Question

Express Faraday-Lenz's law of electromagnetic induction in an equation form.

Answer 1

Assume that the magnetic flux across a coil or circuit changes by dΦ_m over time dt. Then, according to electromagnetic induction's second rule of Faraday, the amount of induced emf is

e α `(dΦ_m)/dt` or e = k `(dΦ_m)/dt`

where k is a proportionality constant and dΦ_m dt is the rate of change of magnetic flux associated with the coil. The Weber per second (dΦ_m/dt) and e (the volt) are chosen in SI units such that the constant of proportionality, k, equals unity. By combining Lenz's law of electromagnetic induction with Faraday's law, the induced emf

e = − `(dΦ_m)/dt`

where Lenz's rule specifies the polarity of the induced emf, and the minus sign is added to represent that polarity. In a closed loop, this polarity only establishes the direction of the induced current. The induced emf of a coil with N tightly wound loops will be N times larger than that of a single loop, meaning that

e = `− N (dΦ_m)/dt`

where dΦ_m/dt is the rate of change of magnetic flux through one loop.