Coaching Centre
Electric charge and charging
Positive and negative charge, the elementary charge and quantisation, conservation of charge, conductors and insulators, charging by friction, conduction and induction, polarisation, and how a gold-leaf electroscope detects charge and tests its sign.
Before a plane is refuelled at Sydney Airport, the crew clip a cable from the tanker to the aircraft. Fuel rushing through a hose can strip electrons from one surface and dump them on another, and a few thousand volts of built-up charge is enough to throw a spark into fuel vapour. The cable lets the charge flow away safely. Everything in this page, from why the charge builds up to why the cable fixes it, comes down to electrons moving from one place to another.
What charge is
Charge is a property of particles, like mass. Unlike mass it comes in two kinds, which Benjamin Franklin named positive and negative. Protons carry positive charge and electrons carry an equal amount of negative charge. Like charges repel and unlike charges attract.
The SI unit of charge is the coulomb (C). One coulomb is a very large amount of static charge: a rubbed balloon carries a few nanocoulombs (1 nC = 10−9 C). The charge on a proton is the elementary charge
$$e = 1.602 \times 10^{-19}\ \text{C}$$
Since the 2019 redefinition of the SI units this value is exact by definition ($e = 1.602\,176\,634 \times 10^{-19}$ C), and the ampere and the coulomb are now built on it. Older textbooks give it as a measured value; the 4-significant-figure value on the HSC data sheet is all you need.
Two rules govern charge everywhere in physics:
- Charge is quantised. Every free charge is a whole-number multiple of e: $q = ne$. You can't have half an electron's charge on a balloon. (Quarks carry ⅓e and ⅔e, but they are never found on their own.)
- Charge is conserved. Charge is never created or destroyed, only moved. When a rod becomes negative, whatever rubbed it becomes equally positive.
Ordinary objects contain huge, equal numbers of protons and electrons. An object is "charged" when it has a slight excess or shortage of electrons. In solids it is almost always electrons that move; protons are locked in the nuclei.
A polythene rod rubbed with wool ends up with a charge of −3.2 nC. How many electrons did it gain, and what charge did the wool end up with?
$n = \dfrac{q}{e} = \dfrac{3.2 \times 10^{-9}}{1.602 \times 10^{-19}} = 2.0 \times 10^{10}$ electrons gained.
Those electrons came from the wool, so the wool is left with +3.2 nC. The total charge of rod plus wool is still zero.
The rod has around 1024 electrons in it, so 2 × 1010 extra is an imbalance of about one part in 1014. Tiny imbalances give very noticeable forces.
Conductors and insulators
In a metal, each atom releases one or more outer electrons into a shared "sea" of free electrons that can drift through the whole solid. Charge placed on a metal spreads out over its surface within a tiny fraction of a second. These materials are conductors: metals, graphite, salt solutions, the human body and moist ground.
In an insulator (plastic, glass, rubber, dry air, wood) every electron is bound to its own atom or molecule. Charge put on an insulator stays where it was put. That is why you can charge a plastic rod by rubbing one end but not a metal rod held in your hand: charge on the metal simply flows away through you. Semiconductors such as silicon sit in between, and their conductivity rises sharply with temperature or light (you'll see this in thermistors in 4F).
Three ways to charge an object
Year 7 (topic 8H) showed that rubbing a balloon charges it. At Stage 6 you need to explain each method in terms of electron transfer and say what sign of charge results.
- Friction. When two different insulators are rubbed together, close contact lets electrons move from the material that holds them less tightly to the one that holds them more tightly. Polythene rubbed with wool gains electrons and becomes negative; acetate rubbed with a cloth loses electrons and becomes positive. The two objects always end up with equal and opposite charges.
- Conduction (contact). A charged object touches a neutral conductor and some charge flows across. The conductor ends up with the same sign of charge as the object that touched it. Two identical metal spheres that touch end up sharing their total charge equally.
- Induction. A charged object is brought near a conductor without touching. Its field pushes free electrons to one side, leaving the near side with the opposite charge. If the conductor is earthed while the charged object is near, electrons flow to or from Earth. Break the earth connection, then remove the charged object, and the conductor keeps a charge of the opposite sign.
Two identical small metal spheres carry +6.0 nC and −2.0 nC. They are touched together and then separated. Find the final charge on each and the number of electrons that moved.
Total = +6.0 + (−2.0) = +4.0 nC. Identical spheres share it equally: +2.0 nC each.
The second sphere went from −2.0 nC to +2.0 nC, a change of +4.0 nC, so it lost electrons to the first sphere: $n = \dfrac{4.0 \times 10^{-9}}{1.602 \times 10^{-19}} = 2.5 \times 10^{10}$ electrons. Positive charge did not move; the first sphere became less positive because it gained electrons.
