Electric Charges and Fields
Pull off a polyester sweater on a dry winter evening and you hear a crackle and may see tiny sparks. Touch a car door after a long drive and you feel a small shock. During a storm, a lightning flash carries a huge charge from a cloud to the ground. All of these come from electric charge (വൈദ്യുത ചാർജ്) that has piled up and then suddenly moves. This chapter is the start of electrostatics (സ്ഥിതവൈദ്യുതി), the physics of charges at rest. You will learn what charge is and how objects get charged. You will learn how two charges push or pull each other (Coulomb's law) and how many charges add up (superposition). You will meet the electric field (വൈദ്യുത മണ്ഡലം) and its field lines, the electric dipole, electric flux and one of the most powerful results in physics, Gauss's law. This animated self-study guide starts with a toolkit of vectors, maths and mechanics that assumes nothing. It solves every textbook example and exercise in the board-exam layout and ends with a full 70-mark model question paper.
The chapter in one picture
Scene 1: silk rubbing a glass rod pulls some electrons off the glass. The glass is left with more protons than electrons, so it is positive. The silk has extra electrons, so it is negative. No charge is created or destroyed; it only moves, and the total stays zero. This is conservation of charge (ചാർജ് സംരക്ഷണം). Scene 2: the electric field lines (വൈദ്യുത മണ്ഡലരേഖകൾ) of a positive and a negative charge, an electric dipole (വൈദ്യുത ദ്വിധ്രുവം). Lines start on + and end on −, and they never cross. Scene 3: a Gaussian surface (ഗോസിയൻ ഉപരിതലം) around a charge. As the sphere grows, the field on it gets weaker (∝ 1/r²) but its area grows (∝ r²). So the electric flux (വൈദ്യുത ഫ്ലക്സ്) through it is always q/ε₀. That is Gauss's law (ഗോസ് നിയമം). The electrons shown are a cartoon: real rubbing moves billions of them.
How to use this guide
🎬 Watch the animations
Charges hop, forces add as arrows, field lines grow and Gaussian surfaces swell, one step at a time. Press Next ▶ or ▶▶ Auto play. Animations pause by themselves when you scroll away; click a lab to start it again.
🧪 Do the virtual experiments
Drag charges, vectors and Gaussian surfaces, move sliders and read the live numbers. Every number in the labs is worked out with the real formulas of the chapter.
✍️ Try before you see
Every numerical is laid out the board-exam way: Given → Formula → Substitution → Answer with unit. Use 💡 Show a hint first and work in your notebook. Only then open ✅ Show final answer.
🧰 Start with the toolkit
Pages 1–3 teach vectors, powers of ten, areas, ∑ → ∫ and Newton's laws from scratch. If you are confident, skim them and do their quizzes. The chapter uses these ideas on almost every page.
🗣 English medium, Malayalam help
The guide is in English, like your textbook and exam. Purple മലയാളം words give the Malayalam name of a technical term the first time it appears on a page, to help you connect it with what you already know.
Exam focus (Karnataka 2nd PUC board)
The theory paper is for 70 marks and lasts 3 hours, plus 15 minutes of reading time. It has Part A (MCQs and fill in the blanks, 1 mark each), Part B (2-mark questions), Part C (3-mark questions) and Part D (5-mark long answers and 5-mark numericals). Electric Charges and Fields is a favourite unit for all four parts:
- 1 mark: SI unit of charge or flux, the value of k or ε₀, quantisation (q = ne), the direction of a dipole moment, properties of field lines.
- 2–3 marks: properties of charge, Coulomb's law in vector form, defining the electric field and dipole moment, why field lines never cross, charging by induction (with diagrams), stating Gauss's law.
- 5-mark derivations: field on the axis or equatorial line of a dipole, torque on a dipole in a uniform field, and Gauss's law applied to an infinite line, an infinite plane sheet or a thin spherical shell. Practise each with a labelled diagram.
- 5-mark numericals: Coulomb force and superposition (charges on a line, triangle or square), the field of two charges and the null point, dipole fields and torque, flux and Gauss's law.
