Faraday's Law Calculator
Find the induced EMF from a changing magnetic flux.
A changing magnetic flux through a coil induces a voltage — the basis of generators.
How the Math Works
Faraday's Law of electromagnetic induction reveals how a changing magnetic field generates an electric voltage. The formula EMF = -N * (deltaPhi / deltaT) tells us that the induced electromotive force (EMF) equals the negative of the number of coil turns N multiplied by the rate of change of magnetic flux deltaPhi over time deltaT. The negative sign represents Lenz's Law, ensuring the induced current opposes the flux change causing it. Magnetic flux itself depends on the magnetic field strength, the area it penetrates, and the angle between them. When any of these factors change over time, the law quantifies exactly how much voltage will be produced.
Practical Applications
Engineers use Faraday's Law to design generators, transformers, and induction motors by calculating how much voltage different coil configurations will produce under various magnetic field conditions. The formula helps determine optimal number of coil turns and the required rate of magnetic field change to achieve desired output voltages. In transformer design, it predicts how voltage ratios between primary and secondary coils depend on their turns ratio. For medical applications like MRI machines and electromagnetic therapy devices, the law ensures proper current generation in conductive tissues. It's also essential for designing wireless charging systems, where changing magnetic fields must induce sufficient current in receiving coils.
Day-to-Day Use
Faraday's Law makes possible the electricity powering your home, from the generators in power plants that convert mechanical energy into electrical energy to the transformers that adjust voltages for safe household use. Your smartphone's wireless charger relies on this principle, creating current in the phone's coil without physical connections. Electric guitars use electromagnetic pickups that generate signals when guitar strings disturb magnetic fields. Credit card readers, metal detectors, and even the humble dynamo flashlight all operate on this fundamental relationship between changing magnetic flux and induced voltage that Faraday discovered in 1831.
Worked example
200 turns, ΔΦ = 0.05 Wb in 0.1 s → −100 V.
FAQ
What does the negative sign mean?
The induced EMF opposes the flux change that created it.