Faraday’s Law of Electro-Magnetic Induction: Principle, Applications, Experiments

Introduction to Faraday’s Laws of Electromagnetic Induction

Faraday’s law of electromagnetic induction or simply known as Faraday law, is an explanation of the direction of electric and magnetic fields. It describes the behavior of the magnetic field when it interacts with the electric circuit and produces electromotive force (EMF). The whole process is termed as electromagnetic induction.

Michael Faraday, also known as the father of electricity, discovered the laws of electromagnetic induction by performing several experiments and observations. He performed three major experiments to prove his theory and proposed the law in 1831. The phenomenon of electromagnetic induction also comes with the working principle of other devices such as transformers, inductors, induction motors, generators, solenoids etc. Thus, Faraday proved that electricity can be generated through changing magnetic fields.

Understanding Electromagnetic Induction

When a varying magnetic field is introduced to an electric field, a voltage known as electromotive force is developed. This principle of induction is the foundation for the generation of electricity, transformers and various other technologies. The working mechanism of electromagnetic induction depends upon Faraday’s law and Lenz’s law. 

The phenomena of induction can occur when the conductor experiences magnetic variation around its surroundings. Thus induced EMFs are also of two types. As like in transformers, if the change in magnetic field occurs without experiencing a physical movement then the induced EMF is known as statically induced EMF. IN contrast, when a conductor moves through the magnetic field, then the induced EMF is called dynamically induced EMF. This induced EMF is the reason for generating electrical energy, transformers, generators and various other wireless technologies.

Faraday’s Laws of Electromagnetic Induction are a combination of two laws. The first law explains the induction of emf in a conductor, while the second law measures the emf created in the conductor.

Faraday’s First Law: Induced Electromotive Force (EMF)

Faraday and Henry conducted a number of experiments that resulted in the discovery and clarification of electromagnetic induction. Faraday concluded from his findings that an emf develops when the magnetic flux across the coil varies over time. Thus, Faraday’s first law of electromagnetic induction gives the following statements:

When a conductor is kept in a changing magnetic field, an electromotive force is generated. If the conductor is placed in a closed circuit, a current is created, known as induced current. Here are a few methods for changing the magnetic field intensity in a closed loop:

• Movement of the conductor in a stationary magnetic field.
• Variation of the magnetic field strength over time.
• Relative motion between the conductor and the magnetic field.
• Changing the area of the coil lying inside the magnetic field.

Faraday’s Second Law: The Role of Magnetic Flux

The second law of electromagnetic induction according to Faraday claims that, the induced emf in a coil is directly proportional to the rate of change of flux linked to the coil. Mathematically, this can be expressed as: 

E = −NdΦ_B​​/dt [Equation 1]

Where,

• E  is the induced electromotive force or voltage that is measured in volt,
• N is the number of turns present in the coil,
• ΦB is the magnetic flux taken in Weber (Wb), and
• ‘t’ is the time taken in seconds.

Hence it can be observed from equation (1) that faster the rate of change of magnetic flux greater would be the induced EMF. The negative sign indicates the opposite direction of current induced, which is described by Lenz’s law.

Mathematical Expression of Faraday’s Laws

Let us consider a magnet moving towards a coil and two different time instances t1 and t2. Then the flux linked with the coil at time t1 will be NΦ₁ and that at t₂ will be NΦ₂. Now the change in the flux linkage is given by,

N(Φ₂ – Φ₁) (Equation i)

Suppose that this change in flux linkage is

Φ = Φ₂ – Φ₁ (Equation ii)

Hence, the change in flux is given by NΦ.

Again to find the rate of change of flux linkage we perform NΦ/t.

Now taking the derivative of Φ with respect to time we get N dΦ/dt.

We know Faraday’s second law which states that the induced emf is equal to the rate of change of magnetic flux linkage. Therefore,

E =  N dΦ/dt (Equation iii)

Applying Lenz’s law we will get,

E =  – N dΦ/dt (Equation iv)

This is the mathematical expression for the induced emf that is given by Faraday. From the above equation we see that,

• The emf increases if the no. of turns in the coil are increased.
• Emf increases if the magnetic field strength is increased.
• Emf is also increased if the relative motion between the coil and the magnet is increased.

Lenz’s Law and Its Relation to Faraday’s Laws

According to Lenz’s Law, the current induced will always be in the direction opposite to the flux that produced it. This is obviously because of the law of energy conservation, which makes certain that the induced current does not generate energy out of something that is empty. It is actually expressed by the negative sign in Faraday’s equation.

Practical Applications of Electromagnetic Induction

Faraday’s laws have become the base for various equipment and technologies. Some of its important applications are given below:

• Generators: The electric generators convert mechanical energy into electrical energy by rotating coils in a magnetic field. An alternating current is produced by generators which are used in powering industries and also home applications.
• Transformers: The transformers transfer electrical energy between circuits by electromagnetic induction. They use steps up or steps down voltage for power transmission. 
• Induction Motors: Induction motors use the induced current produced by electromagnetic induction to generate motion in motor applications.
• Induction Cooktops: Electromagnetic field is directly employed in induction cook wares. The changing magnetic field generates current in the pots and hence produces heat.
• Wireless Charging: The coils inside the charger produce changing magnetic fields and induce current in the receiving devices. Thus energy is transferred without any physical contact..
• Electric Guitars: Musical instruments like guitars and violin also utilize electromagnetic induction to convert the electrical energy into sound energy.
• Maxwell Equation: The converse of Faraday law is the Maxwell equation which states that a varying magnetic field brings change in the electric field.

