Subatomic particles, such as the electron and the proton, exist that display an ability to affect each other without physical interaction. As an example of the type of interaction we are talking here, consider the pull of gravity between the sun and the earth: the sun and the earth are not touching each other, but they still have a relationship because of the force of gravity. Similar to gravity, the electric force is able to affect objects at a distance.
Some objects are affected by an electric force, and some objects are not. Inside the atom, to continue our example, there are three types of particles: electrons, protons, and neutrons. Of these three, the neutron is not charged and has no electric force. Protons and electrons affect each other in a complicated way, as demonstrated by this table:
Two charges will exert an electric force on each other. This force can either repel (in the case of like-signs) or can attract (in the case of opposite signs). The strength of the force depends on how far away the two charges are: if they are close the force will be strong, if they are far, the force will be weak. We will see the exact relationship that governs this force in the next chapter on Coulomb's Law.
As a matter of mathematical interest, it helps to quantify the different charges in some way. We could, in a naive way, say that an electron has a charge value of 1, and a proton has a charge value of 2. However this system would be of very limited usefulness, and it would actually take more work for us to write equations that used this system. Modern science has settled on the convention of assigning a +1 charge to a proton, and a −1 charge to an electron. The system could easily have been reversed and many of our equations would still hold true (or would need a simple sign change). However, as a matter of convention we say that electrons are negatively charged, and protons are positively charged, and that neutrons are neutrally charged (with a charge of 0).
When dealing with small electric charges mathematically, it is the most easy for us to consider a point charge. Point charges have mass and charge but no volume and are infinitely small. Of the fundamental particles the electron is perhaps the closest approximation to a point charge as all experimental evidence is consistent with it being a point charge. Protons etc. are believed to be composed of quarks and thus have a finite volume but in most cases can be considered as point charges.
We can define a function ρ(x, y, z) to be the charge density. The charge density is a measurement of the average amount of charge per unit volume. If the charge is distributed over a fine layer on a surface, it is also useful to define a superficial or surface charge density σ(x, y, z). The surface charge density measures the amount of charge per unit area.
The amount of charge transferred between two points at 1 ampere over 1 second is the amount of electric charge and its derived SI unit is called a coulomb. It's base SI units are ampere-seconds.