Coulomb's law · electric charge · the inverse-square force · attraction & repulsion · superposition
Two charges never touch, yet they push or pull across empty space. Coulomb measured that reach: the force grows with each charge and falls away as the square of the distance — F = k·q₁q₂/r². Like charges shove apart, opposites pull together, and that one rule runs from a balloon stuck to a wall to the electrons bound inside every atom.
This page covers Coulomb's law — F = k·q₁q₂/r² — together with electric charge, attraction and repulsion, the inverse-square law, the coulomb, permittivity, superposition, and a bridge to the electric field. By the end you'll be able to:
Every spark, every static cling, every atom held together is Coulomb's law at work — and it opens the whole electrostatics chapter the exams lean on. We go beyond the syllabus, but we never skip it:
Searched as: coulomb's law, F = kq1q2/r², electric charge, like and unlike charges, electrostatic force, inverse-square law.
Set the two charges (with their signs) and how far apart they are — the playground draws the force arrows (together for unlike, apart for like) and a live force-versus-distance curve. 🟢 real Coulomb's-law engine
Set the two charges and their distance to see what they mean.
In plain terms: charge is the source, distance sets the reach, and F = k·q₁q₂/r² says how hard two charges push or pull.
Electric charge is a basic property of matter — it comes in two kinds, positive and negative, and is measured in coulombs. Charges feel and exert a force on one another even across empty space: like charges repel, unlike charges attract. Bring two charges close and the push or pull is strong; move them apart and it fades fast. That reach across a gap — no contact, no wire — is the whole surprise of electrostatics, and Coulomb's law is its measure.
Coulomb found that the force grows with each charge and falls as the square of the distance: F = k·q₁q₂/r², with k ≈ 9×10⁹ N·m²/C². Double either charge and the force doubles; double the distance and it drops to a quarter. The sign of the product gives the direction — like charges (a positive product) repel, unlike charges (a negative product) attract. The force always acts along the line joining the two charges, equal and opposite on each, just as Newton's third law demands.
The playground above is a Coulomb machine. Set each charge with its sign and the distance between them, and it works out F = k·q₁q₂/r², draws the force arrows — pulling together for unlike charges, pushing apart for like — with the arrow length growing as the force, and plots a live force-versus-distance curve so you can watch the inverse-square fall-off. Slide the charges closer and the arrows snap longer; pull them apart and the force melts away. 🟡 maths of the picture
The physics is visible in the diagram; the maths usually hides. These little labs make it visible too — drag a slider and watch the numbers and arrows answer.
Pull a jumper off over your head and it crackles and clings. Rubbing has moved electrons between the layers, leaving them oppositely charged — and unlike charges attract, so the fabrics stick together while tiny sparks jump across the gaps.
A laser printer charges a rotating drum, then writes the page onto it with light. Charged toner powder is pulled by the electric force onto exactly the charged spots, then pressed onto the paper — Coulomb's law printing your homework, dot by dot.
Inside a storm cloud, colliding ice and water tear charge apart until the base is hugely negative. Its pull on the positive ground grows until the air itself breaks down and a giant spark — lightning — leaps across to neutralise the charge.
Physics you can hold. Each project below demonstrates a law you just met — and the measuring is what turns a demo into a science-fair winner. Pick one, build it from things at home, and graph something.
Build: rub an inflated balloon on your hair or a wool jumper, then press it to a wall — it clings on its own.
Measure: how long it stays up against how long you rubbed it — more rubbing means more charge and a longer hold.
Build: run a plastic comb through dry hair, then hold it just above tiny torn scraps of paper.
Measure: the greatest height from which a scrap still jumps up to the comb — a quick test of how charged it is.
Build: push a wire through a jar lid with two thin foil leaves hanging from it; bring a charged rod near and the leaves spread.
Measure: the angle the leaves open against how strongly the rod is charged — like charges on the leaves repel.
Build: charge a comb or rod and hold it near a thin, steady stream of water from a tap; the stream curves toward it.
Measure: how far the stream bends against the distance of the rod — closer means a bigger pull.
