Coulomb's law
F = k · q · q'd²
| Quantity | Symbol | Unit |
|---|---|---|
| Force | F | N |
| Charge | q | C |
| Distance | d | m |
| Constant (9 × 10⁹) | k | N·m²/C² |
Elec Class
learn electricity hands-on
Lesson · chapter 2 of 15
Two charges of the same sign repel, two charges of opposite signs attract, with a force that decreases with the square of their distance: this is Coulomb's law. It explains static electricity, lightning and how capacitors work.
The result is worked out before your eyes, line by line, just like on the board.
1I'm looking for
2I enter the known values
Formula used F = k · q · q'd²
3The result
Force F100 mN
Two charges of 1 µC and {q'} placed 300 mm apart each exert a force of 100 mN on the other.
The definition, the key points to remember and everyday examples.
Matter is made of atoms: a nucleus (protons +, neutrons) surrounded by electrons (−). A body losing electrons becomes positive, one gaining electrons negative; the elementary charge is e = 1.6 × 10⁻¹⁹ C.
In a conductor free electrons move; in an insulator they do not. Two charges exert the Coulomb force on each other: attraction for opposite signs, repulsion otherwise. An electric field E exists between two plates at different potentials.
Two charges behave a bit like two magnets: like ones repel, opposite ones attract, and the effect fades very quickly as you move them apart. Where it falls short: a magnet always has two poles that can't be separated, whereas a charge stands alone, positive or negative; and magnetism is a different phenomenon from electrostatics.
| Quantity | Symbol | Unit |
|---|---|---|
| Force | F | N |
| Charge | q | C |
| Distance | d | m |
| Constant (9 × 10⁹) | k | N·m²/C² |
| Quantity | Symbol | Unit |
|---|---|---|
| Electric field | E | V/m |
| Voltage | U | V |
| Plate spacing | e | m |
| Quantity | Symbol | Unit |
|---|---|---|
| Force | F | N |
| Charge | q | C |
| Electric field | E | V/m |
Four steps to solve a problem, then an example solved line by line.
Charges in coulombs (1 µC = 10⁻⁶ C, 1 nC = 10⁻⁹ C), distance in meters (10 cm = 0.10 m).
Apply F = k × q × q' / d² with the absolute values of the charges, and don't forget to square d.
Same signs: repulsion; opposite signs: attraction. Both charges feel the same force, in opposite directions.
Microcoulombs about ten centimeters apart give forces of around a newton; nanocoulombs, a few micronewtons.
Two charges q = 2 µC and q' = −3 µC are 10 cm apart. What force do they exert on each other? Attraction or repulsion?
F = k · q · q' / d² with d = 0.10 m:
F = 9 × 10⁹ × 2 × 10⁻⁶ × 3 × 10⁻⁶ / 0.10² = 5.4 × 10⁻² / 0.01 = 5.4 N.
Opposite signs: attraction.
F = k × q × q' / d², with F in newtons, q and q' in coulombs, d in meters and k ≈ 9 × 10⁹ N·m²/C². If the distance doubles, the force is divided by 4.
It's charge that has built up on an object, often an insulator, after rubbing or contact: it doesn't flow, hence the word "static". It is released all at once, as a spark, when it touches a conductor.
Your body picked up charge as you walked on a carpet or as your clothes rubbed, and the metal handle gives the charges a path: they cross all at once in a small spark. Dry air makes it worse; humidity lets the charges leak away gradually.
It's the region where a charge feels an electric force; it is measured in volts per meter. Between two plates at 1,000 V and 1 cm apart, E = 1,000 / 0.01 = 100,000 V/m, and an electron there feels F = 1.6 × 10⁻¹⁹ × 10⁵ = 1.6 × 10⁻¹⁴ N.
k ≈ 8.99 × 10⁹ N·m²/C², rounded to 9 × 10⁹ in problems. It is also written k = 1 / (4π ε₀), where ε₀ ≈ 8.85 × 10⁻¹² F/m is the permittivity of free space (air is very close to it).
Enormously: between two electrons, the electric repulsion is about 4 × 10⁴² times greater than their gravitational attraction. We don't notice it in everyday life because matter is almost always neutral: its + and − charges cancel out.
It has gained some: the electron carries the negative charge. A body that loses electrons becomes positive.
Its electrons stay bound to their atoms: no free charge can move. In a metal, each atom releases an electron that travels through the whole conductor.
From the simplest to the most complete, each problem comes with a step-by-step solution.
Charge a plastic ruler and a balloon by rubbing them, observe how they attract small pieces of paper and bend a thin stream of tap water, then have students predict the effect of doubling the distance before calculating it with Coulomb's law.
Using Elec Class in class