We saw in the previous chapter that the electric force increases with the strength of the electric charges, and decreases as the charges get farther apart. If we want to be more precise and calculate the exact electric force, we can use Coulomb's Law:
Strictly speaking, this equation gives the force on one point charge due to another point charge. Point charges are objects with charge and maybe mass, but no size. This might make this equation seem rather pointless (ahem), but in practice it serves as a reasonable approximation for the force between any two charged objects, so long as the distance between them is large compared to their size. In later chapters we'll learn how to calculate the force when the objects cannot be approximated as points. To describe the variables in this equation:
From the example above, we see that if you were holding a 1 coulomb charge in each hand, you would definitely notice it! A coulomb is a large charge: most charges in everyday life are measured in microcoulombs (1 µC = 10-6 C), nanocoulombs (1 nC=10-9 C), or even smaller. At the microscopic level, particles tend to have charges which are some small multiple of the charge of a proton e—which, as we mentioned in a previous chapter, is
The formula above gives us the magnitude of the force, but force is a vector so it must have a direction as well. In simple situations we can determine the direction from the rule "like charges repel, opposite charges attract". However, if we want the force in component form then it would be useful to have a version of Coulomb's Law for vectors.