{"id":197,"date":"2026-06-10T01:54:18","date_gmt":"2026-06-10T01:54:18","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=197"},"modified":"2026-06-10T01:54:19","modified_gmt":"2026-06-10T01:54:19","slug":"coulombs-law","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/coulombs-law\/","title":{"rendered":"What Is Coulomb’s Law?"},"content":{"rendered":"\n
Definition<\/div>

\nCoulomb’s law states that the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. As a formula, F = kq\u2081q\u2082\/r\u00b2, where k \u2248 8.99 \u00d7 10\u2079 N\u00b7m\u00b2\/C\u00b2. The force acts along the line joining the charges: like charges repel, opposite charges attract.\n<\/p><\/div>\n\n

Rub a balloon on your hair, press it against a wall, and let go. It stays put \u2014 gravity apparently overruled by a party trick. The invisible hand doing the holding is the electrostatic force, and the rule that sets its exact strength is Coulomb’s law.<\/p>\n\n

The same law is at work far beyond balloons. It crackles in a winter doorknob shock, holds every atom in your body together, and decides where the toner lands inside a laser printer. Master this one equation and a surprising amount of the physical world snaps into focus.<\/p>\n\n

What Is Coulomb’s Law?<\/h2>\n\n

Strip away the symbols and the idea is simple: electric charges push and pull on one another, and just two things decide how hard \u2014 how much charge each object carries, and how far apart the objects sit.<\/p>\n\n

Stated precisely, Coulomb’s law says the electrostatic force between two stationary point charges is proportional to the product of the charges and inversely proportional to the square of their separation. Double either charge and the force doubles. Double the gap and the force drops to a quarter.<\/p>\n\n\n \n The Electrostatic Force Between Two Point Charges<\/text>\n \n \n \n <\/marker>\n <\/defs>\n \n \n \n r<\/text>\n \n \n F<\/text>\n F<\/text>\n \n +q\u2081<\/text>\n \n +q\u2082<\/text>\n Like charges repel<\/text>\n \n \n F<\/text>\n F<\/text>\n \n +q\u2081<\/text>\n \n \u2212q\u2082<\/text>\n Opposite charges attract<\/text>\n F = k \u00b7 q\u2081q\u2082 \/ r\u00b2<\/text>\n<\/svg>\n

Figure 1 \u2014 The force pair always acts along the line joining the charges: outward for like charges, inward for opposite ones.<\/p>\n\n

The law carries the name of Charles-Augustin de Coulomb, the French engineer-turned-physicist who measured it in 1785 with a torsion balance \u2014 a horizontal needle hung on a fine wire that twisted measurably under tiny electric pushes. Henry Cavendish had quietly found much the same result in the early 1770s, but never published it.<\/p>\n\n

\n \"Coulomb's\n
The torsion balance Coulomb used in 1785 to measure the electric force between charges.<\/figcaption>\n<\/figure>\n\n\n

Three conditions sit quietly inside the law. The charges must be at rest (this is electrostatics<\/em>), they must be point-like or uniformly charged spheres, and the simple constant k assumes they sit in a vacuum \u2014 though air is so close to a vacuum electrically that the difference rarely matters.<\/p>\n\n

The Coulomb’s Law Formula<\/h2>\n\n

Here is the equation in the form you will use in almost every problem:<\/p>\n\n

F = k|q\u2081q\u2082| \/ r\u00b2<\/div>\n\n

Every symbol earns its place. Here is what each one means, with its SI unit:<\/p>\n\n

\n\n\n\n\n\n\n\n\n\n
Symbol<\/th>\nMeaning<\/th>\nSI unit \/ value<\/th>\n<\/tr>\n<\/thead>\n
F<\/strong><\/td>\nElectrostatic force between the charges<\/td>\nnewton (N)<\/td>\n<\/tr>\n
q\u2081, q\u2082<\/strong><\/td>\nThe two point charges (sign included)<\/td>\ncoulomb (C)<\/td>\n<\/tr>\n
r<\/strong><\/td>\nCentre-to-centre separation of the charges<\/td>\nmetre (m)<\/td>\n<\/tr>\n
k<\/strong><\/td>\nCoulomb constant, k = 1\/(4\u03c0\u03b5\u2080)<\/td>\n8.99 \u00d7 10\u2079 N\u00b7m\u00b2\/C\u00b2<\/td>\n<\/tr>\n
\u03b5\u2080<\/strong><\/td>\nPermittivity of free space<\/td>\n8.854 \u00d7 10\u207b\u00b9\u00b2 C\u00b2\/(N\u00b7m\u00b2)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n

