Welcome to Charge & Coulomb's Law, the first topic of Electromagnetism. Every force in the mechanics topics was either gravity or a contact force: weight, the normal force, tension, friction, the push of a spring. This topic adds a new kind, the electric force between charged bodies. Like gravity, it acts across empty space. Unlike gravity, it can push as well as pull, and between small bodies it is far stronger: a rubbed plastic comb lifts a scrap of paper against the pull of the whole Earth. This page is about charge itself: what it is, how a body comes to carry it, and the rule that it is never made or destroyed. The second page measures the force between two charges, which is Coulomb's law, and the third adds up the forces from several charges.
The topic has had one or two questions in every paper so far, 7 of the 192. Two of them belong to this page, both from April 2026: what happens to the total charge of two objects charged by rubbing (Q12), and the charge on each of two identical spheres after they touch (Q23). Both are worked through below. The second skill reaches further than its own question. Sharing charge between identical spheres is also the first step of the touch-and-separate questions in December 2025 Q42, January 2026 Q43 and March 2026 Q41, which the next two pages finish. So the rule on this page has been needed in every paper, in 4 of the topic's 7 questions. The marks lost on it come from three slips, which this page names as they come up: forgetting to halve, dropping the sign, and adding the sizes of the charges instead of the charges with their signs.
Two kinds of charge
Rub a glass rod with silk and hang it from a thread so that it can turn freely. Bring up a second glass rod, rubbed with silk in the same way: the hanging rod swings away from it. Now bring up a rubber rod rubbed with fur instead: the hanging rod swings toward it. Hang the rubber rod and repeat, and a second rubbed rubber rod pushes it away, while a rubbed glass rod pulls it closer.
So rubbing gives a body something it did not have before, and that something comes in two kinds: two bodies charged the same way push each other apart, and bodies charged the two different ways pull together. No third kind has ever been found. Every charged body ever tested either repels the glass rod and attracts the rubber one, or attracts the glass rod and repels the rubber one. Benjamin Franklin named the two kinds, and his names are still used. The charge on glass rubbed with silk is positive, and the charge on rubber rubbed with fur is negative. The names are only labels, but they were well chosen. Equal amounts of the two kinds cancel, so a body's overall charge is found by adding its positive and negative amounts with their signs, just as +3 and −3 add to zero.
Two kinds of charge. Charge is positive or negative. Like charges repel; unlike charges attract. A body with equal amounts of the two, and so no overall charge, is neutral (uncharged). The amount of charge on a body is written q, and its SI unit is the coulomb, C, named after Charles-Augustin de Coulomb, whose law is the subject of the next page.
Try it! · Check-in question
Three small charged balls hang from insulating threads. Ball A repels ball B, and ball B attracts ball C. Ball C is positively charged. What charge does ball A carry?
Work back from C. B attracts the positive ball C, and unlike charges attract, so B is negative. A repels B, and like charges repel, so A is negative too, and the answer is B. A treats the repulsion as a sign of opposite charges; it is attraction that goes with opposite charges. C cannot be right: the question says all three balls are charged, and a neutral ball is never repelled by anything. D gives up too early. Each step follows from one rule, so the information is enough.
Electrons and the elementary charge
Why two kinds? Matter is made of atoms, and every atom contains both. At its centre is a tiny nucleus made of protons, which are positive, and neutrons, which carry no charge. Around the nucleus move electrons, which are negative. A proton's charge and an electron's charge are exactly equal in size and opposite in sign, and a neutral atom has as many electrons as protons, so its charges cancel.
The nucleus is held deep inside the atom, and in charging it never moves from one body to another. Some of the outer electrons, though, are held loosely and can be moved. So a body becomes charged by gaining or losing electrons. With extra electrons it is negative. Short of electrons, it is positive. A positive body has not gained protons; electrons have left it.
Since charge comes and goes one electron at a time, it cannot take any value. The size of the electron's charge is e = 1.6 × 10⁻¹⁹ C, and a body that has gained or lost n electrons carries a charge of n times that. In 1909 Robert Millikan measured the charges on tiny oil drops and found every one to be a whole-number multiple of the same amount, and that amount was e. It is the elementary charge: an electron carries −e, a proton +e, and no body has ever been found carrying a fraction of it.
The elementary charge. e = 1.6 × 10⁻¹⁹ C. Every charge is a whole-number multiple of e: q = ne, where n is the number of electrons gained or lost. Negative means extra electrons; positive means missing electrons. One coulomb is 1 ÷ (1.6 × 10⁻¹⁹) = 6.25 × 10¹⁸ elementary charges.
