IB Physics HLTopic 4 — Force FieldsPaper 1 & 2Q = Ne~14 min read
Electric Charge
Rub a balloon on your jumper and it will hang from the wall. Nothing was created. Nothing was destroyed. A few trillion electrons simply moved from one place to another — and that, very nearly, is the whole story of electric charge. It cannot be made or unmade. It only ever gets shifted. And when it shifts, it shifts in whole numbers of one impossibly small lump.
📘 What you need to know
Charge is the property of matter responsible for the electric force
Charge is measured in coulombs (C). One coulomb is the charge carried past a point by a current of one ampere in one second
Charge is a scalar. The sign tells you the type of charge, not a direction
Protons carry +e, electrons carry −e, neutrons carry zero
The elementary charge is e = 1.60 × 10−19 C
Charge is quantised: any charge is a whole-number multiple of e, so Q = Ne
Like charges repel, opposite charges attract
Charge is conserved: the total charge of an isolated system stays constant. It can be transferred, never created or destroyed
Only electrons move. A positive object is one that has lost electrons
Identical conducting spheres brought into contact share their total charge equally
What charge actually is
Mass tells you how an object responds to gravity. Charge tells you how it responds to the electric force. That is the whole definition — charge is simply the property that lets an object push and pull on other objects electrically.
The coulomb — definitionone coulomb is the charge carried by an electric current of one ampere in one second
So a coulomb is not a fundamental thing in its own right. It is defined through current, and the working shortcut is Q = It. A current of 2 A flowing for 3 s delivers 6 C.
Charge is also a scalar. It has a size and a sign, but no direction. The minus sign in −3 µC is not pointing anywhere — it is a label saying “this is the electron sort”.
Students lose marks here every year by calling charge a vector “because it has a sign”. Velocity has a sign because +5 m s−1 and −5 m s−1 point opposite ways along a line. Charge has a sign because there are two kinds of it. Different job entirely. Charge is a scalar. Write it, remember it.
Quantisation of charge
Zoom in far enough and the reason for all this becomes obvious. Matter is made of atoms, and atoms have exactly three ingredients:
Protons in the nucleus, each carrying a charge of +e
Neutrons in the nucleus, carrying no charge at all
Electrons orbiting outside, each carrying −e
An ordinary atom is neutral because the protons and the electrons are matched one for one. Break that balance and you have a charged object.
Because every proton carries exactly +e and every electron exactly −e, any lump of charge you can ever measure is a whole number of these. There is no half-electron to hand out.
Quantisation of chargeQ = NeN = a whole number • e = 1.60 × 10−19 C
Rearranged the other way, N = Q/e, and that is how you count electrons.
Think of charge as a currency that only has 1p coins. You can be handed 3p or 47p or a million pounds — but never 2.5p. Charge works exactly the same way, except the coin is e = 1.60 × 10−19 C. It takes about 6.25 × 1018 of those coins to make one single coulomb. A coulomb is an enormous amount of charge, which is why real answers come out in µC and nC.
Which way does the force point?
Two charges near one another push or pull along the line joining them. Which one it is depends on nothing but the two signs.
Notice that both charges in a pair feel the same size of force, however lopsided the charges are. That is just Newton’s third law, showing up again.
Charge on object 1
Charge on object 2
Attract or repel?
Positive
Positive
Repel
Positive
Negative
Attract
Negative
Positive
Attract
Negative
Negative
Repel
Four rows, one sentence: opposites attract. If you remember that, the other three rows write themselves.
Conservation of charge
Energy cannot be created or destroyed. Neither can charge. This is one of the deepest rules in all of physics, and in an exam it looks disarmingly simple:
Conservation of chargethe total charge in an isolated system remains constant
Read that as: charge can be transferred from one object to another, but it cannot be created or destroyed. “Isolated system” just means the objects doing the swapping, with nothing leaking in or out.
Sharing charge between identical spheres
Here is where conservation earns its keep. Touch two identical metal spheres together and the charge sloshes about until both carry the same amount. It has to: they are identical, so there is no reason for one to keep more than the other. The total has not changed, it has just been split evenly.
Identical spheres in contactQfinal = ( Q1 + Q2 + … + Qn ) / nadd the charges with their signs, then divide by how many spheres touched
The spheres do not swap “positive charge”. Electrons leave the negative sphere and land on the positive one, until both agree.
Only electrons move
Protons are welded into the nucleus. They are going nowhere. So whenever an object becomes charged, ask the only question that matters: did it gain electrons, or lose them?
Rub two insulators
electrons hop across
One gains → negative
so the other must have
One loses → positive
Charge conservation guarantees the two are equal and opposite. If the cloth ends up at −4.8 nC, the rod must be at exactly +4.8 nC. Nothing else is possible.
A quick check on particle decay
Conservation of charge is not just for rubbed balloons. Look at beta-minus decay, where a neutron turns into a proton:
This is exactly why the electron has to be there. A neutron becoming a proton would create a +1 charge out of nothing, and nature will not allow it. So an electron pops out alongside to keep the books at zero. Charge conservation is not a description of what happens — it is a rule that decides what is allowed to happen.
