Faraday's Law
Induced EMF from changing magnetic flux.
Formula
Variables
How it works
Faraday's law says that if the magnetic flux through a loop changes, an electric field is created around the loop and can drive a current. The minus sign is Lenz's law: the induced effect always opposes the change in flux, which is why changing a field can generate usable electrical energy but never from nothing. The factor N appears because a coil with more turns has each turn contributing the same induced EMF, so the voltages add.
When to use it
Use this formula whenever a magnetic field through a loop or coil is changing in time, such as in generators, transformers, induction coils, and eddy-current problems. It is also the starting point for calculating induced voltages in circuits exposed to moving magnets or time-varying fields.
Worked example, step by step
A coil has N = 250 turns. The magnetic flux through each turn changes from 4.0 × 10^-4 Wb to 1.0 × 10^-4 Wb in 0.020 s. Step 1: Find the change in flux. ΔΦ_B = 1.0 × 10^-4 − 4.0 × 10^-4 = -3.0 × 10^-4 Wb Step 2: Use Faraday's law in average form. E = -N(ΔΦ_B/Δt) E = -250 × [(-3.0 × 10^-4) / 0.020] Step 3: Calculate the rate of change of flux. (-3.0 × 10^-4) / 0.020 = -1.5 × 10^-2 Wb/s Step 4: Multiply by the number of turns. E = -250 × (-1.5 × 10^-2) = 3.75 V Final answer: The induced EMF has magnitude 3.75 V, with polarity determined by the direction that opposes the flux decrease.
Common mistakes to avoid
- forgetting the minus sign and therefore giving the wrong induced direction
- using the total magnetic field instead of the change in magnetic flux through the coil
- mixing up flux units (weber) with magnetic field units (tesla)
Did You Know?
Faraday's law of induction turns motion into electricity, powering every generator from dams to wind turbines.
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