Faraday's Laws of Electromagnetic Induction

Faraday distilled his experimental observations into two laws. The First Law (a qualitative law) states that whenever the magnetic flux linked with a closed circuit changes, an emf is induced in it; equivalently, if a conductor cuts across magnetic field lines, an emf is induced between its ends. The Second Law (the quantitative law) states that the magnitude of the induced emf equals the rate of change of the magnetic flux linked with the circuit: $|e| \propto \frac{d\Phi}{dt}$, or $e = K\frac{d\Phi}{dt}$ where K is a constant of proportionality that becomes exactly 1 when e, $\Phi$ and t are all measured in SI units, giving $e = \frac{d\Phi}{dt}$.

Combined with Lenz's law (which fixes the DIRECTION of the induced emf, covered next), the full statement carries a minus sign: $e = -\frac{d\Phi}{dt}$. If the flux linked with a single turn is $\Phi'$, then for a coil of n tightly-wound turns the total flux is $\Phi = n\Phi'$, so the induced emf is $e = -n\frac{d\Phi_B}{dt}$. This relation is often called the 'flux rule': the induced emf equals the (negative of the) rate at which the magnetic flux through a conducting circuit changes. In SI units e is measured in volts and $\frac{d\Phi}{dt}$ in weber per second. …