# What is Faraday’s Law? Laws of Electromagnetic Induction

**Faraday’s Law of Electromagnetic Induction**

Table of Contents

**Electromagnetism**

The interaction between magnetic field and electric current is termed electromagnetism. Current carrying conductors produce a magnetic field when current passes through it. The movement of electrons in a conductor will result in electric current (drifted electrons) which occurs as a result of the EMF set up across the conductor.

The EMF set up across the conductor can be in the form of that stored in chemical energy or a magnetic field. Current carrying conductors placed in a magnetic field will experience mechanical force while a conductor placed in a magnetic field will have its electrons drifted which will result in electric current.

**Field Flux**

Two magnets of unlike poles will attract each other while magnets of like poles will repel each other (so it is with electric charges). Every magnet is surrounded by a force field and is represented by imaginary lines emanating from the north pole of a magnet going into the south pole of the same magnet.

Read the important terms related to Field Flux and Magnetic Filed with formulas Here

**Electromagnetic Induction**

Electromagnetic induction is a phenomenon that explains how EMF and current is or can be induced in a coil when a coil and a magnetic field interact. This phenomenon “electromagnetic induction” is explained by Faraday’s laws of electromagnetic induction. The direction of induced EMF in a coil or inductors is explained by Lenz’s law and Fleming’s right hand rule.

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**Faraday’s Laws of Electromagnetic Induction**

After Andre Marie Ampere (A French mathematician and physicist known as the father of electromagnetism) and others investigated the magnetic effect of current, Michael Faraday tried the opposite. In the course of his work he discovered the principle of electromagnetic induction in 1831 that when there was change in a magnetic field in which a coil or an inductor was placed, EMF was induced in the coil.

This happened only whenever he moved either the coil or the magnet he used in the experiment. EMF was induced in the coil only when there was change in the field flux (if the coil is fixed, moving the magnet towards or away from the coil causes EMF to be induced). Thus Faraday’s laws of electromagnetic induction states as follows;

**Faraday’s First Law**

Faraday’s first law of electromagnetic induction states that “EMF is induced in a coil when there is a change in the flux linking to the coil”.

In other words, whenever the flux associated or linked with a circuits is changed. an E.M.F is induced in the circuit. This EMF lasting only so long as the change is taking place. The induced E.M.F varies as the rate if change of flux.

**Faraday’s Second Law**

Faraday’s second law of electromagnetic induction states that “the magnitude of induced EMF in a coil is directly proportional to the rate of change of flux linking to the coil”.

In other words, the E.M.F induced in an electric circuit is proportional to the time rate of change of the flux of magnetic induction linked with the circuit. The magnitude of the induced E.M.F is directly proportional to the rate of change of current. In short, The more of flux linkage to the coil or conductor, the more of Induced E.M.F (dΦ/dt).

Faraday’s laws of electromagnetic induction can be written mathematically in the form of equation as follows.

**e = N dΦ/dt**

Where

- e = Induced EMF
- N = the number of turns
- dΦ = Change in flux
- dt = Change in time

**Formula & Equation of Faraday’s Law of Electromagnetic Induction:**

Suppose a coil contains on “N” numbers of turns and the flux changes from initial value “Φ_{1}” to the final value “Φ_{2}” in time “t” seconds. Keep in mind that the flux linkage is the multiplication of linked flux to the number of turns in the coil. i.e.

Initial flux linkages = NΦ_{1}

Final flux linkage = NΦ_{2}

Induced EMF

e = NΦ_{1} – NΦ_{2} / t … wb/s or volt

∴ Induced EMF “e” equation converted to the differential form

e = d/dt (NΦ) … volts

e = N (dΦ/dt) … volt

Here, the rate of change in flux (dΦ) occurs in less possible time (dΦ). The minus symbol “-” at the right side of the equation shows that the induced EMF drive the current in such a direction where it opposes its magnetic effect which produced itself the EMF. In simple words, The induced EMF oppose the cause (change in current or motion) which produce it (EMF). This phenomena is also known as Lenz’s Law.

**e = – N (dΦ/dt) … volt**

Finally, this formula shows that the EMF induced in a coil is equal to the rate of change in flux (dΦ/dt) times number of turns (N) in that coil. i.e.

**e = N (dΦ/dt) … volt**

*Related Post: Lenz’s Law of Electromagnetic Induction*

**Explanation and Working of Faraday’s Law**

The following figure shows the different working scenarios of Faraday’s law.

Fig 1.A shows that as magnet moves to the right, magnetic field is changing with respect to the coil, and EMF is induced.

Fig 1.B shows that as magnet moves more rapidly to the right, magnetic field is changing more rapidly with respect to the coil and a greater EMF is induced.

Fig 2.A shows that magnet moves through coil and induces an EMF.

Fig 2.B shows that magnet moves at the same rate through a coil with more turns (loops) and induces a greater EMF.

The fig 2 shows the basic demonstration of the second law of faraday i.e. the amount of induced EMF is directly proportional to the number of tunes in the coil.

**Applications of Faraday’s Law**

The most powerful law of electromagnetic induction by Michael Faraday is used different applications such as electric machines, medical fields, industries etc. Some of them are as follows.

- Electrical transformers (power and distribution t/f), induction motors, generators and alternators (to generate electricity) are based on mutual induction i.e. faraday’s law.
- The working and operation of electromagnetic flow meter and induction cooker is based on faraday’s law of electromagnetism.
- It is also used in Maxwell’s equation based on lines of force.
- Faraday’s law is also applicable in entertainments and musical instruments e.g. electric piano, violin and electric guitar etc.
- Magnetic induction based on faraday’s law used in electric & hybrid vehicle and transcranial magnetic stimulation.
- Computer HD (hard drives) & graphic tablets operates on magnetic induction which is based on faraday’s law.

**Solved Example on Faraday’s law of Electromagnetism**

**Example:**

Apply faraday’s law to find the induced voltage or EMF across a coil with 100 turns that is located in a magnetic field and that is changing at a rate of 5 wb/s.

**Solution:**

Given data:

- Number of Turns = 100
- Magnetic field changing rate = 5 wb/s.

Putting the values in faraday’s law equation

e = N (dΦ/dt)

e = 100 x (5)

e = 500V.

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