Theory — Induced Voltage, Inductance, and AC
One of the most useful discoveries in physics is that a changing magnetic field can create, or induce, a voltage. It is the change that matters, not the mere presence of a field. A steady magnetic field through a coil produces no voltage, but a field that grows or shrinks, or a coil that moves or turns, drives a current.
Magnetic flux and Faraday's law
The magnetic flux through a coil measures how much field passes through it, the field strength times the area it threads through. The induced voltage equals the number of turns times how fast that flux changes.
Induced voltage: EMF = N × (change in Φ) / (change in time) = N × A × (ΔB / Δt)
The minus sign in the full statement of the law, Lenz's law, says the induced voltage opposes the change that made it. For calculating sizes we use the magnitude.
Inductance
Inductance is the property by which a coil or circuit opposes changes in its own current by inducing a voltage that resists the change, much as inertia resists changes in motion. A coil with a large inductance reacts strongly to any attempt to change its current. For a long solenoid the inductance depends only on its geometry.
μ₀ = 4π × 10⁻⁷, N = turns, A = cross-section area, ℓ = length
Inductance is measured in henries. A changing current through an inductor induces a voltage across it proportional to how fast the current changes, which is why inductors smooth and oppose sudden current changes in circuits.
The AC generator
Turning a coil steadily inside a magnetic field changes the flux through it smoothly up and down, so the induced voltage rises and falls as a sine wave. This is alternating current, and the device is an electric generator. The faster the coil spins, the larger and more frequent the voltage swings.
Peak voltage: EMF₀ = N × B × A × ω
Change drives it
A steady field gives no voltage. Only a changing flux, from a changing field or a moving coil, induces a voltage.
Inductance opposes change
A coil induces a voltage in itself that resists any change in its current, the electrical version of inertia.
Generators make AC
A coil rotating in a field produces a sinusoidal voltage, the alternating current that runs the power grid.
| Quantity | Relationship | Units |
|---|---|---|
| Magnetic flux | Φ = B A | weber (Wb) |
| Induced voltage | EMF = N A (ΔB / Δt) | volt (V) |
| Inductance | L = μ₀ N² A / ℓ | henry (H) |
| Inductor voltage | EMF = L (ΔI / Δt) | volt (V) |
| Generator peak | EMF₀ = N B A ω | volt (V) |
Apparatus
The equipment a real electromagnetic-induction experiment uses. In the simulation these are modelled for you, but the readings correspond to what each instrument would measure.
Instructions — Running the Virtual Experiment
This is a record, calculate, and compare lab. In each part you set the apparatus, calculate the quantity by hand, enter your value, and only then does the simulation reveal its instrument reading so you can compare. Record every value in your worksheet.
Simulation — The Induction Bench
| N (turns) | A (cm²) | ΔB/Δt (T/s) | Your EMF (V) | EMF actual (V) |
|---|---|---|---|---|
| No rows yet — set the coil, calculate EMF, enter it, and check. | ||||
Coil and changing field
| Target | N | A (cm²) | ℓ (cm) | Your value | Actual |
|---|---|---|---|---|---|
| No rows yet — set the solenoid, calculate, enter, and check. | |||||
Solenoid
| N | B (T) | A (cm²) | f (Hz) | Your EMF₀ (V) | EMF₀ actual (V) |
|---|---|---|---|---|---|
| No rows yet — set the generator, calculate the peak voltage, enter it, and check. | |||||
Rotating coil generator
Team Questions
Example Lab Report
A worked example showing the expected format and the record, calculate, and compare workflow.
Electromagnetic Induction, Inductance, and Alternating Current
Physics | Section: [Your Section] | Date: [Date]
Lab Members: [Names of all members present]
Objective
To describe and calculate induced voltages, to explain and calculate inductance, and to study the alternating voltage of a generator, comparing every calculated value with the simulation.
Part A — Induced Voltage (worked example)
Coil of N = 100 turns, area A = 50 cm² = 0.0050 m², field changing at ΔB/Δt = 2.0 T/s. EMF = N A (ΔB/Δt) = 100 × 0.0050 × 2.0 = 1.0 V. The voltmeter read 1.0 V.
Part B — Inductance (worked example)
Solenoid N = 500, A = 5 cm² = 5.0 × 10⁻⁴ m², ℓ = 0.20 m. L = μ₀ N² A / ℓ = (4π × 10⁻⁷)(500²)(5.0 × 10⁻⁴) / 0.20 = 7.85 × 10⁻⁴ H = 0.785 mH. With ΔI/Δt = 500 A/s, the induced voltage is L(ΔI/Δt) = 7.85 × 10⁻⁴ × 500 = 0.393 V. Both matched the simulation.
Part C — AC Generator (worked example)
N = 50, B = 0.50 T, A = 100 cm² = 0.010 m², f = 60 Hz, so ω = 2π(60) = 377 rad/s. Peak voltage EMF₀ = N B A ω = 50 × 0.50 × 0.010 × 377 = 94.2 V, matching the simulation.
Discussion and Conclusion
Every calculated value agreed with the simulation. A steady field produced no voltage; only a changing flux did. The induced voltage rose with turns, area, and the rate of field change; the solenoid inductance grew with the square of the turns; and the generator produced a sinusoidal voltage whose peak rose with frequency, confirming the principles of induction.