5.1.1. Electric Charge

Table of Contents

What charge is

Electric charge is a basic property of matter that determines how objects interact electrically. Some objects attract each other, some repel each other, and these effects come from charge. Charge is one of the fundamental quantities in electricity and magnetism.

There are two kinds of electric charge, called positive and negative. An object can have positive charge, negative charge, or no net charge at all. If two objects have the same kind of charge, they repel each other. If they have opposite kinds of charge, they attract each other.

Important rule: like charges repel, unlike charges attract.

Electric charge is usually represented by the symbol $q$, or sometimes $Q$ for a total charge.

Positive, negative, and neutral objects

Matter is made of atoms, and atoms contain smaller particles. Protons carry positive charge, electrons carry negative charge, and neutrons carry no charge. A neutral atom has equal amounts of positive and negative charge, so the total charge adds to zero.

If an object loses some electrons, it becomes positively charged. If it gains extra electrons, it becomes negatively charged. In ordinary situations, charging often happens because electrons move from one object to another. Protons usually remain bound inside atomic nuclei.

This is why rubbing materials together can make them charged. One material may lose electrons and the other may gain them.

The unit of charge

The SI unit of electric charge is the coulomb, written as $\text{C}$.

A coulomb is a large amount of charge on the atomic scale. The charge of a single proton is equal in magnitude to the charge of a single electron, but with opposite sign.

The elementary charge is

$$
e = 1.602 \times 10^{-19}\ \text{C}
$$

A proton has charge $+e$, and an electron has charge $-e$.

Important formula: the charge of a proton is $+1.602 \times 10^{-19}\ \text{C}$, and the charge of an electron is $-1.602 \times 10^{-19}\ \text{C}$.

Quantization of charge

Electric charge comes in discrete packets. This means charge is quantized. The net charge on an isolated object is an integer multiple of the elementary charge:

$$
q = ne
$$

where $n$ is an integer, positive, negative, or zero.

For example, if an object has lost 3 electrons, its charge is

$$
q = +3e
$$

If it has gained 5 electrons, its charge is

$$
q = -5e
$$

Important rule: electric charge is quantized, so any net charge satisfies $q = ne$.

Conservation of charge

One of the most important ideas in physics is that electric charge is conserved. Charge cannot be created or destroyed in ordinary processes. It can only be transferred from one object to another.

If one object becomes more positive, another object must become equally more negative, so that the total charge remains the same.

For example, if rubbing transfers electrons from object A to object B, then object A becomes positive and object B becomes negative by exactly the same amount.

Law of conservation of charge: the total charge of an isolated system remains constant.

Conductors and insulators, in brief

Some materials allow charge to move easily, while others do not. In conductors, charges can move relatively freely. In insulators, charges are much less mobile. This affects how objects become charged and how charge spreads over them.

This chapter only introduces charge itself. The behavior of charge in different materials is developed further in the chapter on conductors and insulators.

How objects become charged

An object can become charged in several simple ways. One is by friction, where rubbing transfers electrons. Another is by contact, where a charged object touches another object and charge is shared. A third is by induction, where a nearby charge causes charges inside an object to rearrange.

Even though the methods differ, the central idea is the same, electrons move or redistribute, and total charge is conserved.

Comparing charges in matter

The table below summarizes the charges of the main atomic particles.

Particle	Charge	Approximate value
Proton	$+e$	$+1.602 \times 10^{-19}\ \text{C}$
Electron	$-e$	$-1.602 \times 10^{-19}\ \text{C}$
Neutron	$0$	$0\ \text{C}$

Net charge

The total charge of an object is called its net charge. It is the algebraic sum of all positive and negative charges in the object.

If an object contains total positive charge $Q_+$ and total negative charge $Q_-$, then its net charge is

$$
Q_{\text{net}} = Q_+ + Q_-
$$

Here $Q_-$ is negative in sign. A neutral object has

$$
Q_{\text{net}} = 0
$$

An object may contain huge amounts of positive and negative charge internally, but if they balance exactly, the object is neutral.

A simple picture

A neutral object has equal positive and negative charge. A positively charged object has fewer electrons than protons. A negatively charged object has more electrons than protons.

Rendering scientific sketch…

Neutral, positive, and negative objects

Why charge matters

Electric charge is the source of electric forces and electric fields. Once an object has charge, it can influence other charges around it. This leads to many physical phenomena, from static electricity to electric circuits, chemical bonding, and much of modern technology.

In the next chapters, charge will be used to define how electric forces act between objects and how electric fields describe the space around charges.

Key ideas to remember

Electric charge is a fundamental property of matter. There are two kinds, positive and negative. The SI unit is the coulomb. The smallest common unit of free charge is the elementary charge $e$. Charge is quantized, $q = ne$, and total charge is conserved in any isolated system.

Essential summary:
$$
q = ne
$$
with $n \in \mathbb{Z}$, and total charge is conserved.
Also, like charges repel and unlike charges attract.

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