber (Wb) = T·m²

Intuition: Flux = "how many field lines pass through the loop"

Three Angle Cases for Flux

• : B perpendicular to loop → (maximum)
• : B parallel to loop surface →

Three Ways to Change Flux

1. Change — move a magnet near the loop
2. Change — stretch or compress the loop
3. Change — rotate the loop in the field

Each induces EMF: .

Rotating a loop ( changing) is the basis of AC generators.

Worked Example: Calculate Magnetic Flux

m², T

Worked Example: Induced EMF from Rotating Loop

, s, T, m²

Quick Check: How Does Flux Change?

is parallel to the surface of a conducting loop.

What is the magnetic flux through the loop?

Think about the angle between B and the loop normal.

Lenz's Law: Opposing the Change

The induced current flows in the direction that opposes the change in flux that caused it.

• Flux increasing → induced current creates B that opposes the increase
• Flux decreasing → induced current creates B that reinforces the existing flux

Why Lenz's Law Must Oppose — Energy Conservation

If induced current reinforced the change:

• Increasing flux → larger induced current → stronger reinforcing field → even larger flux → runaway!
• Perpetual motion machine — violates conservation of energy

Nature requires opposition: the induced current always costs energy to maintain, preventing runaway feedback.

Lenz's Law: Magnet Approaching Coil

Flux increasing → induced B opposes → induced current creates opposing field

Worked Example: Receding Magnet Direction

N pole pulled away from the right end of a coil.

• Flux through coil: decreasing
• Lenz's Law: induced current must maintain the flux
• Induced B inside coil must point right (same as the receding magnet's field)
• Induced current flows clockwise when viewed from the right

Induction Conditions — Quick Summary

Quick Check: Apply Lenz's Law Here

Flux through a loop is decreasing.

• In which direction does the induced B point relative to the existing B?
• What rule did you use?

Real Applications of Faraday's Law

• Wireless charging: changing B from charging pad induces EMF in phone coil
• Metal detectors: loop sends AC field; metal object's induced currents detected
• Induction cooking: changing B induces currents directly in the pot, heating it
• Transformers: AC primary → changing B → induced EMF in secondary

Practice Problems: Induction Scenarios Solved

For each: (1) Does induction occur? (2) If yes, what changes?

1. Stationary bar magnet inside a loop of wire
2. A loop moving away from a bar magnet
3. A loop rotating in a uniform magnetic field
4. Constant DC current in a wire next to a loop

Key Takeaways: Induction and Faraday's Law

✓ — rate of flux change drives EMF

✓ — flux depends on field, area, and angle

✓ Lenz's Law: induced current opposes the change in flux (energy conservation)

Watch Out: Avoid These Three Errors

Strong B field ≠ large EMF — it's rate of change that matters.

Lenz's Law opposes the change in flux, not the current that caused it.

Induction doesn't require physical motion — a stationary loop in a changing B field also induces EMF.

What Comes Next: Motors and Generators

sec-20-3: Motors, Generators, and Transformers

• Motor: current loop in B → torque → rotation (sec-20-1 revisited)
• Generator: rotation → changing flux → EMF (Faraday's Law applied)
• Transformer: AC primary → changing B → induced EMF in secondary

All three are applications of today's induction principles.