# Is Coulomb's law an inverse square law? Why?

May 20, 2015

Yes.

The electric field at some distance from a point charge will decrease as the distance to the charge is increased as described by the equation:
$E = \frac{Q}{r} ^ 2$
where $E$ is the electric field, $Q$ is the charge, and $r$ is the distance from the charge.

We picture electric field as radiating away from a point charge in straight lines. In the absence of any other object in the universe, those field lines would radiate away out to infinity. It is the density of those field lines which determine the strength of the field. Near the center there are many lines, farther away, there are fewer. The density of the lines changes as the square of the distance changes. This is another way of describing the surface area of a larger and larger spheres around the charge. As the radius increases, the ratio between the number of field lines and the surface area and decreases.

The answer to your "Why?" question quickly dives deep into theoretical mathematics of the shape of the universe and something called the Poincare Conjecture. Suffice it to say that the universe is thought to be spherical. But it's kind of like two spheres which are connected together at every point so that you never know if you're in one or the other. And if that idea doesn't make your brain hurt, you're not trying hard enough. :)