Faraday's law of induction explains how generators, transformers, and induction chargers all work: a changing magnetic flux through a coil induces a voltage, and more turns or a faster change both mean more voltage. This calculator computes that induced EMF three ways — from a known flux change, from a field change over a fixed area, or from a conductor physically moving through a field.
How the Faraday's Law Calculator works
The core relationship is EMF = -N (dPhi/dt): the induced EMF equals the number of turns times the rate at which magnetic flux changes through each turn, with a minus sign from Lenz's law indicating the induced EMF opposes that change. When you know the field change instead of the flux change directly, the calculator uses Phi = B A cos(theta) with the field held perpendicular to the loop (cos(theta) = 1), so dPhi = A dB and EMF = N A |dB| / dt. For a conductor moving through a field rather than sitting in a changing one, the equivalent result is the motional EMF, EMF = B L v — the same underlying physics viewed from the moving conductor's reference frame. All three modes report the EMF magnitude in volts.
Inputs and what they mean
Turns (N) is the number of wire loops in the coil; it multiplies directly into the flux-based results. Change in flux (ΔΦ) and change in field (ΔB) are the total change over the time interval, not a rate — divide by Δt yourself first if you only have an instantaneous rate. Loop area (A) is the area of a single loop, assumed perpendicular to the field. For motional EMF, rod length (L) and velocity (v) assume the rod, field, and velocity are all mutually perpendicular, which is the standard textbook setup and gives the maximum possible EMF for those magnitudes.
Limits and edge cases
A time interval (Δt) of zero is physically meaningless for an average rate of change, so both flux-based tabs require Δt greater than 0. On the Field & Area tab, the calculator uses ΔΦ = A·ΔB·cos(θ), where θ is measured from the loop normal; if area, angle, and field all change together, compute the total flux change directly instead. The motional EMF formula includes sin(θ) for the angle between velocity and field. The optional resistive statistics use Ohm's law and, for the AC generator, RMS voltage over one cycle; inductance, capacitance, and core saturation are excluded.