# Faraday’s Law of Electromagnetic Induction

If we consider a closed stationary circuit located in a varying magnetic field, the inducedelectromotive force (e .m.f.) around this circuit is equal to the negative time rate of changeof magnetic flux through the circuit

e=dϕ/dt

whereϕ is the total magnetic flux through the circuit. The negative sign appearing heredefines another law, called Lenz’s law, which indicates that the direction of current opposesthe changes in the flux of B or electromagnetic inertia.

From definition of flux

ϕ=ʃ S B .dS

and since e.m.f. ‘e ‘ is work done per unit charge, we have

In a stationary circuit v = 0 and since v is parallel to dl and v x B is perpendicular to dl.

Thus                            v x B .dl  =0

Hence                          e =ʃ 1E .dl

and finally from equation (2)

This is Faraday’s law written in integral form.

Using Stoke’s law, Faraday’s law can be mentioned in the differential form.

Applying Stoke’s law

Since this is valid for any surface then

Faraday’s law thus establishes that time varying magnetic fields give rise to electric fields. This further supports the fact that the fields are related to each other and we then must speak of electromagnetic fields rather than electric and magnetic fields.