# Chapter 6 – Electromagnetic Induction

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Before the nineteenth century, all scientists thought of magnetism and electricity as two independent phenomena that were not at all related to each other. Only after experiments were conducted on the electric current by well-known scientists like Oersted, Ampere, and others, a relation was discovered. It was observed that a magnetic compass needle deflects in the vicinity of an electric current. In the 1830s, Michael Faraday and Joseph Henry conducted experiments that proved that the opposite was also true- when closed coils were subjected to changing magnetic fields, electric currents were induced in it. This formed the basis of electromagnetic induction.

#### Electromagnetic Induction

It is the phenomenon by which varying magnetic fields generate an electric current. Faraday and Henry conducted a series of experiments that proved this. For example, when a coil is connected to a galvanometer, and we use a bar magnet and push it towards the coil, the galvanometer pointer gets deflected. This led to the introduction of electromagnetism, a special branch of physics related to electromagnetic force between electrically charged particles.

Applications of Electromagnetic Induction: Next time when you observe functioning of any devices like electrical generators, induction cooking, induction motors, transformers, etc. you will automatically know that it’s the theory of electromagnetic induction that is in use!

#### Magnetic Flux

Before introducing Faraday’s laws, it is necessary to understand magnetic flux and its formula.

Magnetic flux is the measurement of the total magnetic field that passes through a given area. Its formula is

ΦB = Magnetic field * Area of given surface= BA cos θ,

where B is the magnitude of the magnetic field, the area of the given surface is A, and the angle between B and A is θ. Magnetic flux has the SI unit weber (Wb) or tesla meter squared (T m2).

Here it is imperative to remember Gauss’s Law of Magnetism, which states that the total flux of the magnetic field is zero outside of the given surface.

#### Faraday’s Law of Electromagnetic Induction

Through experiments, Faraday concluded that when magnetic flux through a coil changes with time, an electromotive force (emf) gets induced in the coil. He made observations from these experiments in the form of a law called Faraday’s law of electromagnetic induction. It states that the magnitude of the induced emf in a circuit is equal to the rate of change of magnetic flux through the circuit with respect to time. The Faraday’s law formula is represented as,

ε = − dΦBdt

where ε is the induced emf, and the magnetic flux is ΦB. This is also called the magnetic induction formula.

The negative sign indicates the direction of the ε and hence the direction of the current in the closed-loop. If the coil is closely wound with N turns, the change of flux associated with each turn is the same. Thus, the total induced emf is

ε = −N dΦBdt

This means that the emf can be increased by increasing the number of turns N of the coil.

#### Lenz’s Law

On observation, we will notice that the 19th century is a milestone in the field of physics. Several discoveries were made, and many laws were formulated. For example, in 1834 we had physicist Heinrich Fredrich Lenz who deduced a law called Lenz’s law based on the induced emf polarity. The law states that the induced emf has such a polarity that it produces a current that opposes a change in the magnetic flux that created it. This is represented by the negative sign in the formula for induced emf.

#### Eddy Currents

We have studied that induced currents flow in well-defined paths in conductors such as circular loops. The shape of these loops resembles eddies in the water. To see these, you will have to go to an oceanside and that too in an aeroplane and fly low. Physicist Foucault discovered this effect.

By Lenz’s law, an eddy current creates a magnetic field that opposes the change in the magnetic field that created it. This makes it undesirable, as it heats the core and dissipates electrical energy in the form of heat.

Applications: The opposing nature of eddy currents is useful in specific applications like magnetic braking in trains, electromagnetic damping, induction furnace, electric power meters, etc.

#### Inductance

It was observed that an electric current is induced in a coil if there is a flux change in another coil nearby or within the same coil. This is called inductance. Here, the magnetic flux through a coil is directly proportional to the current induced.

That is ΦB α I. And if the geometry of the coil does not change with time, then, dΦBdtα dIdt . For a coil with N turns, N ΦB α I.

Mutual Inductance: If there are two solenoids S1 and S2, with turns N1 and N2 respectively, and a current I2 is set up through S2, then the corresponding flux linkage in S1 can be denoted by

N1 Φ1 = M12 I2

where the constant of proportionality M12, is the mutual inductance of solenoid S1 with respect to solenoid S2 and is also called the coefficient of mutual induction. Its SI unit is Henry (H).

Self-Inductance: It is the phenomenon where emf is induced in a coil due to a change of flux through it by varying the current through itself.

Here, N ΦB α I and N ΦB = L I

where L is the constant of proportionality and self-inductance of the coil, and it is named the coefficient of self-induction of the coil. Its SI unit is also Henry (H).