The Impact of Faraday’s Laws on Modern Technology

Faraday’s law has made possible the generation of electricity by using a changing magnetic field. By the evolution of electricity, the world has forwarded its steps to the modern age. Every facility we utilize today is the achievement of electricity. Thus, the power transfer is made easier with the help of Faraday’s laws. Medical field also utilizes electromagnetic induction in several technologies like MRI, X-rays and surgical approaches to detect metal objects. Furthermore, a simple home application like charging, to the huge projects of electricity generation heavily rely on those powerful laws.

Experiments Demonstrating Faraday’s Laws

Several classic experiments illustrate Faraday’s Laws:

Experiment I: Moving a Magnet through a Coil: 

Objective:

To observe induced current, when a magnet moves through a coil.

Materials:

• A bar magnet
  
• A coil of wire
  
• A galvanometer (to measure induced current)
  

Procedure:

1. Connect the coil to the galvanometer.
   
2. Move the magnet toward the coil.
   
   • The galvanometer needle deflects, indicating induced current.
     
3. Move the magnet away from the coil.
   
   • The needle deflects in the opposite direction.
     
4. Keep the magnet stationary inside the coil.
   
   • No current is induced.
     

Experiment II: Rotating Coil in a Magnetic Field

Objective:

To demonstrate how mechanical motion generates electricity.

Materials required:

• A rotating coil
  
• A strong magnet
  
• A galvanometer
  

Procedure:

• Place the coil between the poles of the magnet.
  
• Rotate the coil using a hand crank.
  
• Observe the galvanometer as the coil rotates.

Historical Context: Michael Faraday’s Contributions to Electromagnetism

Faraday had not received any formal education. However, his pioneer deeds ended with major discoveries such as electromagnetic induction and electrolysis. His work laid the groundwork for later scientists who elevated electromagnetic theory.

Michael Faraday and Joseph Henry discovered electromagnetic induction individually in 1831 and 1832. Faraday became the first person to publish the outcomes of his research. Faraday’s notebook published on August 29, 1831, describes a practical experiment of electromagnetic induction in which two wires are twisted around both opposite sides of an iron ring. The analysis of his experiment of electromagnets showed that when current began to flow in one wire, a wave that produced an electric event, travelled on the opposite side of the ring. When he linked or removed the left side wire to a battery, the needle of a galvanometer noted a transient current on the right side.This induction was the result of the change in magnetic flux which took place when the battery was connected and removed. His notebook also mentioned that using fewer coils on the battery side caused more fluctuations in the galvanometer.

Michael Faraday explored his theory on the basis of lines of force which we call as flux. Scientists of that period didn’t value his theories as they lacked a strong mathematical formulation. However, in 1862 James Clerk Maxwell highly utilized Faraday’s theories for quantitative development of electromagnetic theory. Maxwell’s articles explain the time-varying aspect of electromagnetic induction as a differential equation. Although Faraday’s law has not mentioned about motional emf, Oliver Heaviside addressed Maxwell’s differential equations as Faraday’s law. 

 Emil Lenz in 1834 formulated Lenz’s law by observing the flux through the circuit and described the direction of induced emf and current caused by the flux. Albert Einstein also gave an honor to Faraday’s law for developing a basic framework to pave a way for his special theory of relativity.

Conclusion

Faraday’s Laws of Electromagnetic Induction is a primary base for understanding electromagnetism. The application of electromagnetic induction is wide ranging from theoretical physics to the practical and experimental world of physics, engineering and medical science. Many basic electrical devices and systems are the outcomes of this law that is providing significant beneficiaries to modern life. Many upcoming theories and research keep Faraday’s law as their role model which shows that Faraday’s law of induction is a timeless theory of nature.

References

Giuliani, G. (2008). A general law for electromagnetic induction. Europhysics Letters, 81(6), 60002.

Guisasola, J., Zuza, K., & Almudi, J. M. (2013). An analysis of how electromagnetic induction and Faraday’s law are presented in general physics textbooks, focusing on learning difficulties. European Journal of Physics, 34(4), 1015.

Galili, I., Kaplan, D., & Lehavi, Y. (2006). Teaching Faraday’s law of electromagnetic induction in an introductory physics course. American journal of physics, 74(4), 337-343.

Kingman, R., Rowland, S. C., & Popescu, S. (2002). An experimental observation of Faraday’s law of induction. American Journal of Physics, 70(6), 595-598.

Patero, J. (2023). Electromagnetic Induction: Unraveling Faraday’s Laws and their applications in generators and transformers. International Journal of Advanced Research in Science Communication and Technology, 814-819.

Faraday’s Law