# Understanding Electromagnetic Induction: Concept, Application, and Example Problems

Electromagnetic induction is a symptom of the emergence of an electric current in an electric conductor due to a change in the magnetic field around the conductor. The concept of electromagnetic induction is based on the discovery of Michael Faraday and Joseph Henry in 1831. A changing magnetic field produces a potential difference called an induced electromotive force and the resulting electric current is called an induced electric current.

## Understanding Electromagnetic Induction

Electromagnetic induction is the occurrence of an electric current due to a change in magnetic flux. Magnetic flux is the number of lines of magnetic force that penetrate a field. A scientist from Germany named Michael Faraday had the idea that magnetic fields can produce electric currents. In 1821 Michael Faraday proved that a changing magnetic field can give rise to an electric current.

Galvanometer is a tool that can be used to determine whether there is an electric current flowing. The electromotive force that arises as a result of changing the number of lines of magnetic force is called an induced emf, while the flowing current is called an induced current and the event is called electromagnetic induction.

Factors that affect the amount of induced emf include:

• The speed of change in the magnetic field, the faster the change in the magnetic field, the greater the induced emf that arises.
• The number of turns, the more turns, the greater the induced emf that arises.
• Magnetic strength. The stronger the magnetic phenomena, the greater the induced emf that arises.

## Electromagnetic Induction Concept

Induction electromotive force is the emergence of an electromotive force in the coil which includes a number of flux lines of magnetic field force, when the number of flux lines of force is varied. In other words, an electromotive force will arise in the coil if the coil is in a magnetic field where the field strength varies with time.

In general, electromagnetic induction is a symptom of the emergence of an electromotive force in a coil or conductor when there is a change in the magnetic flux in the conductor or when the conductor moves relatively across a magnetic field.

When the north pole of a magnet is moved into the coil, the galvanometer needle deviates in one direction (eg to the right). The galvanometer needle immediately returns to zero (does not deviate) when the magnet is placed in the coil for a moment. When the bar magnet is removed, the galvanometer needle will deviate in the opposite direction (eg to the left).

The galvanometer needle deviates due to the current flowing in the coil. An electric current arises because a potential difference arises at the ends of the coil when the bar magnet is moved in or out of the coil. The potential difference that arises is called “Induction Electromotive Force (induced emf)”.

When the bar magnet is moved in, there is an increase in the number of lines of magnetic force that cut the coil (the galvanometer deviates or there is current flowing). When the bar magnet is silent for a moment, the galvanometer needle returns to zero (no current flows). When the bar magnet is removed there is a reduction in the number of lines of magnetic force cutting the coil (the galvanometer deflects in the opposite direction).

So, due to changes in the number of magnetic force lines that cut the coil, a potential difference or induced emf arises at both ends of the coil. An electric current caused by a change in the number of magnetic lines of force cutting a coil is called an induced current.

The magnitude of the induced emf depends on three factors, namely:

• Number of coil turns.
• The speed in and out of the magnet from and out of the coil.
• The strength of the bar magnet used.

## The Law of Electromagnetic Induction

### 1. Faraday’s Law of Electromagnetic Induction

Faraday’s law of induction states that an electric circuit has an induced electromotive force whose value is directly proportional to the speed of change of the magnetic flux surrounding it. The line of magnetic force enclosed by a certain area in a perpendicular direction is defined as the magnetic flux.

Faraday found that induction is very time dependent, that is, the faster the magnetic field changes, the greater the induced emf. On the other hand, the emf is not proportional to the rate of change of the magnetic field B, but is proportional to the rate of change of the magnetic flux, ΦB, moving across a loop of area A, which is expressed mathematically as follows:

Φ = BA cos θ

With B equal to the magnetic flux density, that is, the number of flux lines of magnetic force per unit cross-sectional area penetrated by the lines of force of magnetic flux perpendicular to it, and θ is the angle between B and the line perpendicular to the surface of the coil. If the surface of the coil is perpendicular to B, θ = 90o and ΦB = 0, but if B is parallel to the coil, θ = 0o, so:

ΦB = BA

The coil is a square with side i as wide as A = i2. Line B can be drawn in such a way that the number of lines per unit area is proportional to the field strength. So, the flux ΦB can be considered as proportional to the number of lines passing through the coil. The magnitude of the magnetic flux is expressed in units of webers (Wb) which is equivalent to tesla.meter2 (1Wb = 1 T.m2).

