Last updated: 2026-07-01

What Faraday's law describes

When the magnetic flux passing through a loop of wire changes, a voltage appears across the ends of that loop. Faraday's law of induction ties the size of that voltage to how fast the flux changes and how many loops share the change. It is one of the foundations of electrical engineering: every generator, transformer, and induction charger works because of it.

The formula

For a coil of N turns, the induced electromotive force (EMF) is:

Here N is the number of turns, ΔΦ is the change in magnetic flux through one turn (in webers), and Δt is the time over which the change happens. The minus sign records the direction set by Lenz's law; the magnitude of the EMF is:

Lenz's law and the minus sign

The minus sign in Faraday's law is Lenz's law in disguise. It says the induced current flows in whatever direction opposes the change that created it. Push a magnet toward a coil and the coil pushes back; pull it away and the coil tries to hold it. This opposition is what makes the energy bookkeeping work — the electrical energy you get out is paid for by the mechanical work done against that resistance. Because the sign only fixes direction, this calculator reports the magnitude of the EMF.

Worked example

A coil of 100 turns sits in a magnetic field. Over 0.1 seconds the flux through each turn changes by 0.02 Wb. Find the induced EMF.

1. Identify the values: N = 100, ΔΦ = 0.02 Wb, Δt = 0.1 s.
2. Apply Faraday's law (magnitude): |ε| = N × ΔΦ / Δt = 100 × 0.02 / 0.1.
3. Compute: |ε| = 100 × 0.2 = 20 V.

So the coil develops a 20 V EMF while the flux is changing.

How to get a larger EMF

The formula shows three independent levers:

• More turns. Doubling N doubles the EMF. This is why coils are wound with many turns of fine wire.
• A bigger flux change. A stronger magnetic field, a larger loop area, or a bigger swing in the angle between them all increase ΔΦ.
• A faster change. The same flux change squeezed into half the time produces twice the EMF, which is why spinning a generator faster raises its output voltage.

Generators and transformers

In a generator, a coil rotates inside a magnetic field. As it turns, the flux through it rises and falls, inducing an alternating EMF — this is how mechanical motion becomes electricity. In a transformer, an alternating current in the primary winding creates a changing flux in a shared iron core; that flux induces an EMF in the secondary winding. The ratio of turns between the two windings sets how much the voltage is stepped up or down, a direct consequence of the N in Faraday's law.

Related calculations

Faraday's law works hand in hand with the quantities that set the flux in the first place: the field around a current-carrying wire, the field inside a solenoid, and the reactance a coil presents to alternating current. Computing the flux for a given field and area is the natural first step before applying the law here.