The weightage of each chapter is fixed by the Karnataka School Examination and Assessment Board (KSEAB) blueprint for your year. Check the latest blueprint and model papers with your college. The model paper on pages 19–20 follows the current board pattern.
Learning path
Follow the pages in order. Part A builds the tools (nothing assumed). Part B is the chapter, section by section. Part C solves all the exercises, shows real-life uses, revises and tests you.
Glossary (English ↔ Malayalam)
The technical terms of this chapter with their Malayalam names. In the exam, always write the English term.
| English term | Malayalam | Meaning |
|---|---|---|
| Electric charge | വൈദ്യുത ചാർജ് | The property of matter that causes electric forces; two kinds, positive and negative; SI unit coulomb (C) |
| Electrostatics / static electricity | സ്ഥിതവൈദ്യുതി | The study of forces, fields and potentials of charges at rest |
| Electrification (charging) by friction | ഘർഷണം മൂലമുള്ള വൈദ്യുതീകരണം | Charging two bodies by rubbing: electrons move from one to the other |
| Conductor · insulator | ചാലകം · ഇൻസുലേറ്റർ (കുചാലകം) | Lets charge move freely (metals, earth, human body) · does not (glass, plastic, nylon, porcelain) |
| Semiconductor | അർധചാലകം | Lets charge move, but less easily than a conductor (silicon, germanium) |
| Earthing / grounding | എർത്തിങ് | Connecting a conductor to the earth so that extra charge flows away |
| Charging by induction | പ്രേരണം വഴി ചാർജ് ചെയ്യൽ (വൈദ്യുതപ്രേരണം) | Charging a body without touching it, by bringing a charged body near and earthing |
| Electroscope | ഇലക്ട്രോസ്കോപ്പ് | A device whose metal leaves spread apart to show that a body is charged |
| Point charge | ബിന്ദു ചാർജ് | A charged body whose size is very small compared with the distances involved |
| Additivity of charge | ചാർജിന്റെ സങ്കലനീയത | The total charge of a system is the algebraic sum of its charges (with signs) |
| Conservation of charge | ചാർജ് സംരക്ഷണം | The total charge of an isolated system never changes |
| Quantisation of charge | ചാർജിന്റെ ക്വാണ്ടീകരണം | Every charge is a whole-number multiple of e: q = ne, e = 1.6 × 10−19 C |
| Coulomb's law | കൂളോം നിയമം | F = (1/4πε₀) q₁q₂/r² between two point charges at rest |
| Permittivity of free space | ശൂന്യസ്ഥലത്തിന്റെ പെർമിറ്റിവിറ്റി | ε₀ = 8.854 × 10−12 C² N−1 m−2; 1/4πε₀ ≈ 9 × 10⁹ N m² C−2 |
| Inverse square law | വിപരീത വർഗ നിയമം | A force or field that falls as 1/r²: double the distance, one quarter of the force |
| Superposition principle | അധ്യാരോപണ തത്വം | The total force (or field) is the vector sum of the forces (fields) due to each charge separately |
| Vector · scalar · unit vector | സദിശം · അദിശം · യൂണിറ്റ് സദിശം | Has magnitude and direction · magnitude only · a vector of length 1 that shows a direction |
| Electric field | വൈദ്യുത മണ്ഡലം | E = F/q: the force per unit positive test charge at a point; unit N/C |
| Electric field intensity | വൈദ്യുത മണ്ഡല തീവ്രത | The magnitude (strength) of the electric field at a point |
| Test charge · source charge | പരീക്ഷണ ചാർജ് · സ്രോതസ്സ് ചാർജ് | A tiny charge used to measure a field · the charge that produces the field |
| Electric field lines | വൈദ്യുത മണ്ഡലരേഖകൾ | Curves whose tangent gives the field direction; they start on + and end on − |
| Electric flux | വൈദ്യുത ഫ്ലക്സ് | φ = E·ΔS = E ΔS cos θ, a measure of the field lines crossing a surface; unit N m²/C |
