Question

Faraday’s law of magnetic induction relates voltage to the change in magnetic flux (ΔΦM) and the time interval (Δt). Based on the observations you have made, what is Faraday’s law? Check your answer with your teacher.

Answer 1

Faraday’s law of induction: the induced emf (voltage) around a closed loop equals the negative rate of change of the magnetic flux through the loop.

Integral (simple) form:
emf = E = − ΔΦM / Δt

For a coil of N identical turns:
E = −N (ΔΦM / Δt)

Definitions:
- ΦM (magnetic flux) = ∫ B · dA (for uniform B and flat area, ΦM = B A cosθ). Units: weber (Wb).
- ΔΦM = change in flux, Δt = time interval over which the change occurs.
- The minus sign is Lenz’s law: the induced emf (and resulting current) produces a magnetic field that opposes the change in the original flux.

Differential (Maxwell) form (optional):
∇ × E = −∂B/∂t

Quick example:
If a 50-turn coil’s flux falls from 0.020 Wb to 0.005 Wb in 0.01 s, E = −50[(0.005 − 0.020)/0.01] = +75 V.

Check this statement and the signs with your teacher to be sure it matches your lab observations.