Calculate induced EMF using Faraday's law of electromagnetic induction: ε = −NdΦ/dt. Supports flux, field, and motional EMF modes.
Faraday's law of electromagnetic induction states that a changing magnetic flux through a coil induces an electromotive force (EMF): ε = −NdΦ/dt, where N is the number of turns and Φ is the magnetic flux (in webers) through each turn. The negative sign (Lenz's law) indicates the induced EMF opposes the change that produced it.
Flux change can occur in three ways: changing the magnetic field strength (B), changing the area (A) of the loop, or changing the angle between B and the loop normal. The calculator supports all three: direct flux input, field × area mode (Φ = BA), and motional EMF (ε = BLv for a wire moving through a field).
This fundamental law underpins generators, transformers, inductors, electric motors, induction cooktops, wireless charging, and electromagnetic braking. Every device that converts mechanical energy to electrical energy (or vice versa) relies on Faraday's law. Check the example with realistic values before reporting.
Faraday's law calculations involve flux conversions, time derivatives, turn ratios, and (for the complete circuit) resistance and current. Computing EMF, induced current, power dissipation, and total charge requires careful sign handling and unit management.
This calculator provides three input modes to match different problem types, includes Lenz's law direction indication, and shows how EMF scales with the number of turns. The wire reference table helps in designing real coils. It serves students, electrical engineers, and anyone working with induction machines.
ε = −NΔΦ/Δt. Φ = BA cos θ. Motional: ε = BLv. Current: I = |ε|/R. Power: P = ε²/R. Charge: Q = NΔΦ/R.
Result: EMF = 200 V
ΔΦ = 0 − 0.01 = −0.01 Wb per turn. ε = −1000 × (−0.01)/0.05 = 200 V. With R = 10 Ω: I = 20 A, P = 4000 W.
An electric generator is a direct application of Faraday's law: a coil rotating in a magnetic field experiences a sinusoidally varying flux, inducing an alternating EMF. The frequency equals the rotation rate (for a 2-pole machine) or is multiplied by the number of pole pairs. A 2-pole 3600 RPM generator produces 60 Hz AC; a 4-pole generator achieves 60 Hz at 1800 RPM.
Large power plant generators have hundreds of turns, powerful electromagnets (instead of permanent magnets), and laminated steel cores to minimize eddy current losses. A typical 1 GW generator has a peak flux of ~1 T, core area ~1 m², thousands of turns, and rotates at 3000 or 3600 RPM depending on the grid's 50/60 Hz frequency.
When a conductor moves through a magnetic field, the induced currents (eddy currents) create forces that oppose the motion — this is electromagnetic braking. Unlike friction brakes, electromagnetic brakes produce zero force at zero speed (so they cannot hold a load) but increase braking force with speed. They are used in roller coasters, trains (regenerative braking recovers energy), and laboratory balances.
The braking force is F = B²L²v/R, where R is the effective resistance of the conducting region. Lower resistance means stronger braking (copper plates brake harder than steel). Some high-speed trains use eddy current brakes with no physical contact, eliminating wear and allowing consistent braking from 300+ km/h to 0.
Wireless (inductive) charging is Faraday's law at work: an AC current in the transmitter coil creates an oscillating magnetic field, inducing an EMF in the receiver coil placed nearby. The power transfer efficiency depends on coil alignment, separation distance, operating frequency, and coil quality factors. Modern Qi wireless chargers operate at 100-200 kHz with efficiencies of 80-90% at optimal alignment. Resonant coupling (operating at the coils' resonant frequency) extends effective range and improves efficiency.
It states that the EMF induced in a coil equals the negative rate of change of magnetic flux linkage: ε = −NdΦ/dt. A coil of N turns with flux Φ through each turn has total flux linkage NΦ. Any change in this linkage — whether from changing B, A, or the angle — induces an EMF.
Lenz's law (the minus sign in Faraday's law) states that the induced current flows in a direction that opposes the change causing it. If flux is increasing, the induced current creates a magnetic field opposing the increase. This ensures energy conservation — you must do work to change the flux.
An AC current in the primary coil creates a time-varying magnetic field in the iron core. This changing flux links the secondary coil, inducing an EMF. The voltage ratio equals the turns ratio: V₂/V₁ = N₂/N₁. No relative motion is needed — only a changing current.
When a conductor of length L moves with velocity v through a magnetic field B (all mutually perpendicular), the free charges experience a force F = qv×B, driving them along the wire. The resulting EMF is ε = BLv. This is the principle behind generators and railguns.
Yes — it applies to any closed loop. The integral form is ∮E·dl = −dΦ_B/dt, where the left side is the line integral of the electric field around any closed path. This is one of Maxwell's four equations and applies universally, not just to wire coils.
For a coil of N turns, area A, rotating at angular velocity ω in field B: ε = NBAω sin(ωt). The peak EMF is ε₀ = NBAω. This is an AC generator — the EMF varies sinusoidally. For a 50 Hz generator: ω = 2π × 50 = 314 rad/s.