Electricity and magnetism

Electromagnetic induction, Faraday–Lenz law

An induced emf appears when magnetic flux through a circuit changes: $\\mathcal E=-N\,\,d\Phi_B/dt$.

An induced emf appears when magnetic flux through a circuit changes: $\\mathcal E=-N\,\,d\Phi_B/dt$.

Reading the model

For a flat loop in a uniform field, $\Phi_B=BA\cos\theta$, where $\theta$ is between the loop normal and $\vec B$. For $N$ turns, Faraday’s law gives $\\mathcal E=-N\,\,d\Phi_B/dt$. The minus sign is Lenz’s law: induced current flows so its magnetic field opposes the change in flux that produced it.

For a loop in a uniform field, magnetic flux is $\Phi_B=BA\cos\theta$. An emf can therefore be induced by changing $B$, the loop area, or the angle between its normal and the field. In a generator, rotating the coil makes flux vary periodically. The minus sign in Faraday–Lenz law does not reduce emf magnitude; it encodes the induced direction so that the resulting current’s field opposes the change that produced it.

Flux is measured in webers (Wb) and emf in volts. For $N$ turns, if flux per turn decreases by $3.0\times10^{-3}$ Wb in $0.10$ s, the average emf magnitude is $N|\Delta\Phi_B|/\Delta t$. Determine current direction separately with the right-hand rule after deciding whether it must oppose an increasing or decreasing flux.

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