Faraday's Law Calculator

Faraday's law of induction states that a voltage is induced in a circuit whenever there is a change in the magnetic flux passing through it. Mathematically, magnetic flux ($̇Φ$) equals the product of the magnetic field ($B$) and the loop area ($A$), expressed as Φ = B × A. The induced voltage ($V$) is then calculated using the equation V = -N × (ΔΦ / Δt), where $N$ represents the number of turns in the coil, and ΔΦ divided by Δt is the rate of change of magnetic flux over time. The negative sign, derived from Lenz's law, indicates the direction of the induced current opposes the change in flux.

Imagine you have a circular wire coil with 50 turns ($N = 50$) and a cross-sectional area of 0.2 square meters ($A = 0.2 \text{ m}^2$). A uniform magnetic field passing perpendicularly through the coil changes from 0.1 Tesla to 0.6 Tesla over a time period of 2 seconds ($Δt = 2 \text{ s}$). First, compute the initial magnetic flux: \(Φ_1 = 0.1 \times 0.2 = 0.02 \text{ Wb}\). Next, compute the final magnetic flux: \(Φ_2 = 0.6 \times 0.2 = 0.12 \text{ Wb}\). The change in magnetic flux (ΔΦ) is \(0.12 - 0.02 = 0.10 \text{ Wb}\). Applying Faraday's law formula, \(V = -50 \times (0.10 / 2) = -50 \times 0.05 = -2.5 \text{ volts}\). The magnitude of the induced voltage is thus 2.5 volts.

Ensure all your input values share consistent SI units before running the calculation—use Teslas for magnetic fields, square meters for areas, and seconds for time. Remember that the negative sign in the calculation denotes polarity rather than scalar magnitude, which is vital when designing inductors or transformers. Double-check whether your magnetic field is perpendicular to the loop area; if it enters at an angle, you must multiply by the sine or cosine of that angle depending on how the loop orientation is defined.