Introduction to Electromagnetic Induction
Electromagnetic induction is the foundation of electromagnetism. Most important discoveries of physics and electrical engineering are on the basis of this phenomenon. It is the process of producing an electromotive force (EMF) and hence current in a conductor by changing the magnetic environment around it. Whenever a conductor is placed in a changing magnetic field or magnetic effects, a voltage is generated along its ends. Many technologies such as electric generators, transformers, and wireless charging devices are the major applications of the principle.
The interchanging of mechanical energy or motion into electrical energy and vice versa can be obtained through electromagnetic induction. For example, power stations generate electricity by rotating the turbines (mechanical motion) whereas electric motors use electricity to rotate their rotor.
Historical Background: Faraday and Henry’s Discoveries
Electromagnetic induction is the discovery of two different scientists, independently: Michael Faraday in 1831 and Joseph Henry in 1832.
- Faraday’s experiment: He wrapped two coils of wire around an iron ring on opposite sides. When he passed current through one coil , an unstable current was observed in the other coil. The two coils were connected independently. This showed that a changing magnetic field could cause current in a nearby conductor. He explained this phenomenon on the basis of changing magnetic field lines called the magnetic flux.
However, the concept was highly rejected due to the lack of mathematical basis. Later, James Clerk Maxwell and Heinrich Lens utilized Faraday’s theory to quantitatively derive electromagnetic induction and give the direction of current, flux and the force produced.
- Joseph Henry discovery: Although Faraday got the credits of the discovery of electromagnetic induction as he published his work earlier, Joseph Henry also equally earned the credit because his work was voluminous. Six months later he published his discovery where he first outlined the terms self-inductance and mutual inductance. He stated that any conductor that carries current has self-inductance and, if there is another conductor close to it, they have a mutual inductance. The phenomenon grows when the conductor is presented as a coil, and also when the coil surrounds a magnetic material, such as soft iron. The induction was calculated in Henry which became the unit of induction as an honour to Joseph Henry. He also expressed the relation between two quantities: electricity and magnetism as,
V(t)=L di/dt [Equation 1]
Where V(t) is electrical force (V/sec), di/dt is the rate of change of current with time and L is inductance (H). In other words, the emf or voltage produced by induction is equal to the product of the inductance and the rate at which the current flows through the inductor.
These discoveries brought a revolution in electrostatics and magnetostatics. The greatest inventions like the electric generator and the transformer were possible due to these concepts.
Fundamental Principles of Electromagnetic Induction
Electromagnetic induction is principally stated as The process of generating an electromotive force (EMF) or voltage in a conductor when the magnetic flux linked with it changes.
The change in the flux linkage can occur in three ways:
- By moving a conductor through a magnetic field.
- By changing the strength of the magnetic field around the conductor.
- By changing the position and direction of the conductor with respect to the magnetic field.
If the conductor is arranged in a closed loop, the induced EMF can also drive a current partly from the conductor. This is called induced current.
Faraday’s Laws of Electromagnetic Induction
Faraday’s law of electromagnetic induction was partially derived as first law and second law.
- First Law – Faraday explained that an emf develops when the magnetic lines of force across the coil varies with time. Thus, Faraday’s first law of electromagnetic induction can be stated in the following statements.
When a conductor is kept in a varying magnetic field, an electromotive force is produced. Now, if the conductor is arranged in a closed circuit, a current is generated which is known as induced current. The strength of the magnetic field can be changed in the following ways:
- Moving the conductor in a uniform magnetic field.
- Changing the magnetic field strength over time.
- Creating a relative motion between the conductor and the magnetic field.
- Changing the area of the coil lying inside the magnetic field.
- Second Law – The second law of electromagnetic induction by Faraday is centered in the induced emf in a coil. He states it to be directly proportional to the rate of change of flux linked to the coil. Mathematically,
E = −NdΦB/dt [Equation 2]
Where,
- E is the induced electromotive force,
- N is the number of turns in the coil,
- ΦB is the magnetic flux and
- ‘t’ is the time taken
Hence from [Equation 2] we observe that faster the rate of change of magnetic flux greater would be the induced EMF. The negative sign is to show the opposite direction of current induced to the magnetic flux, which is described by Lenz’s law.
Lenz’s Law and Conservation of Energy
As described above, the path of a current generated by induction is described by Lenz’s Law. Sign convention is an essential part of electromagnetism and cannot be neglected during calculation. This remarkable idea was given by Heinrich Lenz in 1834, after the discovery of Faraday law. This proved that the flow of an induced electromotive force (EMF) and the current thus created in a closed circuit is such that they oppose each other.
In other words, when the magnetic field around a conductor is varied, a current is induced that produces an extra magnetic field which resists the initial flux applied. This law sets the qualification for Faraday law as it emphasizes energy conservation. In the above equation,
E=−dΦ/dt
(-) sign represents this opposition given by Lenz’s law.
Conductor Moving in a Magnetic Field
When a conductor moves in a magnetic field, the charges inside it will be affected by a force. The force is the result of the motor effect and this force is called the Lorentz force.
F→=q(v→ × B→) [Equation 3]
where,
- q = charge of the electron,
- v→ = velocity of the conductor,
- B→ = magnetic field.