From the definition of the flux, it can be stated that if the flux through the conducting wire loop with N turns changes by ΦB in the time Δt, then the magnitude of the induced emf is: What is known as Faraday’s Law of Induction, which reads: “electromotive force (emf) induces arising between the ends of a conducting loop is directly proportional to the rate of change of the magnetic flux enclosed by the conducting loop. The negative sign in equation (6.3) indicates the direction of the induced emf. If the change in flux (ΔΦ) occurs in a short time (Δt → 0).

### 2. Lenz’s Law of Electromagnetic Induction

If the induced emf is connected to a closed circuit with a certain resistance, an electric current will flow. This current is called the induced current. The induced current and induced emf exist only as long as the changing magnetic flux occurs.

Lenz’s law describes induced currents, which means that it applies only to closed conducting circuits. This law was stated by Heinrich Friedrich Lenz (1804-1865), which is actually a form of the law of the conservation of energy. Lenz’s law states that: “an induced emf always generates a current whose magnetic field is opposite to the origin of the change in flux”.

The change in flux induces an emf which creates a current in the coil, and this induced current creates its own magnetic field. The application of Lenz’s Law is in the direction of the induced current. The magnet is stationary so there is no change in the magnetic flux enclosed by the coil. The main magnetic flux that penetrates the coil in a downward direction will increase when the magnetic north pole is brought closer to the coil. The direction of induction can also be known by applying Lenz’s Law.

## Application of the Concept of Electromagnetic Induction

In electromagnetic induction there is a change in the form of motion energy into electrical energy. Electromagnetic induction is used in the generation of electrical energy. Electrical energy generators that apply electromagnetic induction are generators and dynamos.

Inside the generator and dynamo there are coils and magnets. A rotating coil or magnet causes a change in the number of lines of magnetic force in the coil. These changes cause emf induction in the coil.

The mechanical energy provided by generators and dynamos is converted into rotational motion energy. This causes the induced emf to be generated continuously with a pattern that repeats periodically.

### 1. Electromagnetism

Electromagnetism is a branch of physics that studies the relationship between electric and magnetic fields in electric circuits that produce electromotive forces and electromagnetic fields. The main concept in electromagnetism is electromagnetic induction which is based on Faraday’s law of induction. The principle of electromagnetism is applied to the working systems of transformers, inductors, electric motors, electric generators and solenoids.

### 2. Alternating Current

Alternating current is an electric current whose direction changes periodically. The alternating current curve is represented by a sinusoidal shape. The principle of electromagnetic induction is used as the basis for the formation of alternating currents. Making alternating current in a power plant utilizes a permanent magnetic field that rotates a turbine. Types of power plants that utilize the principle of electromagnetic induction are hydroelectric power plants, coal steam power plants, wind power plants, and nuclear power plants.

### 3. Magnetic Field

Electromagnetic induction can be used to create a magnetic field. The flow of electric current to a conductor will cause a magnetic field which can be calculated based on the Lorentz force. The formation of a magnetic field through electromagnetic induction utilizes the force between two magnets that have been given an electric current. In addition, the creation of a magnetic field through electromagnetic induction is based on the use of the Biot-Savart law and Ampere’s law.

## Practical Applications of Electromagnetic Induction

### 1. Power Generators

An electric generator is a machine that converts kinetic energy into electrical energy. The working principle of an electric generator is based on Faraday’s law of induction. Electric generators can produce two types of electric current, namely direct current and alternating current.

Electric generators that produce direct current are called direct current generators, while generators that produce alternating current are called alternating current generators and direct current generators. The number of glide rings in an electric generator determines the type of electric current it produces. An alternating current generator has two glide rings, while a direct current generator has only one glide ring.

