What is Faraday's law?

Faraday's law states that a changing magnetic flux through a coil induces an electromotive force (EMF) equal to the negative rate of change of flux linkage: EMF = -N × dΦ/dt.

What is magnetic flux?

Magnetic flux (Φ) is the total magnetic field passing through an area, measured in webers (Wb). Φ = B × A × cos(θ), where B is field strength, A is area, and θ is the angle between B and the surface normal.

Why is there a negative sign?

The negative sign represents Lenz's law: the induced current flows in a direction that opposes the change causing it. This ensures energy conservation. The calculator shows the magnitude (absolute value).

How does this relate to generators and transformers?

Generators use mechanical rotation to change flux through coils, generating EMF. Transformers use alternating current in one coil to create changing flux that induces EMF in a second coil. Both are direct applications of Faraday's law.

Induced Current Calculator

EMF = −N × ΔΦ/Δt

I = EMF / R

Φ = B × A

Faraday’s Law of Electromagnetic Induction

ΔΦ Flux Change

Change in magnetic flux (webers)

Δt Time Interval

N Number of Turns

Coil turns (default 1)

Ω Circuit Resistance

Total loop resistance (for current calc)

Enter flux change and time interval

Induced EMF & Current

Induced EMF
—
V

Induced Current

—

Power

—

Rate of Change

—

Wb/s

Flux Linkage NΦ

—

Wb-turns

Energy

—

Figure 1: A changing magnetic flux through a coil induces an EMF proportional to the rate of change and the number of turns. The induced current depends on the total circuit resistance.

Table of Contents

Fundamentals

What Is Electromagnetic Induction?
Faraday’s Law Formula

Worked Examples

Generator Coil
Transformer Winding
Moving Wire in a Field

Deep Dive

Lenz’s Law
Applications of Induction

Reference

Frequently Asked Questions
Related Circuit Analysis Calculators

What Is Electromagnetic Induction?

Electromagnetic induction is the production of an electromotive force (EMF) across a conductor when it is exposed to a changing magnetic flux. Discovered by Michael Faraday in 1831, it is the fundamental principle behind generators, transformers, induction motors, and many sensors.

When magnetic flux through a coil changes — whether by moving a magnet, rotating the coil, or changing the field strength — an EMF is induced that can drive current through an external circuit. The Magnetic Force on Wire Calculator explores the complementary effect: the force a magnetic field exerts on a current-carrying conductor.

Faraday’s Law Formula

EMF = −N × ΔΦ/Δt
Where N = number of turns, ΔΦ = change in magnetic flux (Wb), Δt = time interval (s).
The induced current: I = EMF / R (where R = total circuit resistance).

The magnitude of the induced EMF increases with more turns, a larger flux change, or a shorter time interval. Faster changes produce higher voltages — this is why generators spin quickly and why transformers use alternating current.

Worked Example — Generator Coil

Given: ΔΦ = 0.5 Wb, Δt = 10 ms, N = 100 turns, R = 10 Ω

EMF = 100 × 0.5/0.01 = 5000 V

I = 5000/10 = 500 A

This represents a powerful generator producing 5 kV from a rapid flux change across 100 turns. In practice, generator output is controlled by field current and rotational speed. The Circuit Current Calculator verifies the current from the generated EMF.

Worked Example — Transformer Winding

Given: ΔΦ = 0.1 Wb, Δt = 5 ms, N = 500 turns, R = 25 Ω

EMF = 500 × 0.1/0.005 = 10,000 V

I = 10000/25 = 400 A

Worked Example — Moving Wire in a Field

Given: ΔΦ = 0.001 Wb (B × L × v × Δt), Δt = 1 ms, N = 1, R = 50 Ω

EMF = 1 × 0.001/0.001 = 1 V

I = 1/50 = 20 mA

A single wire moving through a magnetic field generates a small but measurable EMF. This principle is used in electromagnetic flow meters and velocity sensors.

Lenz’s Law

Lenz’s law states that the direction of the induced current is such that it opposes the change in flux that caused it. If the flux is increasing, the induced current creates a magnetic field opposing the increase. If the flux is decreasing, the induced current supports it. This is nature’s way of conserving energy and is represented by the negative sign in Faraday’s law.

The Magnetic Force Between Wires Calculator demonstrates the related force between current-carrying conductors, which is also a consequence of electromagnetic interaction.

Applications of Induction

Electromagnetic induction powers the modern world: generators convert mechanical energy to electrical, transformers step voltages up and down for efficient transmission, induction cooktops heat pans directly, wireless chargers transfer power through coils, and induction motors drive everything from fans to trains. The Power Dissipation Calculator helps analyse the losses in inductive systems.

Frequently Asked Questions

Does the coil need to move?

No. The flux through the coil must change, but this can happen by moving the coil, moving the magnet, changing the field strength, or changing the coil’s area or orientation. Any method that changes Φ works.

What is flux linkage?

Flux linkage = N × Φ (number of turns times flux). It represents the total flux threading through all turns of the coil. The unit is weber-turns (Wb·turns). EMF equals the rate of change of flux linkage.

Can I induce current with a permanent magnet?

Yes, but only while the magnet is moving relative to the coil. A stationary magnet produces a constant flux, which does not induce any EMF. You must keep the relative motion going to maintain the induced current.

Why do transformers need AC?

Transformers require alternating current because only a changing flux induces EMF in the secondary winding. DC produces a constant flux after the initial transient, so no sustained EMF is induced. This is why DC transformers do not exist (DC-DC converters use switching to create AC internally).

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Last updated: March 2026