Coulomb's law describes the electric force between two charged particles. It is one of the basic rules for understanding electricity, atoms, circuits, and many forces inside matter. The law shows that larger charges create stronger forces, while greater separation makes the force weaker.
It matters because electric forces hold atoms together and shape the behavior of charged objects in everyday life and technology.
The force acts along the straight line joining the two charges. Like charges repel, so two positive charges or two negative charges push away from each other, while opposite charges attract. The size of the force is proportional to the product of the charges and inversely proportional to the square of the distance between them.
This inverse square relationship means doubling the distance makes the force one fourth as large.
Understanding Physics: Coulomb's Law
Coulomb's law works best when the charged objects can be treated as point charges. This means their size is tiny compared with the gap between them, or their charge is spread evenly in a spherical shape. A small charged bead can often be treated this way.
A long charged rod cannot, unless it is very far away. For an extended object, different parts lie at different distances.
Each part pulls or pushes with a different strength. Physicists then add the forces from many small pieces to find the total force.
Electric force is a vector, which means direction matters as much as size. When several charges are nearby, one charge feels a separate force from every other charge. These forces combine by vector addition.
Forces pointing in the same direction add. Forces in opposite directions partly cancel. This idea is called superposition.
It explains why the force on a charge can be zero even when charged objects are all around it. Zero net force does not mean no electric forces exist. It means their combined effect balances.
The material between charges changes the interaction. Coulomb's constant has its familiar value for empty space, and air is close enough for many school problems. Inside water, glass, plastic, or another insulating material, charges affect each other less strongly than in empty space.
The material responds to the electric field by shifting its own positive and negative charges by tiny amounts. This response is called polarization. It helps explain why water can weaken attractions between ions, which is important when salt dissolves.
Electric force is much stronger than gravity for individual particles. In an atom, the attraction between an electron and a proton is electrical, not gravitational. Yet most everyday objects do not show huge electric forces because they contain almost equal total amounts of positive and negative charge.
Their charges cancel over large distances. Static electricity becomes noticeable when some electrons move from one material to another. A balloon rubbed on hair, a crackle from a jumper, or a tiny shock from a metal handle are familiar results of this imbalance.
When solving problems, first identify the charge that experiences the force. Draw the positions of all charges and mark each force direction before calculating sizes. Use the distance from center to center for small spherical objects.
Keep charge units in coulombs and distance units in metres if using the standard constant. A negative charge does not make the force size negative. The signs tell you whether the interaction is attraction or repulsion, while the direction belongs on the force arrow.
Check the result using patterns. A larger separation should give a much smaller force, and a balanced arrangement can produce cancellation.
Key Facts
- Coulomb's law: F = k|q1q2|/r^2
- Coulomb constant: k = 8.99 x 10^9 N m^2/C^2
- Like charges repel: positive-positive or negative-negative charges push apart.
- Opposite charges attract: positive-negative charges pull together.
- If one charge doubles, the electric force doubles.
- If distance doubles, the electric force becomes 1/4 as large because F is proportional to 1/r^2.
Vocabulary
- Electric charge
- A property of matter that can be positive or negative and causes objects to exert electric forces on each other.
- Coulomb
- The SI unit of electric charge, abbreviated C.
- Electric force
- The push or pull between charged objects due to their electric charges.
- Inverse square law
- A relationship where a quantity decreases in proportion to the square of the distance, such as F proportional to 1/r^2.
- Point charge
- An idealized charged object treated as if all of its charge is concentrated at one point.
Common Mistakes to Avoid
- Forgetting to square the distance, which is wrong because Coulomb's law uses r^2 in the denominator, not just r.
- Using centimeters instead of meters, which is wrong because the SI units in F = k|q1q2|/r^2 require distance in meters.
- Ignoring the signs of the charges when deciding direction, which is wrong because the sign tells whether the force is attractive or repulsive.
- Thinking the larger charge feels a larger force, which is wrong because Newton's third law says the two charges exert equal magnitude forces on each other in opposite directions.
Practice Questions
- 1 Two charges, q1 = 3.0 x 10^-6 C and q2 = 2.0 x 10^-6 C, are separated by 0.50 m. What is the magnitude of the electric force between them?
- 2 A pair of charges exerts a force of 12 N on each other at a distance of 0.20 m. What is the force if the distance is increased to 0.40 m, with the charges unchanged?
- 3 Two equal positive charges are placed near each other, then one charge is replaced by an equal negative charge. Explain how the direction of the force changes and why the magnitude may stay the same.