Induced EMF Calculator (Faraday's Law)
Calculate the induced EMF from changing magnetic flux (Faraday's law) or from motional EMF (B·L·v).
Essential for generator and transformer design.
How Induced EMF Is Calculated
Faraday’s Law of Induction states that a changing magnetic flux through a circuit induces an electromotive force (EMF). This is the operating principle behind generators, transformers, and induction cooktops.
Faraday’s Law:
EMF = −N × ΔΦ / Δt
Where:
- EMF = induced voltage in Volts
- N = number of turns in the coil
- ΔΦ = change in magnetic flux in Webers (Wb)
- Δt = time interval in seconds
- The negative sign indicates Lenz’s Law (induced current opposes the change)
For a rotating coil in a magnetic field (generator):
EMF(t) = N × B × A × ω × sin(ωt)
Where:
- B = magnetic field strength (T)
- A = coil area (m²)
- ω = angular velocity (rad/s)
- Peak EMF = N × B × A × ω
Worked Example: A generator coil: 200 turns, area = 0.05 m², B = 0.3 T, rotating at 50 Hz (ω = 314 rad/s):
- Peak EMF = 200 × 0.3 × 0.05 × 314 = 942 V peak
- RMS voltage = 942 / √2 = 666 V RMS
Lenz’s Law Practical Example: Drop a magnet through a copper tube. The falling magnet induces currents in the tube that create a magnetic field opposing the fall — the magnet falls far slower than free-fall. This is the basis of electromagnetic braking in roller coasters, MRI quench protection, and eddy current dynamometers.