Electrostatics

Lessons

Senior 1 · Physics

Electrostatics

5 lessons

Lesson 1 of 5

Electric Charge and Its SI Unit

22 min

Why does her hair stand on end?

In the dry months of June to August, you may hear a crackle when you pull a nylon sweater over your head, or feel a small shock when you touch a metal door handle after walking across a carpet. A plastic comb pulled through dry hair picks up tiny bits of paper. In the photograph below, a girl touches the metal dome of a machine and every hair on her head lifts away from the others. All of these are effects of electric charge that stays in one place for a while: static electricity. The study of charges at rest is called electrostatics.

Important

Safety. A school Van de Graaff generator gives sparks that sting but are not dangerous to healthy people. Only the teacher runs it, and anyone with a heart pacemaker must never touch it.

Activity: which objects pick up paper?

Tear a sheet of paper into pieces about the size of a grain of rice and spread them on a dry desk.
Run a plastic comb quickly through clean, dry hair about ten times. Hold it 1 cm above the paper and watch.
Repeat with a plastic pen rubbed on a woollen cloth, a glass rod rubbed with silk, and a metal spoon (held in your hand) rubbed with wool.

Object	Rubbed with	Does it pick up paper?
plastic comb	dry hair	yes: the pieces jump up and cling
plastic pen	wool	yes
glass rod	silk	yes
metal spoon held in the hand	wool	no

Rubbing has given the comb, the pen and the rod something that attracts paper across a gap: they have become charged. On a humid day the effect is much weaker, because a thin film of water on the surfaces lets the charge leak away. The metal spoon seems to stay uncharged; lesson 5 explains why.

Where charge comes from: inside the atom

All matter is made of atoms. At the centre of each atom is a tiny, heavy nucleus containing protons and neutrons. Much lighter electrons move around the nucleus in shells. A proton and an electron carry charges of exactly the same size but opposite sign; a neutron has no charge.

Figure 1.1: A lithium atom. It has as many electrons as protons, so its total charge is zero.

Particle	Where it is found	Charge	Mass (kg)
proton	in the nucleus	$+e = +1.6 \times 10^{-19}\,\mathrm{C}$	$1.67 \times 10^{-27}$
neutron	in the nucleus	0	$1.67 \times 10^{-27}$
electron	in shells around the nucleus	$-e = -1.6 \times 10^{-19}\,\mathrm{C}$	$9.11 \times 10^{-31}$

Definition

Electric charge (symbol $Q$ or $q$ ) is the property of protons and electrons that makes them push or pull on each other. There are two kinds: positive (+) and negative (−).

The SI unit of charge is the coulomb ( $\mathrm{C}$ ), named after the French physicist Charles-Augustin de Coulomb. The charge on one proton is the elementary charge, $e = 1.6 \times 10^{-19}\,\mathrm{C}$ ; an electron carries $- e$ .

Example: a rubbed plastic comb may carry a charge of about $-10\,\mathrm{nC}$ , that is $-1.0 \times 10^{-8}\,\mathrm{C}$ .

Charged and uncharged objects

An uncharged (neutral) object contains huge numbers of protons and electrons, in exactly equal numbers, so their charges cancel. The protons are locked inside the nuclei and cannot move from one object to another. Only electrons, the outer ones held loosely by their atoms, can be moved. So:

an object that loses electrons has more protons than electrons: it becomes positively charged;
an object that gains electrons has more electrons than protons: it becomes negatively charged.

Figure 1.2: Each + stands for a proton and each − for an electron; dashed rings mark the electrons that have left or arrived. Only electrons move: losing them makes an object positive, gaining them makes it negative.

Important

Conservation of charge. Charge is never created or destroyed; it is only moved from one object to another. When a comb gains electrons from your hair, your hair loses exactly the same number, so the total charge of comb and hair together stays zero.

Definition

Charge is quantised: every charge is a whole number of elementary charges. An object with $n$ extra (or missing) electrons carries a charge of size

Q = n e

Useful sub-units: $1\,\mu\mathrm{C} = 10^{-6}\,\mathrm{C}$ (microcoulomb) and $1\,\mathrm{nC} = 10^{-9}\,\mathrm{C}$ (nanocoulomb).

Worked example 1: the charge on a comb

A comb gains $5.0 \times 10^{11}$ electrons from dry hair. What is its charge?

Q = ne = (5.0 \times 10^{11}) \times (1.6 \times 10^{-19}\,\mathrm{C}) = 8.0 \times 10^{-8}\,\mathrm{C}

The comb has gained electrons, so its charge is $-8.0 \times 10^{-8}\,\mathrm{C}$ , which is $-80\,\mathrm{nC}$ .

