EG1216 · Physics 2 — Electricity & Magnetism
Theme 1 · Electrostatics — charge & the electric field

Electric charge, conductors & insulators

The starting point of the whole course: what electric charge is, the rule that governs it, and how charge moves through different materials.

Source: Serway & Jewett, Physics for Scientists and Engineers, 7th ed., §23.1–23.2.

Before you start

What you need first

  • The atom — that matter is made of atoms with a central nucleus and electrons around it (basic chemistry).
  • Powers of ten — reading and multiplying numbers like \(1.6\times10^{-19}\) (scientific notation).

This is the entry topic of the course — no earlier physics topic is needed.

What you'll be able to do

  • Say what electric charge is and name its two kinds (+ / −).
  • Apply the rule like repels, unlike attracts.
  • Count charge from a number of electrons with \(q = ne\).
  • Tell a conductor from an insulator and say why.
  • Explain charging by friction, contact, and induction, and why a charged object attracts neutral things.

The idea

What is electric charge?

Electric charge is a basic property of matter — like mass — that makes an object push or pull on other charged objects. That push or pull is the electric force.

Mass causes gravity, which is always a pull. Charge is different: it can cause a push or a pull. Charge comes in two kinds, which we call positive (+) and negative (−).

We measure the amount of charge in coulombs, with the symbol C.

Charge is to the electric force what mass is to gravity: the property that decides how strongly an object feels — and makes — the force.
positive negative
The two kinds of charge. We colour + red and − blue throughout this course.

The golden rule: like repels, unlike attracts

There is one rule that decides the direction of every electric force:

  • Two charges of the same sign (+ and +, or − and −) repel — they push apart.
  • Two charges of opposite sign (+ and −) attract — they pull together.

This is why a balloon rubbed on your hair sticks to a wall, and why the small parts inside every atom hold together.

Same signs push away; opposite signs pull in. Remember this one line and you can predict the direction of any electric force.
like charges repel unlike charges attract
Top: two + charges push apart. Bottom: a + and a − pull together.

Where does charge come from? The atom

Every object is made of atoms, and every atom carries charge in three kinds of particle:

  • Protons — positive (+), packed in the central nucleus.
  • Electrons — negative (−), moving in the space around the nucleus.
  • Neutrons — no charge, also in the nucleus.

A normal atom has an equal number of protons and electrons, so the + and − exactly cancel and the atom is neutral (no net charge).

Objects become charged by moving electrons, not protons. Lose electrons → the object is left positive. Gain electrons → it becomes negative.
nucleus (+)
Protons (+) sit in the nucleus; electrons (−) move around it. After Fig. 23.x.

Charge is never created or destroyed

When you charge something, you are not making charge — you are only moving it from one object to another.

Conservation of charge: in any process, the total charge of an isolated system stays the same.

Rub a balloon on your hair: electrons move from your hair onto the balloon. The balloon gains electrons and becomes negative; your hair loses the same number and becomes positive by exactly the same amount. Nothing is lost — charge is just poured from one place to another, like water between two cups.

Measuring charge: the coulomb and the elementary charge

Charge is measured in coulombs (C). The smallest amount of free charge that exists is the charge on a single proton or electron. We call it the elementary charge, symbol \(e\):

$$ e = 1.60\times10^{-19}\ \text{C} $$
ParticleCharge
Proton\(+e = +1.60\times10^{-19}\) C
Electron\(-e = -1.60\times10^{-19}\) C
Neutron\(0\)

One coulomb is a huge amount of charge — it is the charge of about \(6.25\times10^{18}\) electrons. That is why real charged objects usually carry only microcoulombs (\(1\ \mu\text{C}=10^{-6}\) C) or nanocoulombs (\(1\ \text{nC}=10^{-9}\) C).

The equation

Charge comes in whole steps: \(q = ne\)

Because every electron and proton carries exactly \(e\), the charge of any object is just a whole number of these elementary charges. We say charge is quantized.

$$ q = n\,e $$
where:
SymbolMeaningSI unit
qtotal (net) charge of the object — how much + or − it carriesC
nnumber of extra electrons or protons — a whole number (1, 2, 3, …)— (none)
ethe elementary charge, the fixed charge on one proton \(=1.60\times10^{-19}\) CC
You can have the charge of 1, 2, or a billion electrons — but never half an electron. Charge always comes in whole steps of \(e\).
📐 Worked example

Charge from a number of electrons

A small metal ball has gained \(n = 5.0\times10^{12}\) extra electrons. What is its total charge \(q\)?

