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  • Physics
    • The world around you!
    • Mechanics
      • Preface
      • Units, Vectors and Mathematical Physics
        • Units, Standards & Dimension analysis
        • Measurement
        • Scalars and Vectors
        • Multiplication of Two Vectors
        • Mathematical Physics
      • Kinematics
        • Speed, Velocity and Acceleration
        • Motion in 1-D and free fall
        • Motion in 2-D and Projectile motion
        • Relative velocity
      • Newton's Laws of Motion
        • Force and laws of motion
        • Friction
        • Simple Machines
      • Work, Energy and Power
        • Work and Kinetic energy
        • Potential energy and Energy conservation
        • Power
      • Linear Momentum
        • Momentum and Impulse
        • CM & CG
        • Collisions
      • Circular motion
        • Uniform circular motion
        • Vertical circular motion
      • Rotational Motion
        • Rotational kinematics
        • Moment of inertia
        • Dynamics of rotational motion
        • Angular momentum
        • Rolling Motion
      • Oscillations
        • Simple Harmonic Motion
        • Simple pendulum
      • Gravitation
        • Newton's universal law of gravitation
        • Gravitational potential energy
        • Kepler's Laws
      • Fluid Mechanics
        • Fluid density and pressure
        • Pascal's principle
        • Buoyancy and Archimedes' principle
        • Bernoulli's principle
      • Mechanical Properties of Matter
        • Elasticity
        • Surface tension
        • Viscosity in fluids
        • Stokes' law
    • Thermal Physics
      • Preface
      • Heat & Temperature
        • Internal energy & temperature
        • Sources of heat
      • Calorimetry
        • Specific heat
        • Change of State
        • Calorimeter
      • Thermal Expansion
        • Expansion of solids
        • Expansion of liquids and gases
        • Anomalous expansion of water
      • Heat Transfer
        • Conduction and Convection
        • Radiation
        • Applications of heat transfer
      • Kinetic Theory
        • Kinetic theory of gases
        • Ideal Gas Equations
      • Thermodynamics
        • First law of thermodynamics
        • Specific heat capacities of gases
        • Entropy and second law of thermodynamics
      • Heat Engines
        • Carnot cycle
        • Heat pumps
    • Waves and Optics
      • Preface
      • Wave Motion
        • Transverse and longitudinal waves
        • Wave characteristics
        • Reflection and interference of waves
        • Standing waves
      • Sound Waves
        • Properties of Sound Wave
        • Vibrations of air column
        • Interference of sound waves
        • Doppler effect
        • Musical Sounds
      • Nature of Light
        • Properties of light
        • Shadows and Eclipses
      • Reflection
        • Laws of reflection
        • Image formation in plane mirrors
        • Concave and convex mirrors
      • Refraction
        • Laws of refraction
        • Total internal reflection
        • Prisms and rainbows
        • Lenses
      • Interference and Diffraction
        • Wave nature of light
        • Interference
        • Diffraction
        • Polarization
      • Optical Instruments
        • Human Eye
        • Microscopes & Telescopes
        • Eyepieces & Cameras
    • Electricity
      • Preface
      • Electric Charge and Electric Field
        • Coulomb's law
        • Electric field
      • Electric Potential
        • Electric potentia and potential energy
        • Relation between field and potential
        • Electric dipole
      • Gauss's law
        • Gauss law
        • Spherical charge distribution
        • Linear charge distribution
        • Planar charge distribution
      • Capacitors and Dielectrics
        • Capacitors and Capacitance
        • Types of capacitors
        • Energy stored in a capacitor
        • Dielectric types
      • Current Electricity
        • Current, Resistance and ohm's law
        • Cells, EMF and Internal Resistance
        • Kirchoff's laws and electric circuits
        • Wheatstone bridge and potentiometer
        • Ammeter and Voltmeter
        • RC circuits in DC voltage
      • Thermal and Chemical effects of current
        • Joule's law of heating
        • Seebeck and Peltier effect
        • Thomson's effect
