Faraday’s Law of Electromagnetic Induction

The Law which helps to predict the relationship between Magnetic Field and Electric circuits to produce Electromotive Force (EMF) is called Faraday’s Law. The phenomenon is called Electromagnetic Induction.

History of Faraday’s Law

Faraday found electromagnetic induction in 1831. This is the idea behind this Law. This discovery was a big part of how electricity went from being a strange idea to a powerful new technology. He worked on developing his ideas about electricity for the rest of the decade. He helped come up with a lot of well-known words, like “electrode,” “cathode,” and “ion.” Faraday was a scientific adviser to Trinity House from 1836 to 1865 and a professor of chemistry at the Royal Military Academy in Woolwich. Both of these jobs gave him a chance to use his scientific knowledge (1830-1851).

In 1831, Faraday gave a series of talks to the Royal Society in London, England. He talked about the results of his experiments, which showed that “ordinary magnets can produce an electric current.” He used a battery that held liquid to send electricity through a small coil.

Faraday’s law of induction is a relationship in physics that says a changing magnetic field causes a voltage in a circuit. It was developed by the English scientist Michael Faraday based on his own experiments. He tried something out by wrapping two coils of wire with insulation around an iron ring. He found that when a current went through one coil, it caused a momentary current in the other coil. This is called mutual induction.

Experiments Performed by Faraday Based on the Relationship Between Induced EMF and Flux

• In the First Experiment, he showed that the only time current is caused is when the strength of the Magnetic Field changes. An Ammeter was hooked up to a loop of wire. When a magnet was moved toward the wire, the ammeter moved.
• In the Second Experiment, he showed that an iron rod could become magnetic by running a current through it. He saw that when the magnet and the coil move relative to each other, an electromotive force is created. When the magnet was kept still around its axis, there was no electromotive force, but when the magnet was turned around its axis, the Electromotive force was produced. So, when the magnet was kept still, there was no change in the ammeter.
• During the Third Experiment, he wrote down that the galvanometer did not move and that the coil did not produce an induced current when it was kept away from a stationary magnetic field. When the magnet was kept away from the loop, the ammeter moved in the other direction.

Working Principle of Faraday’s Law

The working Principle of Faraday’s Law is Electromagnetic Induction which states as:

If the moving conductor was connected to a sensitive galvanometer, it would show an electric current flowing through the circuit as long as the moving conductor kept moving in the magnetic field. The emf that is made in the conductor is called the induced emf, and the current that is made is called the induced current. Electromagnetic Induction is the name for this process.

Types of Faraday’s Law

Faraday’s Laws of Electromagnetic Induction are made up of two different rules. The first law talks about How emf is made in a conductor, and the second law talks about How much emf is made in the conductor.

Faraday’s First Law of Electromagnetic Induction

Faraday’s first law of electromagnetic induction says,

“An electromotive force is induced whenever a conductor is placed in a changing magnetic field. Also, if the conductor circuit is closed, a current is caused, which is called an “induced current.“

Factors affecting Magnetic Field Intensity in a closed loop

• By turning the coil while the magnet is still in place.
• By putting or taking the coil into the magnetic field.
• By changing how big a coil that is in a magnetic field.
• By relocating a magnet towards or away from the coil.

Faraday’s Second Law of Electromagnetic Induction

Second law of electromagnetic induction says,

“The size of induced emf in a closed circuit is directly related to the rate of change of magnetic flux linked to the circuit”

Factors affecting 2nd Law

• Amount of Electric Current
• Time duration of the Electrolysis process
• Concentration of Electrolyte
• Temperature affecting the rate of chemical reaction
• Electrode material present in a chemical reaction
• Distance between Electrodes in a chemical reaction

Mathematical derivation of Faraday’s Law

Faraday’s law of electromagnetic induction is one of the most important laws of electromagnetism. It shows how an electric field is caused by a changing magnetic field. Mathematically, it can be written as follows:

Where;

• ε is the Electromotive Force (EMF) of the circuit
• Φ is the Magnetic Flux of the circuit
• N is the Number of turns of the coil

Suppose a magnet comes close to a coil. Think about the two-time situations T1 and T2.

At the time T₁ Flux linkage will be NΦ₁

At the time T₂ Flux linkage will be NΦ₂

Change in Flux will be written in Mathematical form as ;

N(Φ₂ – Φ₁)

Let’s suppose the change in Flux linkage is;

Φ = Φ₂ – Φ₁

So the change in flux linkage will be:

NΦ

The rate of change of Flux will be like

NΦ/t

Using the above equation’s derivative, we get;

N dΦ/dt

Faraday’s second law of electromagnetic induction says that the rate of change of flux linkage is equal to the induced emf in a coil. So,

If we consider Lenz’s Law, Faraday’s Law will be;

Result

The final Equation for Faraday’s Law of Electromagnetic Induction is given below;

Faraday’s law of electromagnetic induction is one of the most important ideas in the field of Electromagnetism. It shows how magnetic fields and electric currents work together. It can be used in a lot of different ways and has been very important in the development of modern technology.