⚡ Working a charge question
Get everything into coulombs. µC = 10−6 C, nC = 10−9 C. Every single time.
Spheres touching? Add the charges with their signs, divide by the number of identical spheres.
Counting electrons?N = Q/e, using the magnitude of Q. The answer must be a whole number.
Which way did they go? Gained electrons → more negative. Lost electrons → more positive.
Final check. Total charge before = total charge after. If it doesn’t, you’ve slipped a sign.
WE 1
Two identical metal spheres A and B carry charges of +9.0 µC and −3.0 µC. They are briefly brought into contact and then separated. (a) Determine the final charge on each sphere. (b) Calculate how many electrons were transferred, and state which way they moved.
(a) Step 1 — add the charges, keeping their signsQtotal = (+9.0) + (−3.0) = +6.0 μCStep 2 — identical spheres, so split it evenlyQfinal = +6.0 / 2+3.0 μC on each sphere(b) Step 3 — how much charge actually moved?A went from +9.0 to +3.0 μC, a change of 6.0 μCStep 4 — count the electronsN = Q / e = (6.0 × 10⁻⁶) / (1.60 × 10⁻¹⁹)N = 3.75 × 10¹³ electrons, moving from B to ASphere A became less positive, so it must have gained electrons. Sphere B had the spare electrons to give. Check the total: +3.0 and +3.0 is +6.0 μC, exactly what we started with.
WE 2
A plastic rod is rubbed with a dry cloth and ends up with a charge of −4.8 nC. (a) Calculate the number of electrons transferred. (b) State the charge left on the cloth, and explain your reasoning.
(a) Step 1 — convert to coulombsQ = 4.8 nC = 4.8 × 10⁻⁹ CStep 2 — use N = Q / eN = (4.8 × 10⁻⁹) / (1.60 × 10⁻¹⁹)N = 3.0 × 10¹⁰ electrons(b) Step 3 — where did they come from?
The rod is negative, so it gained those electrons.
They came from the cloth, which has therefore lost them.
cloth carries +4.8 nCCharge is conserved, so the two must be equal and opposite. Never say the cloth “gained positive charge” — it lost negative charge. Same result, very different physics, and only one of them scores.
WE 3
Three identical conducting spheres X, Y and Z carry charges of +8.0 µC, −2.0 µC and 0 respectively. X is touched to Y and separated. Y is then touched to Z and separated. Determine the final charge on each sphere.
Step 1 — note the total before anything happens8.0 + (−2.0) + 0 = +6.0 μCStep 2 — X touches Y(8.0 − 2.0) / 2 = +3.0 μC each
So X = +3.0 μC and Y = +3.0 μC. Z is untouched at 0.
Step 3 — now Y touches Z(3.0 + 0) / 2 = +1.5 μC eachStep 4 — collect the answersX = +3.0 μC, Y = +1.5 μC, Z = +1.5 μCCheck: 3.0 + 1.5 + 1.5 = +6.0 μC. The total never budged. Notice X keeps the charge it had after its own contact — once it has walked away, later contacts have nothing to do with it. Work strictly in the order the question gives you.
💡 Top tips
Charge is a scalar. The sign is a type, not a direction. Examiners ask this.
Always convert µC and nC into coulombs before dividing by e.
For touching spheres, add the signed charges and divide by how many. It’s that simple.
Explain charging with electrons only: “the rod lost electrons”, never “the rod gained positive charge”.
Your electron count N must come out a whole number. That’s what quantised means.
Learn e = 1.60 × 10−19 C. It is in the data booklet, but you’ll use it constantly.
Finish every conservation question by checking the total before and after.
⚠ Common mistakes
Calling charge a vector because it has a sign. It is a scalar
Saying an object “gained positive charge”. Only electrons move — it lost electrons
Averaging touching spheres without the signs, e.g. (9 + 3)/2 instead of (9 − 3)/2
Forgetting to convert µC or nC to coulombs before using N = Q/e
Thinking protons can be transferred. They are locked in the nucleus
Believing charge is “used up” or “destroyed” when things discharge. It is only moved
Applying the equal-sharing rule to spheres of different sizes. It only works for identical ones
Quick recap: Charge is the property responsible for the electric force, measured in coulombs, and it is a scalar. It is quantised — every charge is a whole-number multiple of the elementary charge, so Q = Ne with e = 1.60 × 10−19 C. Like charges repel, opposite charges attract. And charge is conserved: it is transferred by moving electrons, never created or destroyed. Identical spheres in contact share their total charge equally.
One question is left hanging. How did anybody ever measure a lump as absurdly small as 1.60 × 10−19 C? You cannot put an electron on a balance. In 1909 two physicists in Chicago solved it with a perfume atomiser, a microscope and a great deal of patience: they suspended a single droplet of oil in mid-air, balancing the electric force against its weight, and read the charge straight off. Next page: Millikan’s Oil Drop Experiment.
Signs and electrons getting tangled?
Book a free meeting and we’ll drill charge sharing, electron counting and the “it lost electrons” phrasing until it’s automatic.
