Electricity and magnetism/Electrostatics/Coulomb's Law

Two motionless electric charges exert an electric force on each other proportional to the product of their charges divided by the square of their distance. The two forces, that exerted by A on B and that exerted by B on A, are in the direction of the line which connects the centers of the two charges A and B. These two forces are attractive for charges of opposite signs and repulsive for charges of the same sign. A field is a physical quantity that can vary at every point in space at every instant. For example, temperature is a field. Coulomb's law says that a motionless electric charge permanently produces an electric force field throughout space: where is the vector which goes from the charge to the point considered, is its length, is the unit length vector in the direction of and is a constant which depends on the choice of units of measurement. The force exerted by an electric field on a charge is So the force exerted by a charge on a charge is The field is like a mathematical intermediary for calculating the force exerted by one charge on another. But it is much more than a simple mathematical intermediary. It has an autonomous existence. Maxwell showed that light is an electromagnetic wave, that is to say a movement of propagation of the electromagnetic field (, ) of which the electric field is a component. The electric field on the surface of a positively charged sphere: 240px The force exerted by two charges on a third is the sum of the forces exerted separately by each of them. All the charges in the Universe produce together throughout space an electric field which is the sum of the fields produced separately by each of them. The Coulomb force is mathematically similar to the gravitational force: two masses exert a gravitational force on each other proportional to the product of their masses divided by the square of their distance. But the gravitational force is always attractive, because there is no negative mass. On Earth, the weight of a body is the gravitational force that the Earth exerts on it. According to the theory of relativity, there is no instantaneous interaction at a distance. A charge cannot therefore instantly exert the Coulomb force on another. The force propagation time must be taken into account. This is why Coulomb's law is only a law of electrostatics. It allows the forces between motionless charges to be correctly calculated.