        • Faraday's laws of electrolysis
    • Electromagnetism
      • Preface
      • Magnetism
        • Magnets and magnetic fields
        • Magnetic materials and properties
        • Earth's magnetic field
        • Magnetometers
      • Magnetic Forces
        • Lorentz force
        • Magnetic force on a current carrying conductor
        • Torque on a current carrying loop
      • Magnetic field due to current
        • Biot-Savart's law
        • Ampere's law
      • EM Induction
        • Faraday's and Lenz's law
        • Self and Mutual induction
        • LC/LR circuits
      • A.C. Circuits
        • Current, Voltage and RMS value
        • RLC circuits
        • Resonance and power in AC circuits
        • Machines and Devices
      • Electromagnetic Waves
        • Maxwell's equations
        • Light as EM Wave
        • Properties of EM Waves
    • Modern Physics
      • Preface
      • Bohr's atomic model
        • Rutherford's atomic model
        • Bohr's atomic model
      • Quantum theory
        • Photons and Photoelectric effect
        • Wave Nature of Particles
        • Quantum model of atom
        • X-rays
      • Nucleus
        • Properties of nucleus
        • Isotopes, isobars and isotones
        • Mass defect and binding energy
      • Radioactivity
        • Alpha, beta and gamma rays
        • Laws of radio-activity
        • Applications of radioactivity
      • Nuclear Reactions
        • Nuclear fission
        • Nuclear fusion
        • Radiation hazards
      • Semiconductor Electronics
        • Energy bands in solids
        • Semiconductor diodes
        • Half-wave and Full-wave rectifiers
        • BJTs and FETs
        • Applications of transistors
        • Digital Electronics
      • Communication Systems
        • Electromagnetic Waves
        • Modulation
  • Chemistry
    • Matter is everything!
    • Structure of Matter
      • Preface
      • Elements, Compounds and Mixtures
        • Elements
        • Compounds
        • Mixtures
        • Separation and Purification
      • Properties of Matter
        • Fundamental units
        • Derived units
        • Chemical properties
      • Measurement and Experimental techniques
        • Units and Conversions
        • Measurement and Evaluation
        • Physical constants
      • Atomic Structure
        • Atoms, Molecules and Ions
        • Dalton's atomic theory
        • Electrons, Protons and Neutrons
        • Atomic Models
        • Structure of an atom
        • Isotopes
      • Quantum Theory
        • The nature of light
        • Atomic spectrum
        • Wave Nature of Particle
        • Photoelectric Effect
        • Quantum mechanical model
      • Development of Periodic Table
        • Electronic configuration
        • Genesis of classification
        • Modern Periodic table
      • Periodic Properties
        • Atomic & Ionic radii
        • Ionization energies
        • Electron affinities
        • Electronegativity
      • Chemical Bonding
        • Octet and Fajans' rule
        • Valency
        • Ionic Bonding
        • Chemical Properties
        • Lewis dot structures
        • Resonance Structures
        • Covalent and Metallic Bonding
        • Valence Bond Theory
        • Molecular orbital theory
        • Hybridization of atomic orbitals
        • Molecular Geometry
      • Nuclear Chemistry
        • Alpha, Beta and Gamma radiation
        • Radioactive Transformations
        • Rate of Radioactive Decay
        • Effects of Radiation
        • Applications of radioisotopes
        • Nuclear Fission
        • Nuclear Fusion
    • States of Matter
      • Preface
      • Kinetic particle theory
        • Solids, Liquids and Gases
        • Change in states
        • Latent heat
      • Forces of Attraction
        • Intramolecular forces
        • Dipole forces
        • Intermolecular forces
        • Hydrogen bonding
      • Gases
        • Pressure of gas
        • Gas laws
        • Ideal gas equation
        • Molar mass and density
        • Dalton's law of partial pressure
        • Kinetic molecular theory
        • Effusion & Diffusion
        • Real and Ideal gases
      • Liquids
        • Surface tension
        • Viscosity
        • Evaporation
        • Boiling point
      • Solids
        • Crystalline solids
        • Structure of Solids
        • Properties of Solids