Where does k come from? It is shorthand for a deeper constant:<\/p>\n\n

k = 1\/(4\u03c0\u03b5\u2080) \u2248 8.99 \u00d7 10\u2079 N\u00b7m\u00b2\/C\u00b2<\/div>\n\n

Here \u03b5\u2080 is the permittivity of free space, whose precise value sits among the CODATA recommended constants published by NIST<\/a>. For coursework, k = 8.99 \u00d7 10\u2079 N\u00b7m\u00b2\/C\u00b2 \u2014 or simply 9.0 \u00d7 10\u2079 \u2014 is all you need.<\/p>\n\n

Run a quick sense-check whenever you calculate. Two 1 \u03bcC charges held 10 cm apart push with about 0.9 N, roughly the weight of a small apple. If microcoulomb charges ever hand you millions of newtons, a power of ten has slipped somewhere.<\/p>\n\n

You can handle the signs in two ways. Either keep them in the product, in which case a negative answer signals attraction; or \u2014 the cleaner exam habit \u2014 work with magnitudes using |q\u2081q\u2082| and set the direction from the rule that like charges repel and opposites attract.<\/p>\n\n

How Coulomb’s Law Works<\/h2>\n\n

Why multiply the charges? Because every scrap of charge on one object interacts with every scrap on the other, and effects that pair up multiply rather than add. Triple one charge and there are three times as many interactions \u2014 so three times the force.<\/p>

The inverse square has a beautifully geometric reason. A charge’s influence spreads out equally in all directions, like light from a bare bulb, and at distance r that influence is smeared over a sphere of surface area 4\u03c0r\u00b2. Double the radius and the same influence must cover four times the area, so any single point receives a quarter of the effect.<\/p>\n \n Why Distance Matters: The Inverse-Square Rule<\/text>\n \n \n \n <\/marker>\n <\/defs>\n \n \n \n \n \n \n \n F<\/text>\n F\/4<\/text>\n F\/9<\/text>\n \n +Q<\/text>\n \n +<\/text>\n \n +<\/text>\n \n +<\/text>\n r<\/text>\n 2r<\/text>\n 3r<\/text>\n Double the distance \u2014 a quarter of the force. Triple it \u2014 a ninth.<\/text>\n<\/svg>\n

Figure 2 \u2014 The same pair of charges at growing separations: the force falls with the square of the distance (F \u221d 1\/r\u00b2).<\/p>

Direction comes free with the law: the force always points along the straight line joining the two charges. And it comes in pairs. Whatever force charge A exerts on charge B, B exerts exactly the same magnitude back on A \u2014 Newton’s third law, alive and well in electrostatics.<\/p>

More than two charges? Coulomb’s law still copes. Work out the force from each pair separately, then add the results as vectors \u2014 physicists call this the superposition principle, and Problem 7 below puts it to work.<\/p>

One honest caveat before you calculate. The tidy constant k belongs to charges in a vacuum (air is close enough); inside a material the force shrinks by the material’s relative permittivity, and in water that means a factor of roughly 80. The law also assumes the charges are stationary \u2014 set them moving and magnetism enters the story.<\/p>

Try It Yourself: The Coulomb’s Law Lab<\/h2>

Reading about an inverse-square law is one thing; dragging a slider and watching the force collapse is another. Set both charges positive, then double the separation and check the readout \u2014 it should fall to exactly a quarter.<\/p>

Now flip one charge negative. The magnitude stays identical; only the direction of the arrows changes. That single observation untangles half the sign confusion students bring to this topic.<\/p>

<\/span>Coulomb's Law Lab<\/span><\/div>