As mentioned above, there are numerous applications of Faraday’s laws, of which generating alternating currents is one of the most important. It is even suggested that the migratory patterns of birds must be due to the electromagnetic induction created by the earth’s magnetic field.

Think about it – the Arctic tern, an elegant white sea bird, migrates some 40,000 km every year, and the beautiful pink flamingos migrate from Iran and Pakistan to Mumbai. Is electromagnetic induction involved in this? Find the answer on www.msvgo.com.

### High School Physics

• Alternating Current
• Atoms
• Communication Systems
• Current Electricity
• Dual nature of Radiation and Matter
• Electric Charges and Fields
• Electricity
• Electromagnetic Induction
• Electromagnetic Waves
• Electrons and Photons
• Electrostatic Potential and Capacitance
• Fluid Pressure
• Force and Acceleration
• Force And Laws Of Motion
• Gravitation
• Internal Energy
• Kinetic Theory
• Law of motion
• Light – Reflection And Refraction
• Magnetic Effects Of Electric Current
• Magnetism and Matter
• Management Of Natural Resources
• Mechanical properties of Fluids
• Mechanical properties of Solids
• Motion
• Motion in a plane
• Motion in a straight line
• Moving Charges and Magnetism
• Nuclear Energy
• Nuclei
• Oscillations
• Our Environment
• Paths of Heat
• Physical world
• Ray optics and optical instruments
• Semiconductor Devices
• Semiconductor Electronics: Materials, Devices and Simple Circuits
• Simple Machines
• Sound
• Sources Of Energy
• Specific and Latent Heats
• Spherical Mirrors
• Static Electricity
• Systems of Particles and Rotational motion
• Thermal properties of matter
• Thermodynamics
• Units and Measurement
• Vectors, Scalar Quantities and Elementary Calculus
• Wave Optics
• Waves
• Work, Power and Energy

### High School Chemistry

• Acids, Bases and Salts
• Alcohols, Phenols and Ethers
• Aldehydes, Ketones and Carboxylic Acids
• Aliphatic and Aromatic Hydrocarbons
• Alkyl and Aryl Halides
• Amines
• Analytical Chemistry
• Atomic Structure
• Atoms And Molecules
• Basic concepts of Chemistry
• Biomolecules
• Carbon And Its Compounds
• Carboxylic acids and Acid Derivatives
• Chemical Bonding and Molecular Structures
• Chemical Energetics
• Chemical Equilibria
• Chemical Kinetics
• Chemical Reactions And Equations
• Chemical Reactions and Their Mechanisms
• Chemistry in Everyday Life
• Chemistry of p-Block elements
• Chemistry of Transition and Inner Transition
• Classification of Elements
• Coordination Compounds
• Cyanide, Isocyanide, Nitro compounds and Amines
• Electrochemistry
• Electrolysis
• Elements, Compounds and Mixtures
• Environmental Chemistry
• Equilibrium
• Ethers and Carbonyl compounds
• Haloalkanes and Haloarenes
• Hydrocarbons
• Hydrogen
• Ideal solutions
• Introduction to Organic Chemistry
• Ionic equilibria
• Matter
• Matter Around Us
• Matter In Our Surroundings
• Metallurgy
• Metals And Non-Metals
• Mole Concept and Stoichiometry
• Natural Resources
• Organic Chemistry – Basic Principles
• Periodic Classification of Elements
• Physical and Chemical Changes
• Physical and Chemical Properties of Water
• Polymers
• Preparation, Properties and Uses of Compounds
• Principles and Processes of Isolation of Elements
• Redox Reactions
• Relative Molecular Mass and Mole
• States of Matter
• Structure Of The Atom
• Study of Compounds
• Study of Gas Laws
• Study of Representative Elements
• Surface Chemistry
• The d-block and f-block elements
• The Gaseous State
• The p-Block Elements
• The Periodic Table
• The s-Block Elements
• The Solid State
• Thermodynamics

