New Formulas and Concepts

We begin our discussion of Electromagnetism by considering electric fields. Electric fields behave a lot like gravitational fields. Every particle has mass. This mass creates a gravitational 'field' which pulls other things with mass toward it. The more mass, the greater the field, and the stronger the pull. Finally, the the further away you get from a mass, the weaker the field.

In addition to possessing mass, most matter also possesses something called charge. Charge works almost the same as mass - it creates a field, called the electric field. This field exerts a force on other things that have charge, and the further away the weaker the effect. The major difference is that, while all mass attracts all other mass, charge comes in two flavors - called positive and negative. The rule is that likes repel and opposites attract.

It actually turns out that the electric force is much, much stronger than gravitation (see problem 65). But, because of these two flavors, opposites tend to attract each other, leading to an object that, overall, has no net charge. Most things tend to end up neutralized, so we don't tend to notice this force as much as gravity, since nothing can diminish it (we think).

Now, charge is measured in units called coulombs [C]. Charge, like mass, is a conserved quantity - it is neither created nor destroyed. Finally, the basic equation of force between two charges is Coulomb's Law

$$F=k\frac{\vert q_1q_2\vert}{r^2},$$

where $q_1$ and $q_2$ are the two charges, r is the distance between them, and $k$ is a constant, with value $9\times10^9$ in MKS units (can you figure out the units from Coulomb's Law?). This formula gives the force magnitude. The direction is given by the above likes/opposites rule.

Finally, this constant is often given in the form

$$k=\frac{1}{4\pi\epsilon_0}$$

where $\epsilon_0$ is called the permittivity of free space (something which means nothing to you now, but will make more sense later) and has the value $8.85\times10^{-12}$ (again, you give the units).