PHYS102: Introduction to Electromagnetism

Coulomb's force law contains the assumption that the two charged objects involved in the interaction are either spherical (charged uniformly) or are so far apart that it is okay to consider both of them as point-like (that is, objects without a shape altogether). Then the direction of the electric force is always along the straight line connecting the objects. In the case of spheres, we consider that to be from center to center.

It can be confusing to figure out in what direction the force should point. To figure out the correct force direction, remember this simple rule: the forces at opposite ends of the straight line connecting the charges must always point in opposite directions. That is the same as for the tension forces at both ends of a spring. Either both ends are pulling inward, or both ends are pushing outward. Since two charges with opposite signs attract, the forces in Coulomb's Law point inward at both ends of the line connecting the charges. And since two charges with equal sign repel, the Coulomb force, in that case, points outward at both ends of the connecting line.

You may ask yourself how Coulomb's Law can be true for the electrons and protons inside a material if it is electrically neutral overall. After all, even though electric forces fall off with increasing distance, the force is never precisely zero, no matter how far away you are from an individual point-like charge.

In fact, when we say an object is electrically neutral, it is really a statement about the electrical forces that the object is (or is not) able to create over relatively large distances. To measure such a force, you would approach the neutral object with an electrically charged test object and observe if it feels a push or a pull. When you are far enough away from a neutral object, the repulsive and attractive forces created by the positively- and negatively-charged fundamental particles inside of it cancel out when their combined effect on your test particle is measured. The combined effect of several simultaneous forces is what we call the resultant, and the resultant of two opposing forces of equal strength is zero.

Almost all applications of electrostatics (including the explanation of what "neutral" means) involve large numbers of charges. In contrast, Coulomb's Law only applies to the limited special scenario of two charged objects that essentially behave like points. This is why we need additional tools to make practical use of Coulomb's Law.