A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
The principles of Faraday's law and Lenz's law underpin some of the most consequential technologies in electrical engineering. Electric generators convert mechanical rotation into alternating EMF by spinning a coil in a magnetic field, producing a sinusoidal voltage whose amplitude depends on the rotation speed, coil area, number of turns, and field strength. Transformers exploit mutual induction between two coils sharing a magnetic core to step voltage up or down according to the turns ratio V_s/V_p = N_s/N_p, enabling efficient long-distance power transmission at high voltage. Eddy currents — loops of induced current in bulk conductors exposed to changing magnetic flux — are exploited in electromagnetic braking (where Lenz's law opposition dissipates kinetic energy as heat) and induction heating, but must be minimized in transformer cores through lamination to reduce energy loss.
Derive the EMF output of a simple AC generator as a function of time, then use the transformer turns-ratio equation to design a step-up and step-down transformer for a given application. Explain qualitatively how electromagnetic braking works using Lenz's law, and why laminated cores reduce eddy current losses.
You already know Faraday's law: a changing magnetic flux through a loop induces an EMF. The applications in this topic are all answers to the question: what happens when you engineer that changing flux deliberately? The three technologies — generators, transformers, and eddy-current devices — each exploit the same law in a different geometry and for a different purpose.
An AC generator creates a continuously changing flux by rotating a coil in a uniform magnetic field. If the coil has area A, N turns, and rotates at angular frequency ω in a field B, the flux through it varies as Φ = NBA cos(ωt). Faraday's law then gives EMF = NBAω sin(ωt) — a sinusoid whose peak value depends on how fast you spin and how large the coil is. The mechanical energy you invest in spinning the coil is converted to electrical energy in the circuit. This is how virtually all electricity is generated at scale: a turbine (steam, water, or wind-driven) spins a coil in a magnetic field. The sinusoidal output is the origin of alternating current.
A transformer uses mutual induction between two coils wound on a shared iron core. Alternating current in the primary coil creates a continuously changing flux in the core, which threads through every turn of the secondary coil. Because the same flux change passes through both coils, Faraday's law applied to each gives V_p = N_p dΦ/dt and V_s = N_s dΦ/dt, yielding the turns ratio V_s/V_p = N_s/N_p. Step up the turns count and you step up the voltage. But energy conservation demands that power in equals power out (neglecting losses): V_p I_p = V_s I_s. So stepping up voltage necessarily steps down current by the same ratio. High-voltage power transmission exploits this — step voltage up to hundreds of kilovolts to reduce current and thus I²R resistive losses in long-distance lines, then step back down before delivery to homes.
Eddy currents arise whenever a bulk conductor moves through a magnetic field or sits in a changing one. The induced EMF drives circulating currents within the conductor itself, and by Lenz's law these currents create forces opposing the motion that caused them. In electromagnetic braking, a metal disc spinning in a magnetic field experiences a retarding torque proportional to its speed — the braking force is smooth and requires no physical contact or wear. In transformer cores the same physics is the enemy: eddy currents waste energy as heat. Engineers combat this by building cores from thin laminated sheets insulated from each other, forcing current paths to be short and resistive. The two faces of eddy currents — useful braking versus wasteful heating — follow from the same physics, and managing them is a central challenge in electrical machine design.