        • Elasticity and Hooke's law
        • Lattice Energy
      • Solutions
        • Types of Solutions
        • Colloids
        • Solubility
        • Concentration
        • Volumetric analysis
        • Enthalpy of Solutions
        • Raoult's Law
        • Colligative properties
        • Phase Diagrams
      • Atmosphere and Environment
        • Spheres of Earth
        • Atmosphere
        • Biogeochemical Cycles
      • Air, Water & Soil
        • Composition of air
        • Air pollution
        • Greenhouse effect
        • Water and its sources
        • Properties of Water
        • Water - treatment and pollution
        • Soil - pollution and control
        • Green chemistry
    • Chemical Reactions
      • Preface
      • Chemical Equations
        • Chemical Changes
        • Types of chemical reactions
        • Characteristics of chemical reactions
        • Balancing chemical equations
      • Chemical Calculations
        • Stoichiometry
        • The Mole
        • Mass Spectrometer
        • Molecular formulae
      • Acids, Bases and Salts
        • Acids
        • Bases
        • Salts
        • Acid-base Theories
        • Acid-base Classification
        • Nomenclature of acids, bases & salts
        • pH Scale and Buffer Solution
        • Acid-base titration
      • Thermo Chemistry
        • Energy changes
        • System, Surroundings and Types
        • Energy, heat and work
        • First law of thermodynamics
        • Enthalpy and Hess' law
        • Second law of thermodynamics
        • Gibbs free energy
      • Chemical Kinetics
        • Rate (speed) of reaction
        • Integrated Rate laws
        • Order of reaction
        • Catalyst
      • Chemical Equilibrium
        • Reversible and Irreversible reactions
        • Law of mass action
        • Equilibrium constants
        • Le Chatelier Principle
      • Oxidation and Reduction
        • Redox reactions
        • Oxidizing and reducing agents
        • Oxidation number
        • Balancing of reactions
        • Everyday examples
      • Electrochemistry
        • Conductors and Semiconductors
        • Ohm's Law
        • Electrolysis
        • Corrosion
        • Faraday's laws
        • Voltaic or Galvanic cell
        • Electromotive Force (EMF)
        • Cells or batteries
    • Metals and Non-metals
      • Preface
      • Overview
        • Properties of metals
        • Uses of metals
        • Properties of non-metals
        • Uses of non-metals
      • Hydrogen
        • Properties of Hydrogen
        • Preparation and Uses of Hydrogen
        • Water
        • Heavy water
        • Hydrogen peroxide
      • Alkali & Alkaline Earth Metals
        • s-Block elements
        • Properties of s-Block elements
        • Sodium and its compounds
        • Potassium and its compounds
        • Magnesium and its compounds
        • Calcium and its compounds
      • Boron Family
        • Properties of IIIA Elements
        • Boron and its compounds
        • Aluminum and its compounds
      • Carbon Family
        • Extraction and Uses of IV A elements
        • Physical Properties of IVA elements
        • Physical Properties of Carbon
        • Chemical Properties of Carbon
        • Silicon and its compounds
      • Nitrogen Family
        • Properties of VA elements
        • Compounds of VA elements
        • Nitrogen and its compounds
        • Ammonia
        • Phosphorus and its compounds
      • Oxygen Family
        • Properties of VIA elements
        • Oxygen and its compounds
        • Sulfur and its compounds
      • Halogens
        • Production of Halogens
        • Properties of Halogens
        • Compounds of Halogens
        • Uses of Halogens
      • Noble Gases
        • Discovery and Isolation of noble gases
        • Properties of noble gases
        • Xenon and its Compounds
      • Transition Metals
        • Physical Properties of d-Block elements
        • Chemical Properties of d-Block elements
        • Metal Oxoanions Salts
        • Iron
        • Copper
      • Inner transition Metals
        • Lanthanides
        • Actinides
      • Metallurgy & Alloys
        • Concentration of Ores
        • Extraction of Metals
        • Corrosion of Metals
        • Alloys of Metals
      • Coordination Compounds
        • Metal complexes
        • Ligands
        • Bonding Theories
        • Properties of Coordination Compounds
