Faraday's Law Calculator

Faraday's law states that the induced EMF in a coil of $$N$$ turns is equal to the negative rate of change of magnetic flux through the coil:

$$\varepsilon = -N \frac{d\Phi_B}{dt}$$

For a discrete (average) calculation over a finite time interval:

$$\varepsilon = -N \frac{\Delta\Phi}{\Delta t}$$

where $$\Delta\Phi = \Phi_{final} - \Phi_{initial}$$ is the change in magnetic flux (in webers, Wb) and $$\Delta t$$ is the time interval (in seconds).

The magnetic flux through a single loop is $$\Phi_B = BA\cos\alpha$$ where $$B$$ is the field strength, $$A$$ is the loop area, and $$\alpha$$ is the angle between the field and the area normal. Any change in $$B$$, $$A$$, or $$\alpha$$ produces a changing flux and therefore an induced EMF.

The negative sign (Lenz's law) indicates that the induced EMF opposes the change that produces it — a fundamental consequence of energy conservation. If the flux is increasing, the induced current creates a magnetic field opposing the increase; if decreasing, the current supports the field.

The magnitude of the EMF is proportional to both the number of turns $$N$$ and the rate of flux change. More turns and faster changes produce larger voltages — this is why transformers use many turns and AC power operates at specific frequencies.

Induced EMF (|ε|) shows the magnitude of the voltage generated across the coil terminals. EMF with Sign (ε) includes the Lenz's law negative sign — a negative value means the EMF opposes an increasing flux, while positive means it supports a decreasing flux. Rate of Flux Change (dΦ/dt) shows how quickly the flux is changing in Wb/s. Note that 1 Wb/s = 1 V, so this rate directly gives the per-turn EMF contribution.