This force causes the charges to move towards the end of the conductor. Thus, the flow of charge certainly produces a potential difference between the two ends. This voltage is called the Electromotive Force (EMF) in motion.
Electric generators are the major applications of this force. Here coils rotate inside a magnetic field, where moving conductors generate large voltages.
Induced EMF in a Stationary Conductor with Changing Flux
Induction can also occur in the stationary conductor. If the magnetic field around a stationary conductor changes itself then also an EMF is induced. This is called Faraday’s law of electromagnetic induction or self induction.
Consider a conducting circuit placed in a magnetic field. If the magnetic field strength is increased or decreased, the magnetic flux through the circuit changes.This changing flux results in a current flow or a potential difference across the ends of the conductor. The induced current always produces its own magnetic field that opposes the original one.
A best example is the transformer where a changing current in the primary coil produces a varying magnetic flux in the secondary coil and inducing EMF in the coil.
Also in the AC generators, when the magnetic field is varied around a stationary coil with time, an alternating current is produced.
Magnetic Flux and Induction
The key quantity that matters in induction is the magnetic flux (Φ). The calculation of flux is done by the formula,
Φ=B⋅Acosθ [Equation 4]
where B = magnetic field strength, A = area of the loop, and θ = angle between the field and the area vector. Maximum flux is obtained when the angle θ is perpendicular to the area vector and zero when it is parallel.
For a coil with N turns, the total flux linkage is NΦ. The induced EMF is calculated from the Faraday’s law as:
E=−NdΦ/dt [Equation 5]
Thus, greater the change in flux, greater will be the emf induced. To increase the rate of change of flux, the no. of turns in the coil is increased. Thus, induced emf has a direct relationship with the rate of change of flux.
[Equation 5] gives the reason for generators using large numbers of turns and strong magnetic fields to produce high voltages.
Factors Affecting Induced EMF
The major factors affecting the EMF induced are given below:
- Strength of Magnetic Field (B): Stronger fields give larger voltages.
- Speed of Motion (v): Faster motion of charges in the conductor inside a magnetic field produces greater EMF.
- Area of the Coil (A): Larger area of the coil results in more flux (Φ=B⋅Acosθ), that increases EMF.
- Number of Turns (N): Greater number of turns gives more flux linkage (E=−NdΦ/dt ), and hence increases the EMF.
- Angle (θ): EMF is maximum when the flux is perpendicular to the field and zero for parallel cases.
Eddy Currents: Origin, Effects, and Applications
If the conductor is a plane surface like a solid metal sheet or block, the induced EMF does not produce a circular current inside the material. This circulating current is called the eddy current. They are also explained by Lenz’s Law: the induced currents always flow in such a direction that their magnetic field opposes the change in flux that produced them..
This current can cause heating effects and energy loss in metals. The devices like generators, transformers etc. may suffer power loss. This also creates a probable risk of damage of the device and decreases the efficiency.
Beside having some negative effects, they are used in certain machineries that need to generate heat. For example, induction cooktops, induction furnaces etc. Electromagnetic braking systems are also famous for smooth braking like in trains and roller coasters. It is also used in metal detectors and electromagnetic damping instruments.
Types of Induction
- Self-induction: It uses a single coil and when the current in a coil changes, the magnetic flux through the coil also changes. This change induces an EMF in that coil which opposes the change in current. The property of a coil to resist the current is called inductance (L).
For self-induction,
E = −LdI/dt [Equation 6], where L is the length of the coil.
Thus, the length of the inductors determine smooth changes in current.
- Mutual Induction: Principle of Transformers
It uses two coils placed nearby and a changing current in one coil induces EMF in the other. It occurs without the direct connection of the circuit and is the principle of transformers. Thus, the voltage control is easier by increasing or decreasing the no. of turns in the coils. It makes power transmission easier and smoother in longer distances.
For mutual induction,
E2=−MdI1/dt [Equation 6]
where M is the mutual inductance.
Applications of Electromagnetic Induction
Most of the electric systems today are based on electromagnetic induction. Some of the major uses are as follows:
- Electric Generators: Generators convert kinetic or mechanical energy into electrical energy. The coils rotate in a magnetic field and induce emf by the change of magnetic flux. Hence, electricity is generated.
- Transformers: Lying on mutual induction transformers operate when the primary coil induces current in the secondary coil by varying magnetic flux.
- Induction Motors: Induced currents produce torque and change electrical energy into kinetic energy.
- Induction Cooktops: Cooking is made easier by the combined work of electricity and magnetism. The base of the pot is heated using eddy currents.
- Wireless Charging: Self induction is required to transfer power without wires.
- Maglev Trains: Maglev levitation trains use induction and eddy currents for levitation and braking.
Conclusion
Electromagnetic induction is a basic need for power generation today. It is known as the greatest discovery of scientists in the realm of physics and engineering. Michael Faraday got the title of ‘Father of Electricity’ due to his finding of electromagnetic induction. Similarly, from small cooking devices to larger power plants are based on this concept.
Electromagnetism is also a key for the upcoming discoveries and facilities. The natural phenomena of inducing magnetic fields by a current carrying conductor has left behind all the traditional technologies. However, the direction of current, magnetic field, Lorentz force and induced EMF must be thoroughly studied for an efficient and correct functioning of an electrical system.
References
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https://en.wikipedia.org/wiki/Electromagnetic_induction