Build: hang two foil-covered balls on threads; charge them and watch them swing apart or together.
Measure: the angle between the threads against the charge — like charges repel, unlike attract.
Build: rub a PVC pipe hard with wool or fur to build a large charge, then use it to lift paper, bend water and raise hair.
Measure: the biggest effect (height of paper lifted, hair raised) against rubbing time — and explain the limit.
Coulomb's law sits under every spark and every atom. Here are the questions that come up most — each answer reads on its own, lifted clean off the page.
Coulomb's law states that the electrostatic force between two point charges is F = k·q₁q₂/r², where q₁ and q₂ are the charges, r is the distance between them, and k ≈ 9×10⁹ N·m²/C². The force is proportional to the product of the charges and inversely proportional to the square of the distance. To use it, put in the two charges and their separation to get the size, then use the signs to get the direction — unlike charges attract, like charges repel.
Electric charge is a basic property of matter that makes it feel and exert electric forces. It comes in two kinds, positive and negative, and is measured in coulombs. Charge is carried by particles — protons are positive and electrons negative — and it is quantized, meaning every charge is a whole-number multiple of the elementary charge e ≈ 1.6×10⁻¹⁹ C. Like charges repel and unlike charges attract.
The electrostatic force is inverse-square because the influence of a point charge spreads out evenly over the surface of an imaginary sphere around it, and the area of that sphere grows as the square of its radius. So the same influence is shared over an area ∝ r², and the force per charge falls as 1/r². This is the same geometric reason gravity, light intensity and sound also follow inverse-square laws.
| Feature | Coulomb's law | Gravitation |
|---|---|---|
| Form | F = k·q₁q₂/r² (inverse-square) | F = G·m₁m₂/r² (inverse-square) |
| Direction | Attract or repel (signs of charge) | Always attractive |
| Strength | Enormous — ~10³⁶× gravity for two protons | Very weak |
The coulomb (C) is the SI unit of electric charge. One coulomb is the charge that passes a point when a current of one ampere flows for one second, and it equals the combined charge of about 6.25×10¹⁸ electrons. Because the charge on a single electron is so tiny (1.6×10⁻¹⁹ C), one coulomb is actually a very large amount of charge.
Like charges repel and unlike charges attract because that is the observed behaviour of the electric force, captured by the signs in Coulomb's law. When you multiply two like charges (both positive or both negative) the product is positive, which corresponds to a repulsive force; when you multiply a positive and a negative charge the product is negative, corresponding to an attractive force. This single rule explains every electrostatics demonstration, from a charged balloon to an electroscope.
Permittivity (ε) is a property of the medium between two charges that sets how strongly they interact; it appears in Coulomb's constant as k = 1/4πε₀ for vacuum. Placing the charges in a material of dielectric constant K reduces the force to F/K, because the medium partly screens the charges. Water, with K ≈ 80, weakens electric forces so much that it can pull ionic crystals like salt apart.
You use the principle of superposition: work out the Coulomb force between the charge of interest and each other charge one pair at a time, then add those forces as vectors to get the net force. The presence of other charges does not change any individual pair's force; you simply add them all, taking directions into account. This lets you handle any arrangement of charges, however complicated.
A charged comb attracts neutral paper because of polarization. The comb's charge pulls the opposite charges in the paper slightly toward it and pushes the like charges slightly away, so the near side of each scrap becomes oppositely charged. Since the opposite charge is now a little closer than the like charge, the attraction wins over the repulsion and the paper is pulled to the comb — even though the paper has no net charge.
Seven question formats, the way Beyond Dictionary serves them — multiple choice, multiple-correct, fill-in-the-blank, match, sequence, read-think-connect, and write-your-own. Every question has layered hints: a quick nudge, the reasoning, then a deeper connection — so a wrong answer opens a door, never a dead end. 🟢 received from a board-tagged question bank · seed toward 2,000
Pick your board — the set re-tunes to its wording and emphasis. Competitive draws the JEE / NEET / Olympiad lane.
Charge keeps its distances — the nearer two charges sit, the louder they speak.