1Start from the quantization rule:
$$ q = n\,e $$
2Put in the numbers (\(n = 5.0\times10^{12}\), \(e = 1.60\times10^{-19}\) C):
$$ q = (5.0\times10^{12})(1.60\times10^{-19}\ \text{C}) $$
3Multiply (add the powers of ten: \(10^{12}\times10^{-19}=10^{-7}\)):
$$ q = 8.0\times10^{-7}\ \text{C} = 0.80\ \mu\text{C} $$
The ball gained electrons, so its charge is negative: \(q = -0.80\ \mu\text{C}\). We use \(n\) to get the size; the kind of particle (electrons) tells us the sign.

✏️ Try it yourself

A plastic rod is rubbed with cloth and loses \(n = 2.5\times10^{13}\) electrons. What is the rod's charge — its size and its sign?

Hint: losing electrons leaves an object positive. Use \(q = ne\).

Step 1. \(q = n\,e = (2.5\times10^{13})(1.60\times10^{-19}\ \text{C})\) Step 2. \(q = 4.0\times10^{-6}\ \text{C} = 4.0\ \mu\text{C}\) Answer: \(q = +4.0\ \mu\text{C}\) — positive, because electrons left the rod.

Conductors and insulators

Materials differ in how easily charge can move through them. This single difference decides almost everything about how we build electrical things.

ConductorInsulator
Charge can…move freely through itstay stuck where it is put
Whysome electrons are loose and free to roamevery electron is held tightly to its atom
Examplescopper, gold, most metals, salt waterplastic, glass, rubber, dry air
Conductor free electrons roam between fixed + ions
Insulator each electron is held tightly to its own atom
A third kind — semiconductors. Materials like silicon sit in between: they conduct only a little, and we can control how much. They are the basis of every computer chip — but in this course we only need conductors and insulators.
🔌 Looking ahead: a wire is a conductor, so charge flows through it — that flow is electric current, which we study in Theme 3. The plastic coating around a wire is an insulator that keeps the charge inside.

Three ways to charge an object

All three methods do the same thing — move electrons — but in different ways.

1. By friction (rubbing)

Rub two different materials together and electrons rub off one onto the other. The balloon on your hair works this way: the balloon ends up negative, your hair positive.

2. By contact (conduction)

Touch a charged object to a neutral conductor. Charge spreads across both until they share it. Both objects end up with the same sign as the original charge.

3. By induction (no contact)

You can charge a conductor without touching it, using only the field of a nearby charge. This is the clever one, so we draw it step by step.

1. Bring a − rod near + + + electrons pushed to far side 2. Ground the far side + + + electrons escape to ground 3. Remove rod → + sphere + + + + left positively charged
Charging by induction. The sphere ends up charged opposite to the rod — and the rod never touched it.

Why a charged object attracts neutral things

Hold a charged rod near small pieces of paper and they jump to it — even though the paper has no net charge. Why?

Inside the neutral insulator, the rod's field pulls the + and − parts of each atom slightly in opposite directions. The atoms become tiny stretched pairs called dipoles; we say the material is polarized.

Now the side of the paper facing the rod has the opposite sign to the rod. Opposite charges are closer than like charges, so the pull wins over the push and the paper is attracted.

A neutral object can still be attracted: the field separates its charge a little, putting the unlike charge nearest — and nearest wins.
+ rod neutral insulator (aligned dipoles) + + + + + +
The + rod pulls the − side of every atom toward it: the near face becomes −, so the block is attracted.

✏️ Try it yourself

You bring a positively charged rod near (but not touching) a metal sphere, connect the far side of the sphere to the ground for a moment, then disconnect the ground and finally remove the rod. What is the final sign of the sphere's charge?

Reasoning. The + rod pulls the sphere's free electrons toward the near side. Grounding the far side lets extra electrons flow up from the ground onto the sphere. Answer: after the ground and rod are removed, the sphere is left negative — always the opposite sign to the rod in induction.

Common mistakes

MistakeFix
Saying protons move when an object charges.Only electrons move. Lose electrons → +, gain electrons → −.
Thinking charging "creates" charge.Charge is conserved — it is only moved. What one object gains, another loses.
Expecting induction to give the same sign as the rod.Induction leaves the opposite sign to the rod; contact gives the same sign.
Saying a neutral object cannot be attracted.It can — polarization puts the unlike charge nearest, and nearest wins.

Recap — the whole topic on one screen

IdeaWhat you own now
Two kindsCharge is + or −; like repels, unlike attracts.
Source of chargeAtoms; moving electrons charges objects (lose → +, gain → −).
ConservationTotal charge never changes — it is only moved around.
Quantization\(q = ne\), with \(e = 1.60\times10^{-19}\) C; charge comes in whole steps.
MaterialsConductor: charge moves freely. Insulator: charge stays put.
ChargingFriction, contact (same sign), induction (opposite sign, no touch).
PolarizationA field separates charge in a neutral object, so it is still attracted.

Next topic

Coulomb's law

You now know charges push and pull, and which way. Next we put a number on that force: how strong is the push or pull between two charges, and how it changes with their size and distance.

→ Topic 2 · Coulomb's law