## What is meant by induced voltage?

A conductor such as a coil or a wire loop when exposed to a varying magnitude of magnetic field experiences an induced electromotive force. The credit for this discovery of induced voltage or electromotive force goes to Michael Faraday. Michael Faraday coined this phenomenon as electromagnetic induction. It was James Clerk Maxwell who mathematically formulated Faraday's discovery, which is later known as Faraday's law of electromagnetic induction. The mathematical form of Faraday's law was later introduced into the sets of Maxwell's equations in the area of electromagnetism. The induced voltage, which is a result of electromagnetic induction has various applications in practical life such as electric motors, electric generators, transformers, and inductors.

The induced voltage can be achieved either by exposing a current-carrying coil in a varying magnetic field or by a conductor which moves through a magnetic field. The magnitude of the induced voltage is dependent on various factors such as:

**The strength of the magnetic field:**The strength of a magnetic field is directly linked to the number of magnetic flux lines, hence the magnitude of induced voltage is directly proportional to the number of magnetic flux lines.**The length of the conductor:**It is also known as the effective length of the conductor which is influenced by the magnetic field. The effective length of the conductor is proportional to the induced voltage.- In case the conductor is moving across the magnetic field, the induced voltage is directly linked to the speed at which it is moved. In this case, the electromotive force is known as motional electromotive force or motional EMF.

The magnetic field can be produced by either a bar magnet or an electromagnet. The change in the magnetic field can be achieved by physically moving the magnet in and out across a conductor coil or a wire loop. Here in this article, a basic introduction has been provided about the fundamentals of induced voltage by the phenomena of electromagnetic induction.

## Faraday's law and motional EMF

Faraday's law of electromagnetic induction establishes a relationship between change in the magnitude of electric field and induced voltage. Faraday's law states that due to a relative motion between a conductor and a magnetic field, a voltage is induced in the conductor, the magnitude of the induced voltage is proportional to the change in the magnetic flux. The magnetic flux through any surface can be estimated by performing a surface integration of the normal component of the magnetic field B. The magnetic flux is denoted by ${\varphi}_{B}$ and its SI unit is weber (Wb). The amount of magnetic flux associated with a magnetic field is measured by a flux meter.

For a constant magnetic field, the magnetic flux associated with a surface is given by:

${\varphi}_{B}=BA\mathrm{cos}\theta $

where $B$ represents the magnetic field, $A$ represents the area of the surface and $\theta $ represents the angle between perpendicular vector to the area $A$ and magnetic field $B$

When the magnetic field is varying, the magnitude of magnetic flux is given by the surface integral:

${\varphi}_{B}=\int {\int}_{A}B.dA$

The motional EMF accounts for the movement of the conductor in the magnetic field which leads to an induced electromotive force (EMF). The magnitude of the motional EMF is directly proportional to the magnitude of flux density, the velocity of the conductor, and the length of the conductor. Mathematically, it is given as-

$\epsilon =-\beta \times l\times v$ volts.

Where $\epsilon $ represents the induced EMF, $\beta $ represents the magnetic flux density $l$ represents the length of the conductor, and $v$ represents the velocity of the conductor at which it is moved in the magnetic field. It should be noted that the above expression is valid if the conductor moves at right angles to the magnetic field.

When the conductor moves at an angle to the magnetic field, the expression is given as,

$\epsilon =-\beta \times l\times v\times \mathrm{sin\theta}$ volts

Where $\theta $ represents the angle at which the conductor moves through the magnetic field.

## Transformer and self-inductance

Self-inductance is also termed as back EMF. It is a phenomenon experienced by a current-carrying coil under the influence of change in magnitude of current flowing through it. When current flows through a coil, it generates an induced magnetic field around it that extends outward from the conductor. This magnetic field is characterized as concentric loops of flux known as magnetic flux. A change in the current flow in the coil induces a voltage in the current-carrying coil in the opposite direction, whose nature is to oppose the flowing current, as stated by Lenz's law.

A transformer is a device whose main job is to increase or decrease the voltage of the flowing current. The transformer does so without changing the frequency of the AC signal. The working of the transformer generally follows Faraday's law of electromagnetic induction and mutual induction. The principle of mutual inductance signifies the generation of an induced voltage in a secondary coil due to the magnetic field of a primary coil when a current flows through it. This principle is greatly used in the construction of transformers, which have two windings in them- the primary winding and secondary winding. The number of coils in the winding decides the strength of the induced voltage. The below figure shows the cross-sectional view of a transformer. In the diagram, the transformer has a red coil, which represents the primary coil or primary winding, while the blue coil represents the secondary coil or secondary winding. A current flowing through the primary coil induces a similar voltage into the secondary coil, the strength of the induced voltage can be regulated by increasing the turns in the coils.

## Lorentz force

In the theory of electromagnetism, the Lorentz force is the result of a combination of an electric and magnetic force on the charge due to associated electromagnetic fields. The Lorentz force is a function of the magnetic field, electric field, and the velocity at which the charge is moving, i.e.,

$F=f\left(B,E,{V}_{c}\right)$

where $E$ is the electric field and ${V}_{c}$ is the velocity of the moving charge. Mathematically the equation of Lorentz can be written as,

$F=qE+\left(qV\times B\right)$

where $q$ represents the charged particle.

## Context and Applications

The topic of EMF and Faraday's law of electromagnetic induction is widely taught in many elementary school curriculums and diploma courses. Besides this, the topic is widely taught in many graduate and postgraduate degree courses of:

- Bachelors in Technology (Electrical Engineering)
- Bachelors in Technology (Electronics Engineering)
- Bachelors in Technology (Electrical and Electronics Engineering)
- Masters in Technology (Electrical Engineering)
- Masters in Science (Physics)

## Practical Problems

**Q1**. Which of the following law introduces the concept of EMF?

- Faraday's law of electromagnetic induction
- Faraday's law of self-inductance
- Faraday's law of mutual inductance
- Faraday's law of EMF

**Answer:** Option a

**Explanation:** The concept of EMF is introduced by Faraday's law of electromagnetic induction. It represents the induced voltage in a current-carrying coil when exposed to a changing magnetic field.

**Q2.** Which of the following expresses the force experienced by a moving charge?

- Lenz's force
- Lorentz force
- Both Lorentz and Lenz's force
- None of these

**Answer:** Option b

**Explanation:** The Lorentz force expresses the force experienced by a moving charged particle in an electromagnetic field. The Lorentz force is a function of the magnetic field, electric field, and the velocity of the moving charge.

**Q3.** Which of the following device makes use of the principle of electromagnetic induction?

- Gas turbines
- Electric generators
- Both a and b
- None of these

**Answer:** Option b

**Explanation:** The electric generators make use of the principle of electromagnetic induction. The electric generators are the devices that convert the mechanical energy of armature rotation into electrical energy.

**Q4.** Which of the following symbol represents the magnetic flux?

- ${\mu}_{H}$
- ${\varphi}_{B}$
- $\partial $
- $\psi $

**Answer:** Option b

**Explanation:** Magnetic flux is the surface integral of the normal component of the magnetic field. The magnetic flux is represented by ${\varphi}_{B}$.

**Q5.** What is the abbreviation for EMF?

- Electromagnetic force
- Electromotive force
- Electrochemical force
- Electromagnetic fluctuations

**Answer:** Option b

**Explanation:** The abbreviation for EMF is electromotive force. EMF is induced when a conductor is exposed to a magnetic field. However, EMF can also be induced if a conductor is moved with a certain velocity in a magnetic field.

## Related Concepts

- Lenz's law
- Eddy current
- Electric flux and electric flux density

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