Final answer:
Faraday's law describes how a changing magnetic flux induces an electromotive force and an electric field, where the induced current opposes the change in flux. This is the third of Maxwell's equations and includes Lenz's law. Faraday's law is represented in both an integral form, applicable to practical devices, and a differential form, which is a part of Maxwell's fundamental equations of electromagnetism.
Step-by-step explanation:
Faraday's law of electromagnetic induction states that a changing magnetic flux through an area enclosed by a conducting loop induces an electromotive force (emf) in the loop. This law, which is the third of Maxwell's equations, can be expressed in both differential and integral forms and also includes Lenz's law. The latter signifies that the direction of the induced emf and hence the induced current in a closed circuit is such that it opposes the change in magnetic flux that produces it.
The differential form of Faraday's law derives from Maxwell's third equation and can be stated as:
∇ × E = -∂B/∂t
where ∇ × E is the curl of the electric field (E) and ∂B/∂t represents the partial derivative of the magnetic field (B) with respect to time, indicating a time-varying magnetic field.
The integral form of Faraday's law can be expressed as:
∫ E · dl = - dΦ/dt
where the integral of E dot dl around a closed loop (∫ E · dl) is equal to the negative rate of change of the magnetic flux (Φ) through the surface bounded by that loop. This form captures the essence of electromagnetic induction in a way that is easily applied to practical situations such as the design of electrical generators and transformers.