Faraday’s Laws of Electromagnetic Induction

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When a changing magnetic field links to a conductor or coil, an EMF is produced in the conductor or coil, this phenomenon is known as electromagnetic induction. The electromagnetic induction is the most fundamental concept used to design the electrical machines.

Michael Faraday, an English scientist, performed several experiments to demonstrate the phenomenon of electromagnetic induction. He concluded the results of all experiments into two laws, popularly known as Faraday’s laws of electromagnetic induction.

Faraday’s First Law

Faraday’s first law of electromagnetic induction provides information about the condition under which an EMF is induced in a conductor or coil. The first law states that −

When a magnetic flux linking to a conductor or coil changes, an EMF is induced in the conductor or coil.

Therefore, the basic need for inducing EMF in a conductor or coil is the change in the magnetic flux linking to the conductor or coil.

Faraday’s Second Law

Faraday’s second law of electromagnetic induction gives the magnitude of the induced EMF in a conductor or coil and it may be states as follows −

The magnitude of the induced EMF in a conductor or coil is directly proportional to the time rate of change of magnetic flux linkage.

Explanation

Consider a coil has N turns and magnetic flux linking the coil changes from $\mathit{\phi _{\mathrm{1}}}$ weber to $\mathit{\phi _{\mathrm{2}}}$ weber in time t seconds. Now, the magnetic flux linkage ($\mathit{\psi }$) to a coil is the product of magnetic flux and number of turns in the coil. Therefore,

$$\mathrm{\mathrm{Initial\: magnetic\: flux\: linkage,}\mathit{\psi _{\mathrm{1}}}\:=\:\mathit{N\phi _{\mathrm{1}}}}$$

$$\mathrm{\mathrm{Final\: magnetic\: flux\: linkage,}\mathit{\psi _{\mathrm{2}}}\:=\:\mathit{N\phi _{\mathrm{2}}}}$$

According to Faraday’s law of electromagnetic induction,

$$\mathrm{\mathrm{Induced\: EMF,}\mathit{e}\propto \frac{\mathit{N\phi _{\mathrm{2}}}-\mathit{N\phi} _{\mathrm{1}}}{\mathit{t}}\cdot \cdot \cdot (1)}$$

$$\mathrm{\Rightarrow \mathit{e}\:=\:\mathit{k}\left ( \frac{\mathit{N\phi _{\mathrm{2}}}-\mathit{N\phi} _{\mathrm{1}}}{\mathit{t}} \right )}$$

Where, k is a constant of proportionality, its value is unity in SI units.

Therefore, the induced EMF in the coil is given by,

$$\mathrm{\mathit{e}\:=\:\frac{\mathit{N\phi _{\mathrm{2}}}-\mathit{N\phi} _{\mathrm{1}}}{\mathit{t}}\cdot \cdot \cdot (2)}$$

In differential form,

$$\mathrm{\mathit{e}\:=\:\mathit{N}\frac{\mathit{d\phi }}{\mathit{dt}}\cdot \cdot \cdot (3)}$$

The direction of induced EMF is always such that it tends set up a current which produces a magnetic flux that opposes the change of magnetic flux responsible for inducing the EMF. Therefore, the magnitude and direction of the induced EMF in the coil is to be written as,

$$\mathrm{ \mathit{e}\:=\:\mathit{-N}\frac{\mathit{d\phi }}{\mathit{dt}}\cdot \cdot \cdot (4)}$$

Where, the negative (-) sign shows that the direction of the induced EMF is such that it opposes the cause that produces it, i.e., the change in the magnetic flux, this statement is known as Lenz’s law. The equation (4) is the mathematical representation of Lenz’s law.