        • Stereo and Structural isomerism
        • Applications of compounds
    • Organic Chemistry
      • Preface
      • Overview
        • Organic compounds
        • Carbon and its allotropes
        • Classification of organic compounds
        • Nomenclature of organic compounds
        • Homologous series
        • Isomerism
      • Hydrocarbons
        • Alkanes
        • Alkenes
        • Alkynes
        • Aromatic hydrocarbons
      • Alcohols, Phenols & Ethers
        • Alcohols
        • Phenols
        • Ethers
      • Halogen derivatives
        • Aryl and Alkyl halides
        • Chloroform
        • Iodoform and Perflourides
      • Aldehydes and Ketones
        • Carbonyl Compounds
        • Preparation of aldehydes and ketones
        • Properties of aldehydes and ketones
      • Carboxylic Acids
        • Structure and Acidity
        • Acetic acid
        • Carboxylic acid derivatives
        • Soaps and Detergents
      • Nitrogen Derivatives
        • Amines
        • Cyanides and Cyanates
        • Nitro compounds
      • Reaction Mechanisms
        • Components of reaction
        • Electronic Displacement
        • Structure and Acidity
        • Classification of Reactions
        • Substitution Reactions
        • Elimination reactions
        • Organic Synthesis
      • Polymers
        • Macromolecules and Polymers
        • Classification of polymers
        • Commercial polymers
        • Biodegradable polymers
      • Biochemistry
        • Carbohydrates
        • Glucose and Fructose
        • Sucrose
        • Starch
        • Proteins
        • Vitamins
        • Lipids
        • Enzymes
        • Nucleic acids
      • Organic Chemistry Today
        • Analgesics
        • Antacids
        • Antimicrobials
        • Antivirals
        • Antiseptics
        • Sweetening Agents
  • Biology
    • Wonders of the inner world!
    • Biochemistry
      • Preface
      • Introduction
        • Chemical basis of life
        • Milestones in Biochemistry
        • Applications
      • Structure of matter
        • Matter
        • Elements
        • Isotopes
      • Chemical Bonding
        • Introduction
        • Covalent Bond
        • Ionic Bond
        • Molecular Shape and Function
        • Chemical reactions
      • Water
        • Universal solvent
        • Polarity of Water
        • Properties of water
        • Dissociation of water molecules
      • Carbon
        • Nature of carbon
        • Molecular Diversity
      • Molecules of Life
        • Biological molecules
        • Polymers
        • Carbohydrates
        • Lipids
        • Proteins
        • Enzymes
        • Nucleic acids
    • Cell Biology
      • Preface
      • Basic Unit of Life
        • Cell diversity
        • Cell theory
        • Cell shapes
        • Prokaryotic cells
        • Eukaryotic cells
      • Cell Structure
        • Cell membrane
        • Transport in cells
        • Parts of cell
        • Cell Organelles
        • Summary
      • Cellular Energetics
        • Metabolic activities
        • Coupled Reactions
        • Bioenergetics
        • Enzymes
      • Cellular Respiration
        • Introduction
        • Catabolic Pathways
        • Respiratory Substrates
        • Respiratory Quotient
        • Redox Reactions
        • Stages of Respiration
        • Fermentation
      • Photosynthesis
        • Discovery of photosynthesis
        • Process of photosynthesis
        • Products of photosynthesis
        • Photophosphorylation
        • Calvin Cycle
        • C4 Pathway (Hatch-Slack Cycle)
        • CAM Plants
      • Cell Communication
        • Introduction
        • Cell Signaling
        • Stages of cell signaling
        • Transduction Pathways
        • Response
      • Cell Division
        • Role of cell division
        • Mitosis
        • Cytokinesis
        • Binary Fission
        • Evolution of Mitosis
        • Cell Cycle Control
    • Genetics
      • Preface
      • Heredity
        • Introduction
        • Reproduction
        • Meiosis
        • Mitosis and Meiosis
      • Mendelian Genetics
        • Mendel's experiment
        • Mendel's Laws of Inheritance
        • Inherited disorders
        • Genetic testing and counseling
      • Chromosomal Basis of Inheritance
        • Introduction
        • Chromosomes
        • Linkage and crossing over
        • Sex-linked inheritance
