# Electromagnetic Induction

Electromagnetic induction is a cool process that generates electrical energy by moving a metal wire through a magnetic field. As the wire moves through the field, it causes the magnetic field to change, which creates an electromotive force. This force can generate a voltage that can be used to power electronic devices.

Magnetic flux is the measurement of the total magnetic field in a certain area. It is the total number of magnetic field lines that cross a specific area. When changes occur in magnetic flux, electrical energy is produced, which generates a voltage or an electromotive force through the conductor.

If you want to learn more about electromagnetic induction, check out our explanation on Emf and Internal Resistance. It's a great way to understand how this process works and how it can be used to power electronic devices.

## The discovery of electromagnetic induction

In 1831, a scientist named Michael Faraday discovered the law of induction. He conducted an experiment using a battery, a galvanometer, a magnet, and a conducting wire, as you can see in figure 1.

Faraday observed that when he disconnected the battery, no electric current was flowing, and no magnetic flux was induced in the magnet. However, when he connected the battery, a wave of electricity flowed through the galvanometer. When he disconnected the battery, the current spiked in the opposite direction before returning to zero.

Faraday continued his experiments and discovered other properties of electromagnetic induction. He observed the same transient currents when he moved a bar magnet quickly through a coil of wires. He even generated direct current by rotating a copper disk next to the bar magnet with a sliding electrical lead.

Faraday summarised his findings using a concept called 'lines of force'. When he closed the switch, the magnetic flux within the magnetic core increased from zero to a maximum value. As the flux increased, an induced current on the opposite side was observed. Similarly, when he opened the switch, the magnetic flux in the core decreased from its maximum value back to zero, inducing an opposite current on the right side.

## Faraday’s law of electromagnetic induction

After observing the outcomes of his experiment, Faraday expressed his observations mathematically. He noticed that the sudden change in the magnetic flux within the magnet increased from zero to a maximum value. As a result, he concluded that a changing magnetic flux in a closed circuit induces an electromotive force or voltage.

Faraday's conclusion is shown in the equation below, where ε represents the electromotive force (measured in volts), Φ represents the magnetic flux in the circuit (measured in weber), N represents the number of turns of the coil, and t represents time (measured in seconds).

From this equation, we can determine the parameters that affect the magnetic field, including a stronger magnet (which affects the magnetic flux), more coils (which affects N), and the speed at which the wire moves. By understanding these parameters, we can better understand electromagnetic induction and how it can be used to generate electrical energy.

### The Maxwell-Faraday equation

The Maxwell-Faraday equation is an important equation in electromagnetism that relates changes in the magnetic field to changes in the electric field. This equation states that a time-changing magnetic field creates a spatially varying electric field and vice versa.

The equation is shown below, where × represents the mathematical symbol for the gradient of the electric field E, and B represents the magnetic field. Both fields are a function of position r and time t.

∇ × E = -∂B/∂t

This equation is also known as Faraday's law of electromagnetic induction, and it forms one of the four Maxwell equations that describe the behavior of electric and magnetic fields. The Maxwell-Faraday equation is essential for understanding how electromagnetic waves propagate through space and how they are generated in electrical devices such as transformers and generators.

## Lenz’s law of electromagnetic induction

Lenz's law is an important principle in electromagnetism that states that the direction of the induced current in a conductor will be such that it creates a magnetic field that opposes the initial changes in the magnetic field that induced the current.

This law is expressed mathematically in the equation below, where the minus sign indicates that the direction of the induced force opposes the changes in the magnetic field:

ε = -dΦ/dt

Lenz's law complements Faraday's law by adding that the direction of the induced current will oppose the magnetic field change. This law is important in understanding how electrical devices such as transformers and generators work.

Now, let's consider an example. Suppose we have a coil with wire resistors that consists of 20 loops. The magnetic field changes from -5T to 3T in 0.5 seconds. To find the induced emf in the coil, we can use Faraday's law:

ε = -dΦ/dt

where ε is the induced emf, Φ is the magnetic flux, and t is time.

