Charges and Coulomb’s Law

Have you ever rubbed your feet on the ground then gleefully shocked your friend? If you have then you have experienced the world of charge and electrostatics first hand. But what is charge anyway and why did rubbing your feet allow you to produce a shock?

What is Charge?

Charge is a property of matter that causes other objects to either be attracted or repelled. Electric charge comes in two flavors positive and negative and as the old adage goes opposites attract.

Basically, two positive charges will repel and the same is true of two negative ones. On the other hand, a positive charge and a negative charge will be attracted to one another.

There are also small charges and large charges, which can be quantified and measured using the Coulomb (C). The bigger the charge the larger the attraction or repulsion.

Charge is Conserved

When you rubbed your feet on the ground you transferred charge to your feet and eventually to your friend. Throughout this whole process, no charge was lost it was only moved from place to place. In this way, we say that charge was conserved. That is if you started with 10C of charge then you will also end with 10C of charge.

Materials Matter

When you shocked your friend you were probably wearing socks. This was important because some materials called conductors, allow for the movement of charge. While other materials called insulators don’t.

Conductors

Conductors allow for the movement of charge along their surface and from material to material. If we were to place 10C of charge on the surface of a conductive material it would spread out evenly along the outer surface.

Common conductors include metals because the electrons, which carry negative charges, within the elements are able to move around. Even still not all materials are equal and some are better at conducting charges than others. We call this ability to move charges conductivity (σ; Ω^-1⋅m^-1) and the higher your conductivity the more easily charges move.

This is why most wires are made out of copper or in special cases silver. It is highly conductive and can easily transfer charges from place to place.

Insulators

Insulators are the opposite of conductors in that they don’t allow charge to flow from place to place. If we were to place 10C of charge on an insulator it would be stuck right where we put it.

Common insulators include non-metals because their electrons are stuck and can’t move freely. Just like conductors, some materials are better insulators than others. While we could measure an insulator’s conductivity we don’t. Instead, we measure their resistivity (ρ; Ω⋅m), how well they resist the movement of charge.

Materials like rubber have a high resistivity. This is why the outer covering of wires is made out of rubber to ensure that the charges flowing in the wire aren’t able to escape.

Resistivity and conductivity are really the same thing though! They are inverses of one another so that we can easily measure how easily electrons move as well as how much they are resisted.

[latexpage]
\[ \rho = \frac{1}{\sigma}\:\:\:\:\: \sigma=\frac{1}{\rho}\]

Coulomb’s Law

We have talked about charges at a conceptual level so far, but what if we want to quantify the attractive and repulsive forces between charges? Coulomb’s law allows us to do this so long as we know the size of the charges (q) and the distance between them (r).

[latexpage]
\[F=K\frac{q_1q_2}{r^2}\]

Coulomb’s law, as shown above, mimics the gravitational force equation, and as is the case with gravity the closer together your masses or charges the greater their attractive force. The size of the charges also matters, but since our distance (r) is squared it is the major contributor to the force between two charges. K is a constant just like G and is equal to 9 x 10⁹kg⋅m³⋅s⁻²⋅C⁻².

In the Nervous System

Our nervous system takes advantage of charges to send messages to distant parts of our body. There, neurons are the workhorse of this process and are able to both generate and transmit waves of moving charges called action potentials.

The interior of our neurons are negatively charged, while the extracellular fluid that they sit in is positively charged. The two compartments are separated by a lipid bilayer that prevents the flow of charge in both directions while specialized channels open to allow flow. When channels open they generate action potentials that travel down axons to their destination.

In order to ensure speedy travel of these impulses, our nerves utilize both insulators and conductors. Our axons much like the metal core of wires are highly conductive while some axons have an outer myelin coat that is highly resistive just like rubber.