        • Abnormalities
        • Genetic basis of development
      • Molecular Genetics
        • Introduction
        • The search for genetic material
        • DNA and Replication
        • Gene regulation and expression
        • Genetic Code
        • Protein synthesis
        • DNA packaging
        • DNA mutations
        • Molecular basis of cancer
        • Genetics of Viruses and Bacteria
        • Operons
      • DNA Technology and Applications
        • Recombinant DNA technology
        • Restriction Fragment Analysis
        • DNA Cloning
        • DNA Libraries
        • Genome mapping
        • Genomics
        • Practical applications
    • Evolutionary Biology
      • Preface
      • Exploring Life
        • What is life
        • Origin of life
        • Evolution of Life
        • Unity and Diversity
        • Evolution
      • Understanding Evolution
        • Diversity of life
        • Evidence of Evolution
        • Basic principles of evolution
        • Evolutionary Applications
      • Modern Evolutionary Synthesis
        • Theories of evolution
        • Mechanisms of Change
        • Outcomes of Evolution
        • Sources of Variation in a population
        • Hardy- Weinberg Equilibrium
      • Diversity of Organisms
        • Origin and diversity of life
        • Chemical evolution
        • RNA World
        • Systematics
        • Binomial Nomenclature
      • Monera & Protista
        • Kingdom Monera
        • Bacteria-Reproduction
        • Pathogenic and Useful Bacteria
        • Eubacteria
        • Importance of Prokaryotes
        • Kingdom Protista
        • Classification of Protista
      • Kingdom Fungi
        • Fungus
        • Nutrition and Fungal Lifestyles
        • Classification of Fungi
        • Fungi Impact on Ecosystem
        • Useful Fungi
      • Kingdom Plantae
        • Introduction
        • Thallophyta
        • Bryophyta
        • Pteridophyta
        • Gymnosperms
        • Angiosperms
        • Plants and Human Welfare
      • Kingdom Animalia
        • Evolution of Animals
        • Basis of Classification
        • Animal Development
        • Classifying Animals
        • Human Evolution
        • Microbes in human welfare
      • Ecology and Biosphere
        • Scope of ecology
        • Subfields of Ecology
        • Ecology and Evolutionary Biology
        • Ecosystem
        • Biomes
      • Animal Behavior
        • Introduction
        • The Diversity of Behavior
        • Animal communication
        • Learning and evolution of behavior
      • Community & Population Ecology
        • Community interactions
        • Trophic structure
        • Biological magnification
        • Biomes
        • Biogeochemical cycles
        • Humans and the biosphere
        • The study of Population Ecology
        • Population viability analysis
        • Population cycles
      • Conservation & Restoration Ecology
        • Introduction
        • Conservation of biodiversity
        • Natural resources
        • Air
        • Water
        • Soil
        • Management of Natural Resources
        • Coal and Petroleum
    • Plant Form and Function
      • Preface
      • Plant Structure
        • Basic plant structure
        • Root System
        • Shoot system
        • Leaf and Flower
        • Seed
      • Growth & Development
        • Plant growth and development
        • Primary Growth
        • Secondary Growth
        • Morphogenesis
      • Transport in Plants
        • Introduction
        • Absorption through roots
        • Active transport
        • Ascent of Sap
        • Transpiration
        • Cohesion and Adhesion
        • Transport of Minerals, Food
      • Nutrition in Plants
        • Nutrition - plant growth
        • Modes of Nutrition
        • Minerals and Essential nutrients
        • Photosynthesis for plant nutrition
        • Nutritional Adaptations
      • Plant Reproduction
        • Introduction
        • Asexual reproduction
        • Sexual Reproduction
        • Pollination and Fertilization
        • Seeds
        • Apomixis and Polyembryony
      • Plant Responses
        • Plant response to stimuli
        • Phytohormones (Plant Hormones)
        • Tropisms and Nasties
        • Circadian Rhythms
        • Response to stress
        • Defensive Mechanisms
        • Apoptosis and Senescence
      • Crop and Medicinal Plants