To calculate Φ, we need to know the area of the coil and the magnetic field strength. Let's assume that the area of the coil is 0.1 m^2. Then, the initial magnetic flux is:

Φ1 = B1*A = (-5T)*0.1m^2 = -0.5 Wb

Similarly, the final magnetic flux is:

Φ2 = B2*A = (3T)*0.1m^2 = 0.3 Wb

The change in magnetic flux over 0.5 seconds is:

dΦ/dt = (Φ2 - Φ1)/(0.5s) = (0.3 Wb - (-0.5 Wb))/(0.5s) = 1.6 Wb/s

Substituting this value into Faraday's law, we get:

ε = -dΦ/dt = -(1.6 Wb/s) = -1.6 V

Therefore, the induced emf in the coil is -1.6 volts.

### Lenz’s right-hand rule

The direction of the induced current can be found using Lenz’s right-hand rule. We extend our fingers so that they are mutually perpendicular to one another. The thumb points to the force (F), the index finger points in the direction of the magnetic field (B), and the middle finger gives the direction of the induced current (I).

Electromagnetic induction and magnetic flux linkage

Magnetic flux linkage (ΦΝ) is the product of magnetic flux and the number of turns in a coil.

You can see this in the equation below, where Φ is the magnetic flux (Wb), N is the number of turns, B is the magnetic flux density (T), and A is the cross-sectional area (m2). When we consider the magnetic flux of a coil, the N component is crucial to calculate the magnetic linkage of a coil.

ΦN = BAN

We calculate the total magnetic linkage by multiplying magnetic flux by the number of turns in a coil. We can ignore the N term when the magnetic flux of a given area is considered.

ΦN = BA

## Applications of electromagnetic induction

Electromagnetic induction is a fundamental principle in physics and is essential to many important technologies. It involves inducing an electromotive force by moving a charge-carrying conductor in a magnetic field. The most well-known applications of electromagnetic induction are the AC generator, electrical transformer, and magnetic flow meter.

Michael Faraday discovered the law of electromagnetic induction, which states that the change in magnetic flux in a closed circuit induces an electromotive force or voltage in the circuit. This law forms the basis for many electrical devices and technologies.

The Maxwell-Faraday law is another important principle in electromagnetism that states that a time-changing magnetic field creates a spatially varying electric field and vice versa. This law is essential for understanding how electromagnetic waves propagate through space and how they are generated in electrical devices such as transformers and generators.

Magnetic flux linkage is another important concept in electromagnetic induction. It is the product of magnetic flux and the number of turns in a coil. This concept is important in understanding how electrical transformers work, as well as in the design of electrical motors and generators.

Overall, electromagnetic induction is a critical concept in physics and is essential to many technologies that we rely on every day.

## Electromagnetic Induction

What is electromagnetic induction?

Electromagnetic induction is the process of inducing an electromotive force by moving a charge-carrying conductor in a magnetic field. When an electrical conductor moves through a magnetic field, it crosses the magnetic field lines, causing the magnetic field to change.

How does electromagnetic induction occur?

Electromagnetic induction occurs when an electromotive force is generated in a closed circuit due to varying magnetic flux. When changes in magnetic flux (denoted by Φ) occur, work is done in the form of electrical energy, generating a voltage or an electromotive force through the conductor.

What is Lenz’s law of electromagnetic induction?

This is Lenz’s law of electromagnetic induction: The induced current in the conductor will create a magnetic field. The direction of the current will be such that the magnetic field opposes the initial changes in the magnetic field that induced the current.

What is Faraday's law of electromagnetic induction?

Faraday’s law of electromagnetic induction states that when the flux is changed, an electromotive force is induced on the opposite side opposing the change in the flux.

Where is electromagnetic induction used?

Electromagnetic induction is used in generators, transformers, motors, etc.