[NOTES/EM-09001]-Electromagnetic Induction

1. What is electromagnetic induction?

• When a magnet is brought near a loop of a conducting wire, an e.m.f. is produced in the circuit and a current flows
• If the circuit is made to move and if the magnet is stationary, there is induced e.m.f. and if the circuit is closed a current will flow. 
• if we have a stationary loop in a magnetic field which is changing with time, again there is an induced e.m.f. and a current flows in the loop.

 In the examples mentioned above, the phenomenon of induction is governed by the following two rules. However, it is known that there are exceptions to the flux rule given below.

2. Laws of electromagnetic induction

Flux of magnetic field The flux of magnetic field \(\vec{S}\) through a surface \(S\) is defined as a surface integral \[\iint_S \vec{B}\cdot \hat{n} dS\] As a simple example, the flux of uniform magnetic field \(\vec{B}\) over a planar loop, see \Figref{em-fig-10009}, the flux is given by \begin{equation} \hat{n}\cdot\vec{B}\times \text{area} = B \cos\theta \times {area} \end{equation} where \(\hat{n}\) is the normal to the loop and \(\theta\) is the angle between the normal and the magnetic field \(\vec{B}\). Lenz's law The Lenz's law states that the current in a circuit, caused by the induced e.m.f., flows in a direction so as to oppose the cause that is producing the induced e.m.f..

Faraday' law of induction --- The flux rule The flux rule gives the magnitude of induced e.m.f. as follows. Induced e.m.f. = - rate of change of flux.