        • Agriculture
        • Plant Breeding
        • Medicinal plants
        • Plant Biotechnology
    • Animal Form and Function
      • Preface
      • Basic Principles
        • Nature of animals
        • Tissues and Organs
        • Homeostasis and Thermoregulation
        • Metabolism
      • Life Processes
        • Circulation
        • Respiration
        • Digestion
        • Vision and Sense
        • Immune Mechanism
        • Endocrine and Nervous system
      • Nutrition
        • Need of nutrition
        • Nutrition in Animals
        • Nutrition in Humans
      • Animal Physiology
        • Introduction
        • Physiology of Annelida
        • Physiology of Arthropoda
        • Physiology of Amphibia
        • Physiology of Chordata
      • Reproduction and Development
        • Asexual Reproduction
        • Sexual Reproduction
        • Morphogenesis
        • Mammalian Development
      • Animal Husbandry
        • Farming practices
        • Cattle Farming
        • Poultry Farming
        • Fish Production
        • Aquaculture
        • Bee Keeping
        • Sericulture
    • Human Physiology
      • Preface
      • Introduction to Human Body
        • Physiology
        • Transport system
        • Communication
        • Intake of raw materials and elimination of waste
        • Protection
        • Reproduction
        • Diseases and illness
      • Human cells & Tissues
        • Human Cells
        • Tissues
        • General Principles
        • Movement of substances with in body fluids
        • Cell division
      • Nervous System
        • Introduction
        • Neurons
        • Nerves
        • Types of Nervous System
        • Brain
        • Reflex Action and Arcs
        • Diseases and Disorders
      • Sensory System
        • Eye
        • Ear
        • Nose
        • Taste buds
      • Endocrine & Reproductive System
        • Hormones
        • Hormonal Signaling
        • Adrenal glands
        • Thyroid & Parathyroid glands
        • Pituitary gland & Hypothalamus
        • Pancreas
        • Other hormones
        • Hormones from Non-endocrine tissues
        • Reproductive system
        • Female Reproductive Anatomy
        • Male Reproductive Anatomy
        • Fertilization
        • Embryonic Development and Birth
      • Digestive System
        • Nutrition
        • Organs of digestive system
        • Digestion & Absorption
        • Disorders
      • Cardiovascular System
        • Heart
        • Blood Vessels - Intricate networks
        • Heart Diseases
        • Tests for Diagnosis
        • Cholesterol test
        • Radionuclide imaging
      • Respiratory System
        • Lungs
        • Respiratory Cycle
        • Breathing Control
        • Aerobic and Anaerobic respiration
        • Lung Diseases
      • Muscular System
        • Introduction
        • Skeletal system
        • Skull
        • Thoracic cage
        • Appendicular Skeleton
        • Types of muscle fibers
      • Immune System
        • Defense Mechanisms
        • Innate Immunity
        • Leukocytes
        • Adaptive Immunity
        • Humoral and cell-mediated Immunity
        • Summary
      • Lymphatic System
        • Introduction
        • Basic Anatomy
        • Importance of Lymphatic System
        • Lymphatic disorders
      • Urinary System
        • Structure of urinary system
        • Kidney
        • Osmoregulation & Excretion
        • Disorders
        • Diagnosis and treatment
      • Health & Diseases
        • Health
        • Types of Disease
        • Spread of Infectious Diseases
        • Symptoms of Disease
        • Diseases caused by bacteria
        • Diseases Caused by Protozoa
        • Other diseases
      • Common Health Problems
        • Anemia
        • Hypertension
        • Cholesterol
        • Hypothermia
        • Obesity
        • Diabetes
        • Hypoglycemia
        • Systemic lupus erythematosus
        • Tests
      • Medical Diagnostics
        • Diagnosis
        • Creatinine Test
        • Blood Urea Nitrogen Test
        • Sodium in blood
        • Blood sugar test
        • Musculoskeletal Tests
        • Chest x-ray
        • Tuberculin skin test
        • UGI Endoscopy
        • Liver and thyroid tests
        • Mammogram
        • Electro encephalogram
        • Other Blood tests
        • Cancer markers
  • Math
    • The language of science!
