What is Faraday's law of electromagnetic induction?

Faraday's law states that a changing magnetic flux through a coil induces an electromotive force (EMF). The magnitude is EMF = N × |dΦ/dt|, where N is the number of turns and dΦ/dt is the rate of flux change. The negative sign (EMF = -N × dΦ/dt) reflects Lenz's law: the induced EMF opposes the change that caused it.

What is magnetic flux (Φ)?

Magnetic flux (Φ) is the total magnetic field (B) passing through a surface area (A): Φ = B·A·cos(θ), where θ is the angle between the field and the normal to the surface. The SI unit is the weber (Wb), equivalent to volt-second (V·s).

What does dΦ/dt mean?

dΦ/dt is the time-derivative of magnetic flux — how fast the flux changes over time. Its SI unit is Wb/s, which is equivalent to volts (V). A larger dΦ/dt produces a larger induced EMF.

What is the significance of the negative sign?

The negative sign encodes Lenz's law: the induced current flows in a direction that creates a magnetic field opposing the change in flux. This is a consequence of energy conservation — the induced EMF resists the very change causing it.

What are the units of induced EMF?

The induced EMF is measured in volts (V). Since N is dimensionless and dΦ/dt is in Wb/s = V, the product N × dΦ/dt has units of volts.

How does the number of turns affect the induced EMF?

The induced EMF is directly proportional to the number of turns N. Doubling N doubles the EMF, which is why transformers and generators use many-turn coils to achieve high voltages from modest flux changes.

Can the induced EMF be zero?

Yes. If the magnetic flux is constant (dΦ/dt = 0), no EMF is induced regardless of how strong the field is. Induction only occurs when the flux is changing — for example, when the coil moves, rotates, or the field strength varies over time.

Faraday's Law Calculator

Name: Faraday's Law Calculator
Availability: InStock
Author: Nham Vu

Enter the number of coil turns and the rate of magnetic flux change to calculate the induced EMF using Faraday's law (EMF = -N × dΦ/dt).

Inputs

EMF = −N × dΦ/dt

Number of Turns (N)

turns

Positive integer — the total number of loops in the coil.

Rate of Flux Change (dΦ/dt)

Wb/s

Positive = flux increasing; negative = flux decreasing.

Quick Reference

Formula: EMF = −N × dΦ/dt
N: Number of coil turns (dimensionless)
dΦ/dt: Rate of flux change (Wb/s = V)
EMF unit: Volts (V)
Negative sign: Lenz’s law (opposes change)

Enter values on the left and click Calculate to see the induced EMF.

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Summary

Enter the number of coil turns and the rate of magnetic flux change to calculate the induced EMF using Faraday's law (EMF = -N × dΦ/dt).

How it works

Enter the number of turns (N) in the coil — a positive integer such as 100.
Enter the rate of magnetic flux change (dΦ/dt) in webers per second (Wb/s = V).
Click Calculate; the tool applies EMF = -N × (dΦ/dt) and displays the result.
Review the result panel for the induced EMF magnitude, sign, and a step-by-step equation breakdown.
Use the Copy Result button to copy all values to your clipboard.
Click Reset to clear all fields and start a new calculation.

Use cases

Calculate the induced voltage in a transformer coil from a known flux variation.
Solve electromagnetic induction problems in physics and electrical engineering courses.
Determine the EMF generated by a rotating coil in a magnetic field.
Verify hand-calculated Faraday induction results for lab reports or homework.
Analyze generator design by exploring how turn count affects induced voltage.
Understand Lenz's law by observing the sign of the induced EMF relative to flux change.
Estimate induced voltage in inductive sensors and pick-up coils.
Prepare for AP Physics, university electromagnetics, or engineering electromagnetics exams.

Frequently Asked Questions

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Last updated: 2026-05-28 · Reviewed by Nham Vu