What Is Faraday's Law of Induction?

Faraday's law states that an emf is induced when the magnetic flux linking a circuit changes. The magnitude of the induced emf equals the rate of change of flux linkage, while its direction is described by the negative sign in the equation.

The Reasoning and Mechanism

This is an Additional Higher Level (AHL) concept in IB Physics topic D.4 Induction. The law is written as

$$\varepsilon=-N\frac{\Delta\Phi}{\Delta t}$$

where $\varepsilon$ is the induced emf in volts, $N$ is the number of turns in the coil, and $\Phi$ is the magnetic flux through one turn:

$$\Phi=BA\cos\theta$$

Here, $B$ is magnetic field strength, $A$ is the coil's area, and $\theta$ is the angle between the magnetic field and the normal to the coil. Therefore, flux can change when $B$, $A$, or $\theta$ changes.

The product $N\Phi$ is the magnetic flux linkage. A larger number of turns or a faster change in flux produces a larger induced emf. Constant flux produces no induced emf, even if the flux itself is large.

For example, a 200-turn coil experiences a flux change from $3.0\times10^{-4}\,\text{Wb}$ to zero in $0.020\,\text{s}$:

$$|\varepsilon|=200\left|\frac{0-3.0\times10^{-4}}{0.020}\right|=3.0\,\text{V}$$

The negative sign represents Lenz's law: the induced emf drives a current whose magnetic effect opposes the change in flux that produced it. This is a consequence of conservation of energy, not an instruction to report every emf magnitude as negative.

A common misconception is that magnetic flux alone induces an emf. The correction is that the flux must change with time.

IB Exam Technique

For a calculation, state Faraday's law, calculate the change in flux linkage, divide by the time interval, and include volts. For an Explain question, connect the change in flux to the induced emf and use Lenz's law to determine the current's direction.