Overview: Electricity

Two facts are responsible for the dominant importance of electric forces in understanding matter and how it behaves.

  1. All ordinary matter is made up of a combination of electrical charge, both negative (electrons) and positive (nuclei).
  2. Electric forces are much stronger than the other long range force we encounter (gravity).

As a result, essentially all the properties of matter that we observe, whether at the macroscopic or the microscopic level, are a result of how the charges from which matter is made behave. For some properties, such as chemical bonding rules, we have to use electric forces in the context of quantum mechanics. But quite a lot can be understood using Newton's laws and our understanding of statistical mechanics of thermal systems. 

Electric forces play critical roles in the interaction of molecules and in establishing an understanding of the behavior of charged molecules (proteins, DNA, ...) in fluid environments. 

The motion of electric charges through matter — electric currents — plays a critical role in the construction of the electrical devices that intertwine with our everyday lives, and with signaling in animal systems through neurons.

Since these ideas are often subtle and complex, we follow the path of considering carefully chosen toy models at each stage to build up an understanding of basic concepts. The presence of a few core anchor equations can also help in organizing your understanding of the subject.

We begin by building an understanding of the electric force, the potential energy associated with it, and introduce the incredibly useful concept of field (really just a function of position). Once we have the basic concepts down, we consider its application to charges in matter, including charges in ionic solutions and conductors. Finally, we consider the basic models for motion of electric currents, allowing us both to understand the functioning of electrical devices and to begin to build models for the study of neural signaling.

  • Electric forces — The basic force law between charges, Coulomb's law, is built up from experimental observations and mathematical reasoning.
    • The electric field — The idea of an electric field permits the handling of the effects of many charges on a charge. In this section, we work through three simple models that will form the basis of more complex modeling and of understanding electric devices.
  • Electric potential energy — Since the electric force is conservative, we can define a potential energy. Thinking in terms of potential energy is often simpler than using forces since you don't have to do vectors.
    • The electric potential — This is the crucial concept in understanding how charges interact with matter. The definition is subtle, so think about it carefully!
    • Motivating capacitance — Because the electric force is so strong, most matter is neutral and remains so, even in small regions. As a result small separations of + and - charge can play a critical role in the forces a charge feels. The concept of capacitance relates how a charge separation on a particular shape produces differences in electric potentials.
  • Electric fields in matter — How neutral matter responds to the presence of an unbalanced charge is essential in understanding electric phenomena. Charges in conductors and within ionic fluids are both important. In ionic fluids, the balance between electric forces and entropic effects due to thermal motion have biologically important consequences, such as the mechanism for creating electric potential differences across cell membranes (the Nernst potential).
  • Electric currents — This section builds the tools for understanding electric circuits and current flow.

Joe Redish 5/15/19

Article 619
Last Modified: May 27, 2019