Worked example 2: counting the missing electrons

A glass rod rubbed with silk has a charge of $+3.2\,\mu\mathrm{C}$ . How many electrons has it lost?

n = \frac{Q}{e} = \frac{3.2 \times 10^{-6}\,\mathrm{C}}{1.6 \times 10^{-19}\,\mathrm{C}} = 2.0 \times 10^{13}

Twenty million million electrons left the rod, yet this is a tiny fraction of the electrons it contains.

Worked example 3: how many electrons make one coulomb?

n = \frac{1\,\mathrm{C}}{1.6 \times 10^{-19}\,\mathrm{C}} = 6.25 \times 10^{18}

One coulomb is a very large charge for static electricity: rubbed objects usually carry nanocoulombs or microcoulombs.

Warning

Common mistakes. (1) Saying a positive object has "gained protons". Protons never move between objects; a positive object has LOST electrons. (2) Forgetting the sign: an object that gains electrons has a negative charge. (3) Mixing up prefixes: $μ \mu$ (micro) means $10^{-6}$ , n (nano) means $10^{-9}$ .

Tip

Only electrons move. Ask one question: did the object gain electrons (it is now negative) or lose them (it is now positive)?

Static charge in daily life

In Rwanda's dry seasons the air holds little water, so charge stays on clothes, hair and plastic much longer: sweaters crackle, and dust clings to television and computer screens. Photocopiers and laser printers in every school office use static charge on purpose, to make black toner powder stick to the paper in the shape of the letters. And in the rainy seasons, the thunderclouds over the hills build up charge on a giant scale: a rubbed comb carries a few nanocoulombs, while one lightning flash can move several coulombs. Lesson 5 returns to lightning and how to stay safe.

Electric Charge: Crash Course Physics #25 (CrashCourse). Watch for the atom picture of charge, the two kinds of charge and the conservation of charge. The second half introduces Coulomb's law, which you will meet in lesson 4.

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Practice

Name the three particles in an atom, and give the charge of each.
Explain, in terms of electrons, how a neutral object becomes (a) negatively charged; (b) positively charged.
Convert: (a) $250\,\mathrm{nC}$ into coulombs; (b) $0.40\,\mu\mathrm{C}$ into coulombs.
A neutral piece of cloth loses $3.0 \times 10^{12}$ electrons. What is its charge now?
A plastic ruler has a charge of $-1.6\,\mathrm{nC}$ . How many extra electrons does it carry?
A comb rubbed on hair gains a charge of $-12\,\mathrm{nC}$ . What is the charge on the hair? Which law did you use?
A classmate says, "A positively charged rod has extra protons on it." Evaluate this statement.

Show answersHide answers

Proton: positive ( $+ e$ ); neutron: no charge; electron: negative ( $- e$ ).
(a) It gains electrons, so it has more electrons than protons. (b) It loses electrons, so it has more protons than electrons.
(a) $250 \times 10^{-9} = 2.5 \times 10^{-7}\,\mathrm{C}$ ; (b) $0.40 \times 10^{-6} = 4.0 \times 10^{-7}\,\mathrm{C}$ .
$Q = ne = 3.0 \times 10^{12} \times 1.6 \times 10^{-19} = 4.8 \times 10^{-7}\,\mathrm{C}$ , positive: $+0.48\,\mu\mathrm{C}$ .
$n = \frac{1.6 \times 10^{-9}}{1.6 \times 10^{-19}} = 1.0 \times 10^{10}$ electrons.
$+12\,\mathrm{nC}$ . By the conservation of charge, the electrons the comb gained came from the hair, so the total charge is still zero.
The statement is wrong. Protons are held in the nuclei and do not move between objects. The rod is positive because it has LOST electrons, so it now has more protons than electrons.

Key points

Atoms contain protons (+), neutrons (no charge) and electrons (−); a neutral object has equal numbers of protons and electrons.
Only electrons move: gaining electrons makes an object negative, losing them makes it positive. Charge is conserved.
The SI unit of charge is the coulomb (C); $e = 1.6 \times 10^{-19}\,\mathrm{C}$ and $Q = n e$ .

Sources and credits

18.1: Static Electricity and Charge: Conservation of Charge, from College Physics (1st edition) by Paul Peter Urone and Roger Hinrichs, OpenStax, hosted by LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
Photo: Van de Graaff Generator - Science City - Calcutta 1997 444.JPG by Biswarup Ganguly, Wikimedia Commons, licensed under CC BY 3.0.
Video: Electric Charge: Crash Course Physics #25, CrashCourse, embedded from YouTube.

The activity, the diagrams, the worked examples, the Rwandan applications and the practice exercises are written by Ganzaa.

1Why does her hair stand on end?

2Activity: which objects pick up paper?

3Where charge comes from: inside the atom

4Charged and uncharged objects

5Static charge in daily life

Why does her hair stand on end?

Activity: which objects pick up paper?

Where charge comes from: inside the atom

Charged and uncharged objects

Static charge in daily life