PHYS 2212 Module 1

1: Electric Charges and Fields

Electric charges exist all around us. They can cause objects to be repelled from each other or to be attracted to each other. (credit: modification of work by Sean McGrath)

Back when we were studying Newton’s laws, we identified several physical phenomena as forces. We did so based on the effect they had on a physical object: Specifically, they caused the object to accelerate. Later, when we studied impulse and momentum, we expanded this idea to identify a force as any physical phenomenon that changed the momentum of an object. In either case, the result is the same: We recognize a force by the effect that it has on an object.

In Gravitation, we examined the force of gravity, which acts on all objects with mass. In this module, we begin the study of the electric force, which acts on all objects with a property called charge. The electric force is much stronger than gravity (in most systems where both appear), but it can be a force of attraction or a force of repulsion, which leads to very different effects on objects. The electric force helps keep atoms together, so it is of fundamental importance in matter. But it also governs most everyday interactions we deal with, from chemical interactions to biological processes.

The first lesson in our discussion of electricity and magnetism is all about electric charge. You’ve heard of electric charge before, and how “like charges repel and unlike charges attract,” right? Well, that’s true. But now we will go much deeper into the interactions between electrically charged objects, how those electric charges behave within different materials, and how electric charge is the source of an electric field. But first, let me give you a little history…

Let’s go back in time, to around 600 BC in ancient Greece. Before great philosophers like Socrates, there was Thales of Miletus. Thales was a polymath — a man of many talents: philosopher, scientist, mathematician, and even worked in a mine in the city of Magnesia. He found a strange rock, called lodestone, that would make nearby pieces of iron stick to it. To him it seemed like magic because the metal pieces moved due a strange invisible force. He called the rock magnetic.

This discovery sparked Thales’ curiosity and motivated him to find more “magical” rocks like lodestone. He took amber — which is fossilized resin — and rubbed it with wool, which made the amber attract pieces of dry leaves and straw. The Greek word for amber is electric, which is where this interaction got its name. But this electric interaction seemed weaker than the magnetic interaction, since it could only move leaves and not iron, so it was ignored for about 2000 years.

Now let’s travel in time to about 1600 AD and visit with William Gilbert. He wanted to find other rocks that acted like amber, so he rubbed rocks with wool. There were some rocks like acted like amber, which he called good electrics, but today we call them insulators. Insulators are materials like amber and other gems, glass, plastic, that do not allow electric charges to move throughout them freely. Insulators can hold electric charge but the charge will stay fixed in place. Other rocks Gilbert named bad electrics, or conductors, which allow electric charges to move easily throughout due to electric forces. Metals are conductors. For example, copper (Cu), silver (Ag), gold (Au), and aluminum (Al) are good conductors of electric charge. Although Gilbert did not study these, semiconductors are materials that are a blend of conducting and insulating. Today, we use semiconductors in pretty much all of our electronic devices. A basic computer chip is made from semiconductors like silicon (Si) or germanium (Ge).

About 150 years after Gilbert, Benjamin Franklin came along. He made many discoveries, too many to discuss here. But one thing he’s known for is naming the two types of electric charge: positive and negative. He also observed that like charges repel and unlike charges attract. What he didn’t know, which we know today, is that the electric charge is in each and every atom, with positive charge carried by protons in the atom’s nucleus and negative charge carried by the atom’s electrons. When electric charge is transferred from one object to another — like when Gilbert was rubbing rocks — it is the electrons that are transferred. This is because the protons are very tightly bound within the atom’s nucleus and little rubbing is not enough energy or force to remove them. But electrons are very loosely bound to the atom and can easily be removed.

Robert Millikan followed in Franklin’s footsteps and investigated electric charge even further. About 100 or so years after Ben Franklin, Millikan performed his famous Oil Drop Experiment. What he was able to determine is that charge is quantized, which means that it comes in discrete amounts. Like if you have eggs (still in their shell) you can have a dozen, you can have three, but you can’t have 3.7 eggs, right? Well, that’s what we mean by quantized. The smallest amount of charge is called the elementary charge, e, and has an amount equal to 1.602 x 10^-19 C, where C is coulombs or the SI unit for electric charge. The amount of charge carried by an electron is –e = -1.602 x 10^-19 C and the amount of charge carried by a proton is +e = +1.602 x 10^-19 C.

After these discoveries, many many more followed. This module will delve deeper into “like charges repel and unlike charges attract” by understanding the forces between charges and the properties that affect these forces. We will also quantify the “repel” and “attract” with calculations that allow us to determine the strength of the electric forces.

We will also discuss everyday examples of electricity. Here is a quick video to give you a preview of what I mean.

1.1 Electric Charge

Describe the concept of electric charge
Explain qualitatively the force electric charge creates

1.2 Conductors, Insulators, and Charging by Induction

Explain what a conductor is
Explain what an insulator is
List the differences and similarities between conductors and insulators
Describe the process of charging by induction

1.3 Coulomb’s Law

Describe the electric force, both qualitatively and quantitatively
Calculate the force that charges exert on each other
Determine the direction of the electric force for different source charges
Correctly describe and apply the superposition principle for multiple source charges

1.4 Electric Field

Explain the purpose of the electric field concept
Describe the properties of the electric field
Calculate the field of a collection of source charges of either sign

1.5 Calculating Electric Fields of Charge Distributions

Explain what a continuous source charge distribution is and how it is related to the concept of quantization of charge
Describe line charges, surface charges, and volume charges
Calculate the field of a continuous source charge distribution of either sign

1.6 Electric Field Lines

Explain the purpose of an electric field diagram
Describe the relationship between a vector diagram and a field line diagram
Explain the rules for creating a field diagram and why these rules make physical sense
Sketch the field of an arbitrary source charge