Worked example · counting electrons
A plastic rod rubbed with wool carries a charge of −4.8 × 10⁻⁸ C. How many electrons has it gained?
The charge is negative, so the rod has gained electrons. The number is n = q/e = 4.8 × 10⁻⁸ ÷ 1.6 × 10⁻¹⁹.
Divide the numbers and the powers of ten separately: 4.8 ÷ 1.6 = 3, and 10⁻⁸ ÷ 10⁻¹⁹ = 10⁻⁸⁺¹⁹ = 10¹¹. So n = 3 × 10¹¹ electrons.
That sounds like a great many, but it is a tiny fraction of the electrons in the rod. A coulomb is a very large amount of charge: a rubbed rod carries around a hundred-millionth of one. A metal sphere the size of a fist holding even a millionth of a coulomb would spark into the air around it. The April paper's spheres of +4 C and −6 C, below, could not exist; the paper uses whole coulombs only to keep the arithmetic simple, and the method is the same at any size.
Try it! · Check-in question
Which of these cannot be the charge on a body?
Every charge is a whole number of elementary charges, q = ne, so divide each value by e = 1.6 × 10⁻¹⁹ C. D gives 4.0 ÷ 1.6 = 2.5. Half an electron cannot be moved, so 4.0 × 10⁻¹⁹ C is impossible, and the answer is D. A gives 2 and B gives 3: two and three elementary charges, both possible. C is the one to read carefully. Its power of ten is one higher, so it is 1.6 × 10⁻¹⁸ ÷ 1.6 × 10⁻¹⁹ = 10 elementary charges, a perfectly possible charge.
Charging by friction
When two different materials are rubbed together, they are pressed into close contact at many points, and electrons pass across from the material that holds them more weakly to the one that holds them more strongly. Glass holds its outer electrons less firmly than silk, so electrons move from the glass to the silk: the glass is left positive and the silk becomes negative. Fur holds its electrons less firmly than rubber, so electrons move from the fur to the rubber: the rubber becomes negative and the fur is left positive.
Now count. Both objects start neutral. Suppose n electrons cross from the glass to the silk. The glass is now short of n electrons, so its charge is +ne. The silk has n extra, so its charge is −ne. Two things follow. The two objects always end with charges of opposite sign and equal size. And their total is +ne + (−ne) = 0, exactly what it was before the rubbing. Rubbing has separated charge that was already there; it has not made any.
Charging by friction, with a few charges standing for very many. Only electrons cross, so the glass loses exactly what the silk gains. The two end with equal and opposite charges, and the total stays zero.
Worked example · the total charge in rubbing (April 2026, Q12)
During the process of two objects being charged by friction, the total amount of charge they possess ( )
A. Remains constant B. Increases C. Cannot be determined due to insufficient conditions D. Decreases
Rubbing only moves electrons from one object to the other. Every electron that leaves one arrives on the other, so whatever charge one object gains, the other loses. The total does not change: zero before, +ne + (−ne) = 0 after. The answer is A.
B treats rubbing as a way of making charge. The work done in rubbing goes into pulling electrons away from one material, and into heat, not into creating charge; both objects do become charged, but in equal and opposite amounts. D is the opposite idea, that charge is used up or worn away. C is there for students who think the materials must be known. The materials decide which object ends positive and how much charge moves, but not the total, which stays the same whatever they are.
The answer to April's question is one case of a law that holds in every process ever observed, from rubbing a comb to the collisions of particles in accelerators.
Conservation of charge. Charge is never created or destroyed. It can only move from one body to another, or from one part of a body to another, so the total charge of a group of bodies that exchange charge only among themselves stays the same. Charging by friction, by contact and by induction all obey it.
Try it! · Check-in question
A plastic comb is pulled through dry hair and ends with a charge of −3.2 × 10⁻⁹ C. No charge escapes to the air. What charge does the hair now carry, and what moved?
The comb is negative, so it has gained electrons, and in rubbing they can only have come from the hair. The hair lost exactly what the comb gained, so it is left with +3.2 × 10⁻⁹ C and the total is still zero, so the answer is A. B has the right charge for the wrong reason: protons sit in the nuclei and do not move in charging. The hair is positive because it is short of electrons. C gives both objects the same sign, which would make the total −6.4 × 10⁻⁹ C out of nothing. D is the idea that rubbing creates charge; it only moves it, so the comb's charge must have come from somewhere.