| Area vector | ഏരിയ സദിശം | A vector of length ΔS along the outward normal to a small surface |
| Solid angle | ഘനകോൺ | The 3-D “angle” of a cone: ΔΩ = ΔS/r²; a whole sphere is 4π steradian |
| Electric dipole | വൈദ്യുത ദ്വിധ്രുവം | A pair of equal and opposite charges, q and −q, a small distance 2a apart |
| Dipole moment | ദ്വിധ്രുവ മൊമെന്റ് | p = q × 2a, directed from −q to +q; unit C m |
| Torque | ടോർക്ക് (ബലാഘൂർണം) | The turning effect of a force: τ = r × F; on a dipole τ = p × E |
| Uniform electric field | ഏകീകൃത വൈദ്യുത മണ്ഡലം | A field with the same magnitude and direction everywhere (parallel, equally spaced lines) |
| Polar / non-polar molecule | ധ്രുവീയ / അധ്രുവീയ തന്മാത്ര | Has a permanent dipole moment (H₂O) / has none until a field induces one (O₂, CO₂) |
| Continuous charge distribution | തുടർച്ചയായ ചാർജ് വിതരണം | Charge spread smoothly over a line, surface or volume |
| Linear / surface / volume charge density | രേഖീയ / ഉപരിതല / വ്യാപ്ത ചാർജ് സാന്ദ്രത | λ = ΔQ/Δl (C/m) / σ = ΔQ/ΔS (C/m²) / ρ = ΔQ/ΔV (C/m³) |
| Gauss's law · Gaussian surface | ഗോസ് നിയമം · ഗോസിയൻ ഉപരിതലം | Flux through any closed surface = qenclosed/ε₀ · the closed surface chosen to apply it |
| Infinitely long straight wire | അനന്തമായ നീളമുള്ള നേർകമ്പി | E = λ/(2πε₀r), pointing away from the wire (for λ > 0) |
| Infinite plane sheet | അനന്തമായ സമതല ഷീറ്റ് | E = σ/(2ε₀), the same at every distance from the sheet |
| Thin spherical shell | നേർത്ത ഗോളീയ കവചം | Outside: E = q/(4πε₀r²), as if all the charge were at the centre; inside: E = 0 |
| Electrostatic shielding | സ്ഥിതവൈദ്യുത കവചനം | The field inside a closed conductor's cavity is zero, so a metal box protects what is inside |
| Equilibrium (stable / unstable) | സന്തുലനം (സ്ഥിര/അസ്ഥിര) | Net force zero; after a small push the body returns (stable) or moves further away (unstable) |
The scientists of this chapter
Five people whose names you will meet again and again. (Simple name cards; no portraits.)
Safety first
🌐 Explore online (optional)
Everything in this guide works offline: each page is a single file. Some pages also have blue “🌐 Explore online” boxes with free simulations and articles, such as the PhET “Balloons and Static Electricity” simulation. Those links need internet and open in a new tab. All of them are collected in the resources hub on page 17.
- 📄 MIT OpenCourseWare 8.02: Electricity and Magnetism MIT OpenCourseWare
Free college course notes for students who want to go further. - 🧪 Balloons and Static Electricity (PhET simulation) PhET, University of Colorado Boulder
Rub a balloon on a sweater and watch electrons move; see induction on the wall. - 🧪 John Travoltage (PhET simulation) PhET, University of Colorado Boulder
Rub a foot on a carpet and get a spark from a door knob. - 📄 Static Electricity tutorial The Physics Classroom
Charge, charging methods, induction and electroscopes explained step by step. - 📄 Charging by Induction The Physics Classroom
Animated steps of charging two spheres by induction. - 📄 Triboelectric effect Wikipedia
Why some materials give electrons and others take them when rubbed. - 📄 Electroscope Wikipedia
The gold-leaf electroscope and how it detects charge. - 📄 Oil drop experiment Wikipedia
How Millikan showed that charge is quantised (Exercise 1.25).
Made for self-learning. Works offline – every page is a single file. Study material prepared by Claude for Madhu's family study folder, October 2026.