5cElectromagnetic Induction
Explore how changing magnetic flux induces EMF, how generators produce electricity, and how transformers change voltage levels using Faraday's law.
Electromagnetic induction is how virtually all the world's electricity is generated — from coal plants to wind turbines to hydroelectric dams. Transformers make long-distance power transmission possible.
Lesson Overview
Electromagnetic induction is the process by which a changing magnetic field produces an electromotive force (EMF). In this lesson you will learn to calculate magnetic flux, apply Faraday's law to find the induced EMF, understand how generators convert mechanical energy to electrical energy, and explore how transformers use induction to change voltage levels.
Key Concepts
Magnetic Flux (Φ)
Φ = BA cosθ; the amount of magnetic field passing through a surface; unit: weber (Wb)
Faraday's Law
EMF = −ΔΦ/Δt; a changing flux induces an EMF; the negative sign reflects Lenz's law
Induced EMF
For N turns: EMF = −N(ΔΦ/Δt); more turns → greater induced EMF
Generator
Converts mechanical energy to electrical energy by rotating a coil in a magnetic field, continuously changing flux
Transformer
Uses mutual induction between two coils; V_s/V_p = N_s/N_p; steps voltage up or down
Energy Conservation
Transformers conserve energy: V_p I_p = V_s I_s (ideal transformer)
A rectangular loop of area 0.040 m² is placed in a uniform magnetic field of 0.50 T perpendicular to the loop. Calculate the magnetic flux through the loop.
The magnetic flux through a coil changes from 0.080 Wb to 0.020 Wb in 0.030 s. Calculate the induced EMF.
A coil of 200 turns has a flux change of 5.0 × 10⁻³ Wb in 0.10 s. Find the induced EMF.
A transformer has 100 turns on the primary and 500 turns on the secondary. If the primary voltage is 120 V, what is the secondary voltage?
An ideal transformer steps voltage from 240 V to 12 V. If the secondary current is 5.0 A, what is the primary current?
A loop of area 0.025 m² is in a field of 0.80 T at 30° to the plane of the loop. Find the magnetic flux.
Hint: The angle in Φ = BA cosθ is between B and the area normal vector. If B makes 30° with the plane, it makes 60° with the normal.
The flux through a 50-turn coil drops from 0.12 Wb to 0 in 0.040 s. Find the induced EMF.
Hint: Use EMF = −N(ΔΦ/Δt). ΔΦ = final − initial.
A generator produces a maximum EMF of 170 V at 60 Hz. What is the rms voltage?
Hint: For a sinusoidal AC source, V_rms = V_max / √2.
A step-down transformer reduces 10,000 V to 120 V. If the primary has 5000 turns, how many turns does the secondary have?
Hint: Use V_s/V_p = N_s/N_p and solve for N_s.
Why does a transformer only work with AC, not DC?
Hint: Think about what Faraday's law requires — what must be changing to induce an EMF?
Key Vocabulary
Magnetic Flux (Φ)
The product of the magnetic field component perpendicular to a surface and the area of that surface; Φ = BA cosθ; measured in webers (Wb).
Example: When a loop is perpendicular to a field, flux is maximum; when parallel to the field, flux is zero.
Electromagnetic Induction
The production of an EMF (and hence a current in a closed circuit) by a changing magnetic flux through a conductor.
Example: Moving a bar magnet into a coil induces a current in the coil — the basis of all generators.
Faraday's Law
The induced EMF in a circuit equals the negative rate of change of magnetic flux: EMF = −N(ΔΦ/Δt).
Example: A coil with 100 turns experiencing a flux change of 0.01 Wb/s has an induced EMF of 1.0 V.
Transformer
A device that uses mutual electromagnetic induction between two coils to transfer electrical energy and change voltage levels.
Example: Power companies use step-up transformers to transmit electricity at high voltage (low current) over long distances.
Interactive Practice — 5 Questions
Magnetic flux is measured in which unit?
According to Faraday's law, an EMF is induced when:
A transformer has N_p = 200 and N_s = 50. If V_p = 120 V, what is V_s?
A generator converts:
For an ideal transformer, which quantity is conserved?
Independent Practice
A circular loop of radius 0.10 m is in a 0.60 T field perpendicular to the loop. Calculate the magnetic flux.
The flux through a 100-turn coil changes from 0.050 Wb to 0.010 Wb in 0.020 s. Find the induced EMF.
A step-up transformer has 400 primary turns and 2000 secondary turns. If the primary voltage is 110 V and primary current is 10 A, find the secondary voltage and current (assume ideal).
Explain in your own words why a generator produces alternating current (AC) rather than direct current (DC).
★ A rectangular coil (N = 150 turns, area = 0.020 m²) rotates at 60 rev/s in a 0.30 T field. Derive and calculate the maximum induced EMF using EMF_max = NBAω.
ChallengeCommon Mistakes
Using θ as the angle between B and the plane of the loop in Φ = BA cosθ.
θ is the angle between B and the area normal vector (perpendicular to the loop). When B is perpendicular to the loop, θ = 0° and Φ is maximum.
Forgetting to multiply by N (number of turns) when using Faraday's law for a coil.
For a coil with N turns: EMF = −N(ΔΦ/Δt). Each turn contributes equally to the total induced EMF.
Math Tips
Transformer ratio shortcut: V_s/V_p = N_s/N_p. If N_s > N_p, it's a step-up transformer (higher voltage out). If N_s < N_p, it's step-down.
Units: 1 Wb = 1 V·s = 1 T·m². So ΔΦ/Δt has units of Wb/s = V, confirming EMF is in volts.