Charge
Motivation
In the first semester of physics we focused on mechanical systems and the laws of nature that govern them. The focus will now shift to the study of electrical and magnetic phenomenon which, as it turns out, are intimately related to one another. Our discussions will ultimately lead to light, and we'll derive light mathematically.
Historically, the realization of the connection between light, electric, and magnetic fields was significant. It was a major leap in understanding to realize that sunshine has anything in common with static electricity and compass needles. As you'll see in this course, you can't have one without the other two.
Where all do we find electric and magnetic phenomena? Almost everywhere. Atoms are held together by electric interactions, and molecules as well. Your brain is an electric computer, your muscles fire due to electrical impulses, all of your senses rely on electrical signals. Lightning energizes the surface of the earth, the magnetic field of earth literally keeps us alive by deflecting other electrically charged particles originating in space from colliding with the planet, and on and on. I didn't even mention the technology on which you're reading this book or the world's electrical grid on which it relies. How do we make electricity anyway? All of these things will be discussed this semester.
Review of Charge
Before we go to any of those topics, we need to start with a rather elementary discussion (and likely a review) of charge. As you are probably aware at this point in your education, charge in nature comes from the electrons and protons that reside within the atoms of which things are made. The electrons are what we call negatively charged and protons are positively charged. There is nothing fundamentally positive or negative about protons or electrons. All it means is that they are opposites - like black and white or left and right. In the context of charge, we find that opposites attract and like charges repel.
It is worth noting that we have no explanation for why the charge on electrons is equal and opposite that of protons. Particle physics experiments indicate that the electron is a fundamental particle in nature - or unable to be further subdivided - and that protons on the other hand are comprised of quarks, which are smaller particles that have or charge associated with them. Here represents the fundamental charge which is the magnitude of charge possessed by both protons and electrons. The value of this fundamental charge is where is the unit of charge called a coulomb named after Charles-Augustin Coulomb about whom you may read by clicking on his name.
If you would like to read more about quarks, please see the Wikipedia link below.
Quarks
Charge is Quantized
While it's true that protons are known to be comprised of quarks which have fractions of the fundamental charge, in nature we never see any fractional charges. In that sense, any time an object is charged, the quantity of charge that it contains is in multiples of the fundamental charge, or where . That last statement is a notation that means "N is an element of the set of natural numbers beginning with zero". If you don't remember from math class, natural numbers are just the counting numbers 0, 1, 2, etc. In other words, positive integers. Zero is sometimes included in the set of natural numbers and sometimes not, so it is best to use a subscript to indicate whether you mean to include zero (as I did) or not, in which case a subscript "1" should be used.
Recognizing that charge is quantized and that integer multiples of the fundamental charge is what we find in nature, can often be irrelevant when an object, for instance, contains a micro-coulomb of charge. That's because the integer is so large in a case like this.
As an example, how many electrons add up to All we do is set and solve for N. in this case, so we tend to not count precisely enough to keep track of each individual electron. If we could somehow count every last one of them, however, you would only ever find an integer number of them.