If a coil with N turns is rotated with an angular speed w, then the induced emf generated by the generator is:

ε = BAω.N.sinθ

The induced emf will be maximum if θ = 90 o  or sin θ = 1 , so that:

ε max = BAω.N , so the equation above can be written as:

ε = ε max sin θ

ε = induced emf (Volts); εmax= maximum induced emf (volts)

N = number of coil turns; B = magnetic induction (T); A=area of ​​the coil (m2)

ω = angular velocity of the coil (rad/s); t = time (s); θ = ω.t = angle (o).

### 2. Electric Motors

An electric motor is a machine that converts electrical energy into mechanical energy. The working principle of an electric motor is based on electromagnetism and dynamic electricity. Mechanical energy is obtained from electromagnets which convert electrical energy into magnetism. The motion is produced by means of repulsion and attraction between like and dissimilar magnetic poles.

Changes in the type of energy only occur if the magnet is placed on a shaft that can rotate. This mechanical energy is used for industrial and household purposes. Industry generally uses electric motors in pumps, fans, compressors, and conveyors, while in households, electric motors are used in mixers, drills, and fans.

### 3. Transformer

A transformer or transformer is a device for changing (increasing or decreasing) AC voltage based on the principle of electromagnetic induction, namely transferring electrical energy by induction through the primary coil to the secondary coil. The transformer creates an emf in the secondary coil due to the changing magnetic field due to the flow of alternating electric current in the primary coil which is induced by soft iron into the secondary coil.

There are two types of transformers, namely step-up and step-down transformers. The step-up transformer functions to increase the AC source voltage, the number of turns in the secondary coil is more than the number of turns in the primary. The step-down transformer serves to lower the AC source voltage, the number of secondary windings is less.

If the output terminal voltage is greater than the changed voltage, the transformer used functions as a voltage booster. Conversely, if the output terminal voltage is smaller than the changed voltage, the transformer used functions as a voltage stepper. Thus, the transformer (transformer) is divided into two, namely step-up transformer and step-down transformer.

Step up transformer is a transformer that functions to increase the AC voltage. This transformer has the following characteristics:

1. The number of primary turns is less than the number of secondary turns.
2. The primary voltage is less than the secondary voltage.
3. The primary current strength is greater than the secondary current strength.

Step down transformer is a transformer that functions to lower the AC voltage. This transformer has the following characteristics:

1. The number of primary turns is more than the number of secondary turns.
2. The primary voltage is greater than the secondary voltage.
3. The primary current strength is smaller than the secondary current strength.

## Examples of Electromagnetic Induction Problems

Question:

A coil with 100 turns in 0.01 seconds causes a change in magnetic flux of 10-4 Wb, how much is the induced emf that arises at the ends of the coil?

a. 1 Volt
b. 5 Voltc
. 50 Volt
d. 7.5 Volt
e. 300 Volts

Discussion:

It is known that

N = 100 turns
dΦ /s = 10-4 Wb/ 0.01 s = 10-2 Wb/s
ε = -N (dΦ/dt)
ε = – 100 (10-2)
ε = -1 volt
(sign negative only indicates the direction of the induced current)

So, the total electromagnetic induction emf generated at the ends of the coil is 1 Volt.

## Conclusion

The emergence of an electric force (EMF) on the coil only when there is a change in the number of lines of magnetic force. The electromotive force that arises as a result of changing the number of lines of magnetic force is called an induced emf, while the flowing current is called an induced current and the event is called electromagnetic induction. There are several factors that affect the amount of induced emf, namely:

1. The speed of change of the magnetic field. The faster the magnetic field changes, the greater the induced emf that arises.
2. The number of turns The more turns, the greater the induced emf that arises.
3. Magnetic strength The stronger the magnetic field, the greater the induced emf that arises.

The concept of electromagnetic induction can be applied in technology products such as:

1. Generator is a device that can convert motion energy into electrical energy. The principle used is the change in angle based on Faraday’s law resulting in a change in magnetic flux.
2. A transformer or transformer is a device for changing (increasing or decreasing) AC voltage based on the principle of electromagnetic induction, namely transferring electrical energy by induction through the primary coil to the secondary coil.
3. An inductor is a component whose way of working is based on magnetic induction. The inductor, also known as a spool, is made of thin enameled wire. An inductor is a wire that is wound into a coil. The ability of an inductor to generate a magnetic field is called conductance.

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