Polarisation: why charged objects attract neutral ones
A charged balloon sticks to a neutral wall, and a charged comb picks up neutral scraps of paper. In an insulator the electrons can't flow away, but within each molecule the electron cloud shifts slightly towards (or away from) the charged object. Each molecule becomes a tiny dipole, with its near side opposite in sign to the charged object. The near side is closer, so its attraction is stronger than the repulsion of the far side, and there is a net attraction. This is polarisation; it is induction on a molecular scale.
This explains a classic trap: attraction does not prove that two objects carry opposite charges, because a charged object attracts neutral objects too. Only repulsion proves that an object is charged (and has the same sign as the other).
The gold-leaf electroscope
An electroscope detects charge. A metal cap is connected by a metal rod to two thin leaves of gold foil (or one fixed plate and one hinged leaf), inside a case that keeps out draughts. Charge on the cap spreads to the leaves, the like-charged leaves repel and they spread apart. The bigger the charge on the leaves, the wider the angle.
Once an electroscope carries a known charge, it can test the sign of an unknown one. Bring the unknown object near the cap. If the leaves spread further, the object has the same sign. If they partly collapse, it has the opposite sign (or is a neutral conductor: check with a known charge too).
- With the polythene rod, press "Bring rod near". The leaves spread although the net charge on the electroscope is still 0: the leaves carry −3.0 nC and the cap +3.0 nC. Explain the separation.
- Charge by induction: keep the rod near, touch the cap with your finger, remove your finger, then take the rod away. The electroscope is left with +6.0 nC, and the sim says 3.75 × 1010 electrons were lost. Check that number with n = q/e. Why must the finger come off before the rod is taken away?
- Reset and use "Touch the cap with the rod" instead. The electroscope now has −2.0 nC (1.25 × 1010 electrons gained): the same sign as the rod.
- Test a charge: charge the electroscope positively by induction (+6.0 nC), then bring the negative rod near again. The leaves collapse to 0. Now switch to the positive acetate rod and predict what happens.
Test yourself
A glass rod rubbed with silk acquires a charge of +4.8 × 10−9 C. Which statement is correct?
n = 4.8 × 10−9 / 1.602 × 10−19 = 3.0 × 1010. Only electrons move, and a positive rod has lost them (to the silk).
Which of these could not be the charge on an isolated object?
Charge is quantised in units of e. −2.4 × 10−19 C is 1.5e, which is impossible. The others are 2e, 100e and 5e.
A neutral metal sphere on an insulating stand is charged by induction using a positively charged rod. The sphere ends up
The positive rod attracts electrons up from Earth while the sphere is earthed. Removing the earth traps them, so the sphere is negative: opposite to the rod.
A charged balloon is held near a small neutral piece of paper, which jumps up to the balloon. The best explanation is that
The paper stays neutral overall. Polarisation puts opposite charge on the near side, and the closer charges win.
Two identical metal spheres carry +8.0 μC and −14.0 μC. They touch and are separated. Each sphere now carries
Total = −6.0 μC, shared equally between identical spheres: −3.0 μC each.
Label the electroscope.
Put the steps for charging a sphere negatively by induction in order.
Sort the materials.
Charge is measured in . All free charges are whole-number multiples of the charge, so charge is . Charge is : it can be moved but never made or destroyed. In solids it is that move. Charging by contact gives the sign as the charging object.
Explain how a neutral, insulated metal sphere can be given a negative charge using a positively charged rod, without the rod touching the sphere. Refer to the movement of charge at each stage.
When the positive rod is brought near, it attracts free electrons in the metal towards the near side, leaving the far side positive. The sphere is still neutral overall. The sphere is then earthed (for example by touching it). Electrons are attracted up from Earth through the earth connection onto the sphere by the positive rod. The earth connection is removed while the rod is still close, so the extra electrons cannot flow back. Finally the rod is removed, and the excess electrons redistribute over the whole surface. The sphere now carries a net negative charge, equal and opposite to the positive charge left behind in the Earth, so charge is conserved.
A metal sphere with a charge of −4.0 nC is touched against an identical neutral sphere and then separated. (a) Find the charge on each sphere. (b) Calculate how many electrons moved, and state in which direction.
(a) Total charge −4.0 nC is shared equally between identical spheres, so each has −2.0 nC.
(b) The neutral sphere gained −2.0 nC: n = q/e = 2.0 × 10−9 ÷ 1.602 × 10−19 = 1.2 × 1010 electrons, which moved from the originally charged sphere onto the neutral one.