Experiments performed by Faraday and Henry

In this section, we will talk about some experiments performed by Faraday and Henry to help people to understand the phenomenon of Electromagnetic Induction because Faraday’s Law is basically based upon the principle of Electromagnetic Induction.

Experiment 1

Faraday hooked up a coil to a galvanometer for this experiment, as shown in the figure. The north pole of a bar magnet was moved toward the coil by pushing it toward the coil. As the bar magnet is moved, the galvanometer’s pointer moves, showing that there is current in the coil being looked at. It can be seen that when the bar magnet is still, the pointer doesn’t move. The pointer only moves when the magnet is moving.

In this case, the direction in which the pointer moves depends on the way the bar magnet is moving. Also, when the south pole of the bar magnet is moved toward or away from the coil, the galvanometer moves in the opposite direction of what is seen when the north pole is moved in the same way. Aside from that, the amount the pointer moves depends on how fast it is pulled towards or away from the coil. The same effect is seen when the coil is moved instead of the bar magnet and the magnet is kept still. This shows that the current in the coil is only caused by the relative movement of the magnet and the coil.

Experiment 2

In the second experiment, Faraday replaced the bar magnet with a second coil that carried electricity and was connected to a battery. Here, the current from the battery going through the coil made a steady magnetic field, so the system was the same as the one before. As we move the secondary coil toward the primary coil, the galvanometer’s pointer moves, showing that there is an electric current in the primary coil.

Like in the previous case, the direction of the pointer’s movement depends on whether the secondary coil is moving toward or away from the primary coil. The speed with which the coil is moved also affects how much it bends. All of these results show that the second system is similar to the first system from the first experiment.

Experiment 3

Faraday learned from the two experiments above that the current in the primary coil was made when the magnet and the coil moved relative to each other. But another experiment Faraday did showed that the movement between the coils wasn’t really needed for the current to be made in the primary.

In this experiment, he set up two fixed coils and used a push-button to connect one of them to the galvanometer and the other to a battery. When the button was pressed, the other coil’s galvanometer moved, which meant that there was current in that coil. Also, the pointer’s movement was temporary, and if the key was held down for a long time, the pointer didn’t move at all. When the key was let go, the pointer moved in the opposite direction.

Difference b/w Faraday’s Law & Lenz’s Law

Applications of Faraday’s Law

This law is one of the most basic rules about electricity and magnetism. This law is used in most things that use electricity. It can explain how motors, generators, inductors, and transformers work. Here are a few ways it can be used, some of which are in everyday life.

• Transformer: It is made up of two coils that are wrapped around a square core. When alternating current flows through one coil, it changes the magnetic field, which causes a current to flow in the second coil.
• Generator: A device that turns mechanical energy into electrical energy that can be used in a circuit outside of the device. Between the poles of a horseshoe-shaped magnet, a conductor coil is quickly turned around. When the magnetic field hits the moving coil, a current is created in it.
• Induction cooker: It is used to heat a pot or pan without a flame or an electric coil. It uses the principle of mutual induction and the idea of mutual inductance.
• Electrical bells: A machine that works with the help of an electromagnet. A sound is made when an electromagnetically powered hammer hits a bell.
• Electromagnetic Flow Meter: A tool that uses a magnetic field to measure the speed of fluids that conduct electricity. The induced emf is equal to the speed of the fluid.
• Magnetic resonance imaging: Faraday’s law is used by MRI machines to make detailed pictures of the human body. They do this by creating a strong magnetic field and then sending a series of electromagnetic pulses through the body to excite the nuclei of hydrogen atoms. The MRI machine picks up the EMF that the excited nuclei make and uses it to make an image.

Limitations of Faraday’s Law

• Faraday’s law is based on the idea that both the magnetic field and the conductor are moving. Faraday’s law can’t be used if the magnetic field is still.
• Faraday’s law is based on the idea that the magnetic field is the same all over the conductor. Faraday’s law might not be able to predict the induced current well if the magnetic field is not uniform.
• Faraday’s law is based on the idea that the wire is a closed loop. If the wire isn’t connected to anything, there won’t be any induced current.
• Faraday’s law only works for things that conduct electricity. It can’t be used to figure out the electric field or current induced in things that don’t conduct electricity.
• Faraday’s law doesn’t account for the conductor’s resistance, which can change the size and direction of the induced current.
• Faraday’s law doesn’t take into account the effects of magnetic hysteresis, eddy currents, and other non-linear effects that can happen in real materials.
• Faraday’s law is based on the idea that the magnetic field changes over time and that the conductor does not move. If the conductor is moving, you have to think about things like the Lorentz force.

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