Electric charge and its properties
Two kinds of charge
On a dry winter day, pull off a synthetic sweater in a dark room. You hear crackles and may even see tiny sparks. Run a plastic comb through dry hair, and it picks up small bits of paper.
These are all effects of electric charge. The word electricity comes from elektron, the Greek word for amber. Around 600 BC, Thales of Miletus noticed that amber rubbed with wool or silk attracts light objects.
Now a simple experiment. Rub two glass rods with silk and hang one up by a thread. Bring the other one near it. The two glass rods push each other away.
Two plastic rods rubbed with fur also repel each other. But bring a rubbed glass rod near a rubbed plastic rod, and they attract.
So there are exactly two kinds of charge. Benjamin Franklin named them positive and negative: the glass rod’s charge is positive, the plastic rod’s is negative. Like charges repel, unlike charges attract.
Where does the charge come from? Every atom has a positive nucleus with negative electrons around it. In a neutral body, the positive and negative charges are exactly equal.
When glass is rubbed with silk, a few electrons move from the glass to the silk. The glass is left short of electrons, so it is positive. The silk has extra electrons, so it is negative.
Rubbing does not create charge. It only moves electrons from one body to the other, and only a tiny fraction of them. The mass hardly changes at all.
In some materials, like metals, the human body and the earth, electrons move freely. These are conductors. In glass, plastic, nylon and porcelain, charges cannot move freely. These are insulators.
Charge put on a conductor spreads over its whole surface at once. On an insulator, it stays where it was put. That is why a metal rod held in your hand never seems charged: the charge leaks through your body to the earth. Connecting a body to the earth like this is called earthing.
Additive, conserved, quantised
When charged bodies are tiny compared with the distances between them, we treat them as point charges: all their charge sits at one point. Now, three basic properties of charge.
First, charges are additive. Charge is a scalar, so the total charge of a system is just the algebraic sum: q equals q₁ plus q₂ plus q₃, and so on.
Take five charges: plus 1, plus 2, minus 3, plus 4 and minus 5, in some unit. The total is 1 plus 2 minus 3 plus 4 minus 5, which is minus 1. Unlike mass, charge can be negative, so the signs matter.
Second, charge is conserved. The total charge of an isolated system never changes. When glass is rubbed with silk, the glass gains exactly as much positive charge as the silk gains negative charge.
This holds even when particles are created or destroyed. A free neutron can turn into a proton and an electron. Before: zero charge. After: plus e and minus e, still zero in total.
Third, charge is quantised. Every charge is a whole-number multiple of a basic charge e: q equals n e, where n is a positive or negative integer. e is 1.6 × 10⁻¹⁹ coulomb. A proton carries plus e, an electron minus e.
The SI unit of charge is the coulomb: the charge that flows in one second through a wire carrying one ampere. In the laboratory we usually meet microcoulombs and nanocoulombs.
Why don’t we notice the steps? One microcoulomb is 10⁻⁶ divided by 1.6 × 10⁻¹⁹, about 6 × 10¹² electrons. Adding or removing one electron is far too small to notice, so on a large scale charge seems continuous.
Example: 10⁹ electrons move from one body to another every second. How long until the second body has one coulomb? One coulomb needs 1 over 1.6 × 10⁻¹⁹, that is 6.25 × 10¹⁸ electrons.
So the time is 6.25 × 10¹⁸ divided by 10⁹, which is 6.25 × 10⁹ seconds. Divide by the seconds in a year, about 3.15 × 10⁷, and you get nearly 200 years. One coulomb is a very large charge.
Try it: rubbing and touching
- Press Rub a few times. Electrons move from the glass to the silk. Watch the charge on each and the total.
- Switch to plastic rod and fur: now the electrons go the other way, and the rod becomes negative.
- Open “Touching spheres”. Two metal spheres share their total charge equally when they touch.
- Make the total odd (say +9 and −2) and touch them. The charge cannot split exactly in half: it comes in whole electrons.
- Untick “Metal spheres” and touch again: insulators keep their charge where it is.
Is it allowed?
Which of these cannot be the charge on a body? (e = 1.6 × 10⁻¹⁹ C)
- 3.2 × 10⁻¹⁹ C
- 2.4 × 10⁻¹⁹ C
- −1.6 × 10⁻¹⁸ C
- 8.0 × 10⁻¹⁹ C
Answer
B. A charge must be q = ne with n a whole number. Divide each by e: 3.2 × 10⁻¹⁹ C = 2e, −1.6 × 10⁻¹⁸ C = −10e and 8.0 × 10⁻¹⁹ C = 5e are all fine. But 2.4 × 10⁻¹⁹ C = 1.5e: half an electron’s charge does not exist on its own.
Two metal spheres
Two identical metal spheres carry charges of +9e and −3e. They are touched together and then separated. What is the charge on each now?
- +6e each
- +3e each
- Still +9e and −3e
- Zero on each: the charges cancel
Answer
B. Charge is conserved, so the total stays (+9e) + (−3e) = +6e. Identical metal spheres share it equally: +3e each. (+6e each would make a total of +12e: you would have added the sizes and ignored the sign.)
Summary
- Quantisation:
q = ne, n = 0, ±1, ±2, … - Basic charge:
e = 1.6 × 10⁻¹⁹ C - Additivity (with signs):
q = q₁ + q₂ + … + qₙ
- There are two kinds of charge, positive and negative. Like charges repel; unlike charges attract.
- Bodies get charged by transfer of electrons: rubbing moves charge, it does not create it.
- Conductors let charge move freely; insulators do not.
- Charge is additive (a scalar), conserved in an isolated system, and quantised in steps of e.