ElectroHub

Faraday's Law EMF Calculator

A changing magnetic flux through a coil induces a voltage. Nothing needs to touch, and the flux can change because the field changes, the coil moves, or the area does — which between them account for every generator, transformer and inductor ever built.

Faraday's Induction — e = N·ΔΦ/Δt

Average EMF induced in an N-turn coil by a change of flux ΔΦ over a time Δt. Fill any three and leave the unknown blank.

Induced EMF
  1. 1.Formulae = N · ΔΦ / ΔtSubstitutee = 200 × 0.05 ÷ 0.1Resulte = 100 V
Common trap: What induces an EMF is the rate of changeof flux, not the flux itself — a coil sat in a strong but steady field generates nothing. The minus sign in e = −N·dΦ/dt is Lenz's law: the induced current always opposes the change that caused it.

The formula

e = −N × (dΦ / dt)

e
induced EMF (volts)
N
number of turns in the coil
dΦ
change in flux (webers)
dt
time over which it changes (seconds)

Worked example

A 200-turn coil whose flux changes by 0.05 Wb in 0.1 s.

  1. Rate of change: dΦ/dt = 0.05 / 0.1 = 0.5 Wb/s
  2. e = −N × dΦ/dt = −200 × 0.5

100 V, with the minus sign meaning the EMF opposes the change that produced it.

Where you'll use it

Generators, transformers and inductive sensors. The minus sign is Lenz's law, and it is not a formality — it is why a motor draws huge current at standstill and settles down once back-EMF builds.

The laws behind it

Parts this applies to

Inductor / CoilTransformer (power)Current / Potential Transformer (CT/PT)DC MotorSpeaker / MicrophoneRCCB / RCD / GFCICurrent Sensor (Hall / Shunt / CT)LVDT & Displacement Transducers

Related calculators

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