Faraday's Law Calculator

Faraday's law relates an induced electromotive force to the rate at which magnetic flux linkage changes. For a coil with identical flux through every turn, flux linkage is the number of turns multiplied by flux per turn. The average induced EMF over a time interval equals the negative number of turns times the change in flux divided by elapsed time. Webers per second are volts, so SI inputs produce an answer directly in volts. The negative sign expresses Lenz's law. An induced current, when a closed conducting path exists, produces a magnetic effect that opposes the change that caused it. If positive flux increases under the chosen sign convention, the signed EMF is negative. If it decreases, the signed EMF is positive. Many practical questions ask only for magnitude, so the calculator displays both. The sign is meaningful only after a positive loop direction and flux direction have been defined. Magnetic flux is the surface integral of magnetic field through the coil area. For a uniform field and flat loop it can be written as field strength times area times the cosine of the angle between the field and the surface normal. Flux can therefore change because the field changes, the loop area changes, the coil rotates, or the coil moves through a nonuniform field. This calculator accepts initial and final flux directly, allowing any of those mechanisms to be represented after flux has been determined. The result is an average EMF over the entered interval. An instantaneous voltage requires the derivative of flux linkage and may vary throughout the event. The model assumes every turn links the same flux and ignores winding resistance, inductance, leakage flux, parasitic capacitance, magnetic saturation, and measurement bandwidth. Those effects influence current and transient behavior even when the induced open-circuit voltage follows Faraday's law. Use the calculator for physics problems and first-pass electromagnetic estimates, then apply a time-dependent circuit or field model for detailed design. High induced voltages can be hazardous, so practical coils also require insulation, switching protection, and safe measurement methods.