Faraday Law of Electromagnetic Induction

A single, elegant principle, Faraday's Law of Electromagnetic Induction, which was established in the early 19th century, is responsible for a great deal of the modern world, which is powered by electricity and innumerable electronic devices. In 1831, the renowned British scientist Michael Faraday developed this revolutionary law, which made it clear that an electric current could be produced by a changing magnetic field. Electric generators, transformers, and the extensive infrastructure that provides power to our homes and businesses were all directly influenced by this discovery, which not only transformed our understanding of physics but also established the groundwork for the entire field of electrical engineering.

Table of Contents

• Historical Context
• The Fundamental Idea of Magnetic Flux
• Faraday's First Law of Electromagnetic Induction(Qualitative)
• Faraday's Second Law of Electromagnetic Induction(Quantitative)
• Lenz's Law: The Essential Function of Negative Sign's
• The uses of Faraday's Law
• Conclusion

Historical Context

As demonstrated by Hans Christian Ørsted, the scientific community was already aware that electric currents could generate magnetic fields at the beginning of the 19th century. Faraday wanted to determine if it was possible for a magnetic field to generate electricity, or if the opposite was true.

Faraday found that an electric current is created when a coil is moved close to a magnetic field or when a magnet is moved close to a coil through a series of experiments involving coils, magnets, and galvanometers. What is now known as Faraday's Law of Electromagnetic Induction was eventually developed as a result of these investigations.

The Fundamental Idea of Magnetic Flux (Φ_B):

The idea of magnetic flux (Φ B) must be understood before one can fully comprehend Faraday's Law. Think of magnetic field lines as imperceptible force lines that radiate from a magnet and show the magnetic field's strength and direction. The total number of these magnetic field lines moving through a specific area is measured quantitatively as magnetic flux. In essence, it indicates the amount of magnetic field that "flows" through a specific surface or loop. Mathematically, for a uniform magnetic field (B) passing perpendicularly through a flat surface of area (A), the magnetic flux is simply the product of the magnetic field strength and the area:

Φ_B=B⋅A

We should consider the angle if the magnetic field lines are not perpendicular to the surface. The general formula for magnetic flux is:

Φ_B​=B⋅A⋅cos(θ)

B = The magnitude of the magnetic field, measured in Tesla (T).

A = The area of the surface, measured in square meters (m²).

θ = The angle between the magnetic field vector and the normal (a line perpendicular) to the surface area.

The unit of magnetic flux is the Weber (Wb), named in honor of Wilhelm Eduard Weber. One Weber is equivalent to one Tesla-square meter (1 Wb=1 T⋅m²). Faraday's key discovery was that an electromotive force (EMF, represented by the letter E), which is basically the voltage or potential difference that propels current in a circuit, is only created when the magnetic flux travelling through a coil or a conductor changes. No EMF is induced and, as a result, no current will flow in a closed circuit if the magnetic flux stays constant, regardless of how strong the magnetic field is.

Understanding Faraday's Law

Faraday's First Law of Electromagnetic Induction(Qualitative)

The basic qualitative description of the phenomenon is given by this law:

"A coil or conductor experiences an electromotive force (EMF) whenever the magnetic flux associated with it varies. An induced current will flow through the circuit if it is closed.” This law emphasizes that a dynamic magnetic environment is a necessary prerequisite for electromagnetic induction. There are multiple ways to cause the change in magnetic flux:

1. A permanent magnet moving toward or away from a stationary coil, or a coil moving toward or away from a stationary magnet, is known as relative motion. The flux is changed by the relative position, which also affects the number of magnetic field lines that flow across the coil's area.
2. Changing Magnetic Field intensity: The magnetic flux through a stationary coil positioned within a magnetic field will change if the magnetic field itself is changing in intensity over time (for example, due to an electromagnet whose current is being increased or lowered).
3. Changing the Coil's Area or Orientation: A coil's effective area through which the magnetic field lines flow will vary if its shape is deformed or its orientation with respect to a magnetic field is changed (for example, by rotating it). This will result in a change in magnetic flux. 

Faraday's Second Law of Electromagnetic Induction(Quantitative):

The mathematical relationship controlling the induced EMF's magnitude is given by this law: "The magnitude of the induced electromotive force (EMF) in a circuit is directly proportional to the rate of change of magnetic flux linked with the circuit."

This can be stated mathematically as:

E = − dΦ_B/dt

Here, Volts (V) are used to measure the induced electromotive force (EMF), or E. dΦ_B/dt shows the rate at which the magnetic flux changes in relation to time, expressed in Webers per second (Wb/s). Crucially, the relationship between changing flux and induced voltage is directly demonstrated by the fact that 1 Wb/s is equal to 1 Volt. For a coil consisting of N turns, the total induced EMF is the sum of the EMFs induced in each individual turn. Therefore, the formula becomes:

E=−NdΦ_B​​/dt

This equation is one of the four Maxwell's equations.

Lenz's Law: The Essential Function of Negative Signs

Faraday's Law's negative sign is not just a mathematical convention; it has a deep physical meaning and results directly from the conservation of energy principle. Lenz's Law, which Heinrich Lenz developed in 1833, formally captures this negative sign. According to Lenz's Law, "The direction of the induced current (or EMF) is such that it opposes the change in magnetic flux that produced it."

To realize this, let's look at an example: A bar magnet's magnetic flux increases through a coil in the direction of the magnet's motion if its North pole is quickly pushed in that direction. Lenz's Law states that the coil's induced current will flow in a way that opposes this rise by producing a magnetic field. In particular, it will produce a North pole on the coil's side that faces the magnet, repelling it and preventing it from moving. Pushing the magnet would cause you to experience this repulsive force. On the other hand, the magnetic flux through the coil drops if the magnet's north pole is pulled away from it. In order to counteract this drop, the induced current will thereafter flow in a direction that produces a magnetic field. By producing a South pole on the coil's side that faces the receding magnet, it will draw the magnet in and prevent its withdrawal.

The uses of Faraday's Law:

1. Electric generators: Coils inside magnetic fields are rotated by mechanical energy in generators. This motion creates an electromagnetic field (EMF), which is then used to power electrical devices in accordance with Faraday's Law.
2. Transformers: Mutual induction is the basis for transformer operation. A magnetic field created by a fluctuating current in the primary coil causes a voltage to be induced in the secondary coil.
3. Cooktops that use induction: These heat cookware directly uses electromagnetic induction. Heat is produced in the metal pot by currents (eddy currents) created by the fluctuating magnetic field.
4. Flow meters that are magnetic: By monitoring the induced voltage as conductive fluids pass through a magnetic field, Faraday's Law can be utilized to calculate their velocity.

Conclusion:

One of the greatest scientific triumphs in history is Faraday's Law of Electromagnetic Induction. It effectively conveys the complex and dynamic interrelationship between electricity and magnetism, showing that these two fundamental forces are actually two aspects of a single electromagnetic force rather than distinct things. These have enabled humanity to harness electromagnetic phenomena, revolutionizing the way we produce, transfer, and use energy. The modern world is still powered and illuminated by Faraday's legacy, from the enormous generators in power plants to the small coils in our smartphones.