    • Arithmetic
      • Preface
      • Number Systems
        • Decimal Number System
        • Types of Numbers
        • HCF & LCM
        • Binary Number System
        • Surds
      • Fractions and Divisibility
        • Fractions
        • Decimals
        • Tests of Divisibility
      • Squares and Cubes
        • Squares and Square Roots
        • Cubes and Cube Roots
      • Ratio and Proportions
        • Ratios
        • Proportions
        • Rate & Speed
      • Commercial Arithmetic
        • Percentage
        • Profit, Loss & Discount
        • Simple & Compound Interest
        • Commercial Applications
    • Algebra
      • Preface
      • Basic Algebra
        • Exponents
        • Expressions and Polynomials
        • Expansions
        • Factorization
      • Higher Algebra
        • Linear equations & inequations
        • Quadratic Equations
        • Theory of equations
        • Partial Fractions
        • Complex Numbers
        • Logarithms
      • Progressions
        • Arithmetic Progressions
        • Geometric Progressions
        • Harmonic Progressions
        • Mathematical Induction
        • Exp. and log series
      • Matrices
        • Types of Matrices
        • Operations on Matrices
        • Determinant of a Square Matrix
        • Inverse of a Square Matrix
        • Solving System of Linear Equations
      • Sets and Relations
        • Types of Sets
        • Operations on Sets
        • Relations
      • Functions and Statements
        • Functions
        • Statements
      • Permutations and Combinations
        • Permutations
        • Combinations
        • Binomial Theorem
      • Vector Algebra
        • Operations on Vectors
        • Dot and Cross products
        • Multiplication of 3 or more vectors
    • Geometry
      • Preface
      • Lines and Angles
        • Points, Lines and Planes
        • Angles
        • Parallel Lines and Transversal
        • Perpendicular and angle bisectors
      • Triangles
        • Classification of Triangles
        • Terms Related to a Triangle
        • Congruency & Similarity
        • Construction of Triangles
      • Polygons
        • Polygon
        • Quadrilaterals
        • Parallelograms
        • Rectangles, Rhombuses & Squares
        • Trapezoids
      • Circles
        • Circumference & Area
        • Angles & Arcs
        • Tangents & Sectors
        • Equation of a Circle
        • System of circles
      • Mensuration
        • Mensuration of 2D figures
        • Mensuration of 3D figures
      • Co-ordinate Geometry
        • Locus
        • Transformation of axes
        • Straight Lines
        • Pair of Straight Lines
        • Polar Co-ordinates
      • Conic Sections
        • Parabola
        • Ellipse
        • Hyperbola
      • 3D Geometry
        • Co-ordinate Axes and Planes
        • Direction Cosines & Ratios
        • Equation of a Line in Space
        • Planes
        • Spheres
    • Trigonometry
      • Preface
      • Pythagorean Theorem
        • Right Triangles and Pythagorean Theorem
        • Applications of Pythagorean theorem
      • Trigonometric Ratios and Identities
        • Trigonometric Ratios
        • Trigonometric Identities
        • Properties of trigonometrical functions
      • Heights & Distances
        • Angle of Elevation
        • Angle of Depression
      • Trigonometric Equations
        • Principal Solution
        • General Solutions
        • Trigonometric Inequalities
      • Properties of Triangles
        • Law of Sines and Cosines
        • Area of a Triangle
        • Miscellaneous
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car on a stormy night Are you safe inside a car on a stormy night? Have you ever wondered what would happen if you were struck by lightning while in a car on a stormy night? What is the cause of this lightning? Lets learn more from such applications that we face in everyday life.

