184_notes:charge

Section 3.1 and 3.7 in Matter and Interactions (4th edition)

The electric interaction is one of the fundamental ways that objects interact in the universe, and we observe its effects every day. The electric interaction is responsible for molecular bonding, keeping objects from falling through surfaces (also known as the normal force), lightning and thunderstorms, electric circuits, defibrillators, and many more phenomena that we use in our daily lives. These notes will start with the basics of the electric interaction and introduce the idea of charge.

Charge is one of the basic properties of matter. Just like how an object has a mass, an object also has a charge.

There are two types of electric charge - positive and negative - that interact in very specific ways. A positive charge will repel another positive charge and a negative charge will repel another negative charge (“likes repel” rule). On the other hand, a positive charge will attract a negative charge and vice versa (“opposites attract” rule). We also know that more charge or a smaller distance means a stronger interaction, which you may have observed from rubbing a balloon on your hair or sweater.

While these rules may seem relatively simple, they are extremely powerful in describing how charges interact with one another, and you can use these rules to check your mathematical solution or reason conceptually about a problem. For example, if you only have two positive charges, but your math says they are moving toward each other, then you know that you have missed a negative sign in your equations. Or if you double the charge on your object, you know that you should see a stronger interaction.

#### Units of Charge

The SI units of charge are called coulombs (coo-loms), which is abbreviated with a capital “C.” A coulomb is similar to a meter or a kilogram - it is the base unit for an amount of charge.

1 C of charge is a LARGE amount of charge. For comparison, 1 electron has a charge of $-1.602 \cdot 10^{-19} C$. When you rub a balloon on your hair, the balloon has a charge of about $1 \cdot 10^{-7} C$. A typical lightning bolt represents a transfer of about 15 C of charge (though the large bolts can be up to 350 C).

You may also see an amount of charge written in terms of the elementary charge (e), where $|1 e| = 1.602 \cdot 10^{-19} C$. This is typically used for very small amounts of charge. In essence, this is how many electrons would it take to make that amount of charge.

In addition to the 3 fundamental principles (conservation of momentum, energy, and angular momentum) you learned about in mechanics, there is a fourth fundamental principle, which is important to electromagnetic situations: conservation of charge. This principle says that the amount of charge in a system should always be constant (or conserved) as long as there is no transfer of charge to/from the surroundings. (This is another reason why defining your system is an important choice).

In general, we can always account for all the charge in every observation we make and experiment we conduct (either in the system or moving across the system boundary). $$Q_{surroundings} = Q_{after}-Q_{before}=\Delta Q$$ If you choose your system wisely, then $Q_{surroundings}=0$ so: $$Q_{before} = Q_{after}$$ That is, the total amount of charge is conserved before and after some event. This is often summarized colloquially as charge can never be created or destroyed.

This conservation theorem reveals deep truths about the fundamental nature of matter and is still being investigated to observe violations. How the universe developed its charge is another important research question in physics.

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