### High School Biology

• Absorption and Movement of Water in Plants
• Anatomy of Flowering Plants
• Animal Kingdom
• Bacteria and Fungi-Friends and Foe
• Biodiversity and Conservation
• Biofertilizers
• Biological Classification
• Biomedical Engineering
• Biomolecules
• Biotechnology and its Applications
• Biotic Community
• Body Fluids and Circulation
• Breathing and Exchange of Gases
• Cell – Unit of Life
• Cell Cycle and Cell Division
• Cell Division and Structure of Chromosomes
• Cell Reproduction
• Cellular Respiration
• Chemical Coordination and Integration
• Circulation
• Control And Coordination
• Crop Improvement
• Digestion and Absorption
• Diversity In Living Organisms
• Ecosystem
• Environmental Issues
• Excretory Products and their Elimination
• Flowering Plants
• Genes and Chromosomes
• Health and Diseases
• Health and Its Significance
• Heredity And Evolution
• Heredity and Variation
• How Do Organisms Reproduce?
• Human Diseases
• Human Eye And Colourful World
• Human Health and Disease
• Human Population
• Human Reproduction
• Hygiene
• Improvement In Food Resources
• Integumentary System- Skin
• Kingdom Fungi
• Kingdom Monera
• Kingdom Protista
• Life Processes
• Locomotion and Movement
• Microbes in Human Welfare
• Mineral Nutrition
• Molecular Basis of Inheritance
• Morphology of Flowering Plants
• Neural Control And Coordination
• Nutrition in Human Beings
• Organism and Population
• Photosynthesis
• Photosynthesis in Higher Plants
• Plant Growth and Development
• Plant Kingdom
• Pollination and Fertilization
• Pollution; Sources and its effects
• Principles of Inheritance and Variation
• Reproduction and Development in Angiosperms
• Reproduction in Organisms
• Reproductive Health
• Respiration in Human Beings
• Respiration in Plants
• Respiratory System
• Sexual Reproduction in Flowering Plants
• Strategies for Enhancement in Food Production
• Structural Organisation in Animals
• Structural Organisation of the Cell
• The Endocrine System
• The Fundamental Unit Of Life
• The Living World
• The Nervous System and Sense Organs
• Tissues
• Transpiration
• Transport in Plants

### High School Math

• Algebra – Arithmatic Progressions
• Algebra – Complex Numbers and Quadratic Equations
• Algebra – Linear Inequalities
• Algebra – Pair of Linear Equations in Two Variables
• Algebra – Polynomials
• Algebra – Principle of Mathematical Induction
• Binomial Theorem
• Calculus – Applications of Derivatives
• Calculus – Applications of the Integrals
• Calculus – Continuity and Differentiability
• Calculus – Differential Equations
• Calculus – Integrals
• Geometry – Area
• Geometry – Circles
• Geometry – Conic Sections
• Geometry – Constructions
• Geometry – Introduction to Euclid’s Geometry
• Geometry – Three-dimensional Geometry
• Geometry – Lines and Angles
• Geometry – Straight Lines
• Geometry – Triangles
• Linear Programming
• Matrices and Determinants
• Mensuration – Areas
• Mensuration – Surface Areas and Volumes
• Number Systems
• Number Systems – Real Numbers
• Permutations and Combinations
• Probability
• Sequence and Series
• Sets and Functions
• Statistics
• Trignometry – Height and Distance
• Trignometry – Identities
• Trignometry – Introduction

### Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
• Body Movements
• Carbon and Its Compounds
• Cell – Structure And Functions
• Changes Around Us
• Chemical Effects Of Electric Current
• Coal And Petroleum
• Combustion And Flame
• Components Of Food
• Conservation Of Plants And Animals
• Crop Production And Management
• Electric Current And Its Effects
• Electricity And Circuits
• Elements and Compounds
• Fibre To Fabric
• Food production and management
• Force And Pressure
• Forests: Our Lifeline
• Friction
• Fun With Magnets
• Garbage In, Garbage Out
• Getting To Know Plants
• Health and Hygiene
• Heat
• Hydrogen
• Life Processes: Nutrition in Animals and Plants
• Materials: Metals And Non-Metals
• Matter and Its States
• Metals and Non-metals
• Micro Organisms: Friend And Foe
• Motion And Measurement Of Distances
• Motion And Time
• Nutrition In Animals
• Nutrition In Plants
• Organization in Living Things
• Our Environment
• Physical And Chemical Changes
• Pollution and conservation
• Pollution Of Air And Water
• Reaching The Age Of Adolescence
• Reproduction In Animals
• Reproduction In Plants
• Respiration In Organisms
• Rocks and Minerals
• Separation Of Substances
• Simple Machines
• Soil
• Some Natural Phenomena
• Sorting Materials Into Groups
• Sound
• Stars And The Solar System
• Structure of Atom
• Synthetic Fibers And Plastics
• The Living Organisms And Their Surroundings
• Transfer of Heat
• Transformation of Substances
• Transportation In Animals And Plants
• Universe
• Waste-water Story
• Water: A Precious Resource
• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

### Middle School Math

• Area and Its Boundary
• Boxes and Sketches
• Data Handling
• Fun With Numbers
• Heavy and Light
• How Many
• Long And Short
• Mapping
• Measurement
• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
• Patterns
• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time