Electromotive Force - EMF - Working Principle - Symbol of Electromotive Force - SI Unit of Electromotive Force - Faraday's Laws of EMF Induction - Fleming's Right Hand Rule - Fleming's Flat Hand Rule - Lenz's Law - Dynamically Induced EMF - Statically Induced EMF - Mutually Induced EMF - Self Induced EMF

Electromotive Force (EMF)

Electromotive Force (EMF) is a current produced in conductor through the magnetic field. EMF is the energy per unit area and its SI unit is volt which is equal to one joule per coulomb. If a battery or a DC source which has 3 volts then it means that it has 3 joules of work on each coulomb of charge. EMF is denoted by ε. EMF works on the principle of Faraday's Law of Electromagnetic Induction which states that ‘When a moving conductor is placed between a magnetic field, A force is produced in the conductor named as Electromotive Force (EMF)”. EMF is also known as no load voltage/ on load voltage which is the force to move electrons in any cross-sectional area/conductor and it helps to flow the current in the conductor.

Symbol of Electromotive Force (EMF)

Electromotive Force (EMF) is denoted by ε. The Symbol of Electromotive Force is also ε. It is also called epsilon.

SI Unit of Electromotive Force (EMF)

Electromotive Force (EMF) is measured as energy per unit area and its SI unit is volt which is equal to one joule per coulomb. If a battery or a DC source which has 3 volts then it means that it has 3 joules of work on each coulomb of charge.

Let's read about Faraday's law of electromagnetic induction.

Faraday’s law of Electromagnetic Induction

Faraday’s law of electromagnetic induction is about magnetic field and it proves that an EMF is produced in a moving conductor when placed it in a magnetic field. Faraday’s law of electromagnetic induction is further divided into two laws:

Faraday’s First Law of Electromagnetic Induction

Faraday’s first law of electromagnetic induction states that “When a conductor cuts a magnetic flux, an EMF is induced in that conductor.” A Simple loop generator/loop generator is based on this law of electromagnetic induction.

Faraday’s Second Law of Electromagnetic Induction
Faraday’s second law of electromagnetic induction states that “The magnitude of generated EMF in a conductor (wire) is equal to the rate of change of flux linkage.”

The conversion of mechanical energy into electrical energy is based on the faraday’s first law of electromagnetic induction and this law is used in the construction of DC Generator. Without this law, DC Generator is not capable to convert mechanical energy to DC Electrical Energy.

Production of EMF

As shown in figure that a coil is connected across the galvanometer and a stationary magnet is placed in space and when we move the stationary magnet inside the coil and we move the stationary magnet inward and outward between the coil so the deflection is produced in galvanometer scale. This deflection states that an EMF is produced in the coil when we move inward and outward between the coil continuously. In this process. A magnetic field is produced across a coil due to the movement of the coil and due to the magnetic field and the continuous movement of a magnet, a force is produced named as electromotive force (emf) through which the current flows in a coil and the deflection is occurred on the scale of the galvanometer. The amount of the current is minor so that the deflection of the galvanometer is steady and it indicates the sensitive current on its scale. If we increase the material and more space is available then we can produce large amount of current in a coil. It all depends on the size of the material and its quality.

Direction of Induced EMF and the Current Produced in a Coil

The direction of the induced current is found by smearing the Fleming right hand rule, Fleming flat hand rule and by Lenz’s law.

Fleming’s Right Hand Rule

These rules are used on those places where magnetic flux is cutting with any other force and where flux linkage is occurred. The figure below indicates that how Fleming right hand rule works and how to use Fleming right hand rule. This rule is used to measure the direction of EMF in a conductor. In the Fleming right hand rule, the thumb indicates the motion of the conductor, the first finger indicates the direction of magnetic field and the second finger indicates the direction of EMF.

Fleming’s Flat Hand Rule

In the process of Fleming flat hand rule, A right hand is used to indicate the direction of the current and the EMF. This rule is used to measure the direction of EMF in a conductor. In this rule, the flat right hand is held perpendicular between the magnet bars and thumb shows the direction of motion of the conductor and the other fingers shows the direction of the induced EMF. Both methods are very easy and you can implement these methods very easily.

