Question

State Faraday’s law of electromagnetic induction.

Hint:

Faraday’s law explains how a changing magnetic field induces an emf, and is the principle behind electrical generators and transformers.

Answer 1

Step 1: Understanding the concept.
Faraday's law of electromagnetic induction is a fundamental principle that describes how a changing magnetic field induces an electromotive force (emf) in a conductor. The induced emf is the result of a time-varying magnetic flux through the conductor.
Step 2: Faraday’s Law Statement.
Faraday's law states that the induced emf in any closed loop is proportional to the rate of change of magnetic flux through the loop. Mathematically, it is expressed as: \[ \mathcal{E} = - \dfrac{d\Phi_B}{dt} \] where: - \( \mathcal{E} \) is the induced emf, - \( \Phi_B \) is the magnetic flux, - \( \dfrac{d\Phi_B}{dt} \) is the rate of change of the magnetic flux. The negative sign indicates that the direction of the induced emf opposes the change in magnetic flux, as described by Lenz's Law. Step 3: Explanation of magnetic flux.
Magnetic flux \( \Phi_B \) is given by the product of the magnetic field \( B \) and the area \( A \) through which the field lines pass, as well as the cosine of the angle \( \theta \) between the magnetic field and the normal to the surface: \[ \Phi_B = B \cdot A \cdot \cos(\theta) \] Step 4: Conclusion.
Faraday's law forms the basis for many electrical devices, including transformers and electric generators. It explains how mechanical energy can be converted into electrical energy through electromagnetic induction.