Learning objectives

After completing the topic, the student will be able to:

  • Explore and validate the concept of electric potential based on various daily life scenarios.
  • Discuss and differentiate between electric potential energy and gravitational potential energy.
  • Explore electrical potential of a point charge and develop electrical potential difference between two point charges and also for a group of point charges.
  • Discuss, explore and relate equipotential of a surface to the electric field strength.
  • Explore and expand bio–medical applications of the electrical potential difference in recording the heart beat of a person and analyze the electrical impulses due to visual or auditory stimuli.
uniform gravitational field Object moving in a uniform gravitational field
  • The work done on a basketball moving in a uniform gravitational field.
  • The work done by the gravitational force is the same for any path from a to b: w = – Δ U = mgh
Introduction

In mechanics, potential energy of a body is described in detail; it was due to its position or internal atomic arrangement. The two main types of potential energy are elastic and gravitational potential energies. When there is no external source of energy, if an object is in motion, its kinetic energy and its potential energy are interchanged between each other and the object’s energy is conserved. For example, motion of a pendulum bob or motion of a ball falling from a height.

When a charge is moving in an electric field that is produced by a source charge, what happens to its potential energy and kinetic energy? Consider a ball held at a height h. Its gravitational potential energy is mgh. If the ball is released, it will fall towards the earth, which has a gravitational potential energy of zero. The ball moves from a higher potential energy level to a lower potential level.

Its potential energy mgh is converted to kinetic energy 1/2mv2. Now replace the ball with a negative charge –q which has a mass mq. Its gravitational potential is mqgh. It will also behave in the same manner as the ball when it falls towards the earth. Place a charge +Q on an insulating pole at a horizontal distance and distance h from –q. The negative charge –q is placed equidistant from the earth and the positive charge +Q. What would happen to the motion of the negative charge?

The negative charge –q would of course be attracted to +Q, since the electric force or Coulomb force is at least 1038 times stronger than the gravitational force.

 Electric Potential Energy Electric potential energy of a charge in analogy with the elastic potential energy of a spring
  • The spring has more elastic PE when compressed.
  • The small charge similarly has more PE when pushed closer to the charged sphere. In both cases the increased PE is the result of work required to reach the closer location.
Electric potential energy

What can we say about the potential energy of the negative charge when it is moving towards the positive charge? We observe that its gravitational potential energy remains the same (mqgh). Since electric or Coulomb force is making the negative charge move, we say that the Coulomb force is arising due to energy, which we name it as electric potential energy.

Motion of the negative charge in an electric field of the positive charge can be compared to the motion of the ball in a gravitational field of the earth. We say that the negative charge moves from a higher electrical potential energy level to a lower electrical potential energy level.

If the ball has to be lifted from height h to a higher height h1, (h1 > h), we have to supply energy to the ball. The energy is used for working against the gravitational force. The potential energy of the ball at the new height is mgh1 and it has increased. Similarly, how can the electrical potential energy of –q be increased? If we shift –q away from +Q (the level of zero potential energy), this can be possible. If we move –q from its position to the left, the potential energy level of –q increases.

Replace –q with +q. Since +q is a positive charge, it will get automatically repelled by the source charge +Q (like charges repel each other). Now we have a scene opposite to –q. The potential energy decreases when +q is moving away and the potential energy increases when +q comes closer to +Q. This is because work has to be done by an external force to push +q towards +Q and the energy is stored as potential energy.

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MODEL TESTS
EAMCET (ENGG) JEE (MAIN) JEE (ADV) NEET

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