Lenz’s Law

Lenz’s law states that “The effect produced always opposes the cause by which the effect is produced”. By Lenz’s law we can measure the direction of induced emf in a coil. The figure below shows the coil and a magnet and when we insert the north pole of the magnet inside the coil the electric current is produced in it due to the induced EMF and the current moves in anti-clockwise direction and the coils become north pole and attracts the bar magnet. If we insert the south pole of the bar magnet inside the coil then the current flows in clockwise direction and the coil becomes south pole and repels the bar magnet.

Two Types of Induced EMF

The EMF induced in a circuit or loop consist of two Types/methods either dynamically and statically induced EMF. Dynamically induced EMF is used in DC Generators and the statically induced EMF is used in transformers.

Dynamically Induced EMF

Dynamically Induced EMF is defined as “The emf induced in a coil due to relative motion of the conductor and the magnetic field”. In this case, the magnetic field is fixed and the conductor moves and cuts the flux so that the EMF is produced. DC generator works on the principle of dynamically induced emf.

Statically Induced EMF

Statically induced EMF is defined as “The emf induced in a coil due to change of flux linked with it is called Statically Induced EMF.” In this case, the conductor is fixed and the flux changes continuously. Transformer is an example of statically induced emf. Here the windings are stationary and the magnetic field is moving around the conductor and produces EMF. Statically induced EMF is divided into mutually induced EMF and self-induced EMF.

Mutually Induced EMF

In this case of EMF Induction, if we place two coils nearly to each other and one coil is connected to the supply and the other is not connected to any source of current and it is connected with the voltmeter only. When we give the supply to the first coil then it will produce a flux across it and this flux starts linking to the other coil and as a result an EMF is produced in the second coil without any electric connection. The EMF is only produced in the second coil due to the flux linkage. It is also known as mutual inductance.

Self - Induced EMF

In this case, when we change the value of the current in a coil then the flux linked with the coil is changed and due to changing in flux linkage of the coil an EMF is produced in it and this EMF is known as self-induced EMF. It is also known as self-inductance

Production of EMF in Direct Current (DC) Circuit

In dc circuits the emf is gained from the battery and the emf of the battery is defined as the maximum voltage of the battery gained from its terminals. The positive terminal of the battery consists of high potential then the negative terminal. In the figure, the resistance is

connected in series with the battery. The battery provides the emf ε and the resistance provides the resistance r. So, the terminal voltage of the battery is equal to:

Where ε are the open circuit voltage and

are the potential difference across the external resistor R so putting the value of

to calculate the EMF of the circuit

and the current will be equal to

The above equation indicates the current in a DC circuit and it depends on an external resistance and internal resistance.

Measurement OF EMF

To measure the emf we use a device which is named as galvanometer. It is a very sensitive device and it measure a minor amount of current. Emf is the amount of current produced in a conductor or a coil. The procedure is given below:

Connect a coil of wire to the galvanometer
Bring the magnet close to the coil.
If the magnet is held constant on one position no current is flowed through the coil.
If the magnet is moving continuously near to the conductor or coil the deflection is occurred in the scale of the galvanometer and the reading is shown on the scale of the galvanometer and it means that current is flowing through the coil and EMF is induced in the conductor.

Motional EMF

Assume a straight rod or a conductor is moving perpendicular in direction with a constant velocity and external driving force. The electrons present in a conductor face a force

along the length of the conductor which is perpendicular to velocity

and the magnetic flux

. Due to this force the electrons move to the lower end of the conductor and added with each other. The electric field

is produced inside the conductor so that the electrons are added on both ends of the conductor and these electrons are added with each other till the downward magnetic force

is balanced with the upward magnetic force qe

So, the force for balancing the electrons on both ends is:

Then the electric field is produced in a conductor so the potential difference

So, the balancing equation is

If the direction of the motion of the conductor is reversed then the potential difference will also be reversed.

Assume a circuit which consists of a conducting bar of length l is placed perpendicular along the two parallel rails and these rails are connected to the resistor in series on the other end. The magnetic field

is functionated on the circuit perpendicularly. The bar has zero resistance and it is pulled to right with velocity due to applied force and the charges starts moving in the magnetic field which bears a magnetic force along the length of the conducting bar. The magnetic flux of the circuit and the produced motional EMF becomes proportional to each other with the area of the circuit.

The area of the circuit is lx where l is the length of the conducting bar and x is the position of the magnetic bar thus the magnetic flux through the area is:

By using Faraday’s law, we find the Induced Motional EMF

The magnitude of the Induced Current is:

The applied force F_app is equal to the magnetic force F_B.

The power due to the applied force is

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