Conductors, insulators and charging by contact
Rubbing works on glass, rubber, plastic and silk because the electrons that arrive stay where they land. In these materials every electron is held by its own atom and cannot travel through the material. They are insulators. In a metal, some electrons from each atom are not tied to any one atom and wander freely through the whole piece. These free electrons make the metal a conductor. Charge put on one spot of a conductor spreads over it at once, because its free electrons move until they are spread as far apart as they can get. The human body and the Earth conduct too. That is why a metal rod held in the hand does not stay charged when it is rubbed: the charge runs away through the hand. A conductor keeps its charge only on an insulating stand or handle.
A charged body can pass some of its charge to a conductor by touching it. Touch a negatively charged metal ball to an uncharged metal sphere on an insulating stand. The ball's extra electrons push each other apart, and once the two touch, some of them spread across onto the sphere. The sphere becomes negative, and the ball is left less negative than before. Touch a positively charged ball to the sphere instead, and the movement runs the other way. The ball is short of electrons and attracts the sphere's free electrons, some of which cross to it. The sphere is left short of electrons: positive. Its positive charge did not arrive from the ball; only electrons move in a metal, because the positive charge belongs to nuclei fixed in place. Either way, the body touched ends with the same sign as the charged body, and what one gains, the other loses.
Try it! · Check-in question
A small metal ball on an insulating handle carries a positive charge. It touches an uncharged metal sphere on an insulating stand and is then taken away. Which describes what happens?
Only electrons move in a metal. The positive ball attracts the sphere's free electrons, and some cross to the ball where the two touch. The sphere, now short of electrons, is positive, and the ball is less positive than before, so the answer is C. A gets the sphere's sign right but names the wrong carrier: protons are fixed in the nuclei and never move in charging. B has electrons leaving a positive ball, but a positive body is short of electrons and pulls them in. D has the rule backwards: a body charged by contact always ends with the same sign as the body that touched it. The next section shows a method that does give the opposite sign.
Charging by induction
A charged body can act on a conductor without touching it at all. Stand two uncharged metal spheres, A and B, on insulating stands so that they touch and form one conductor, and bring a positively charged rod near A, without letting it touch. The rod attracts the free electrons, and they move through the metal toward the end nearer the rod. A gains electrons and becomes negative. B, which they left, is short of electrons and becomes positive. The two charges are equal in size, because every electron A gained came from B, and the total is still zero. This separation of charge in a conductor by a nearby charged body is electrostatic induction.
Take the rod away now and nothing holds the electrons in A any more. They spread back, and both spheres are neutral again. To keep the charges, the order matters. Pull the spheres apart while the rod is still near, and only then take the rod away. Each sphere now keeps what it had: A its extra electrons, B its shortage. A is negative, B is positive, and the two charges are equal in size. This is charging by induction.
Charging by induction. The rod pulls free electrons into A and leaves B short of them. Pulling the spheres apart while the rod is still near traps the charges, so A and B end with equal and opposite charges and a total of zero. Had the rod been taken away first, the electrons would have spread back and left both spheres neutral.
Try it! · Check-in question
A positively charged rod is held near the left end of an uncharged metal bar on an insulating stand, without touching it. While the rod is held there, which describes the metal bar?
The positive rod attracts the bar's free electrons, which move toward the left end. The left end gains electrons and becomes negative; the right end, which they left, is positive. No charge has crossed the gap, so the total is still zero, and the answer is A. B has the electrons pushed away from the rod, which is what a negative rod would do. C needs charge to jump the gap, but nothing touches, and positive charge does not move in a metal anyway. D forgets where the electrons came from. They left the right end, so it must be positive, and the bar's total cannot change when nothing enters or leaves it.
A single conductor can be charged by induction too, with the Earth as the far partner. The Earth is a conductor so large that it can give or take any number of electrons and its own charge hardly changes. Hold a positively charged rod near an uncharged metal sphere on an insulating stand: electrons gather on the near side and the far side is left positive. Now touch the sphere with a finger, which connects it to the Earth, or earths it. Electrons are drawn up from the Earth through the body, attracted by the rod, and the far side's positive charge is cancelled. Take the finger away first, so that the extra electrons cannot go back, and then take the rod away. The sphere keeps the electrons it gained and is negative. Charge is still conserved: the sphere gained exactly what the Earth lost. Charging by induction always gives the opposite sign to the charged rod, while charging by contact gives the same sign.
Try it! · Check-in question
A negatively charged rod is held near an uncharged metal sphere on an insulating stand, without touching it. With the rod still in place, someone touches the sphere briefly with a finger. The finger is taken away, and then the rod is taken away. What charge is left on the sphere?
The negative rod pushes the sphere's free electrons to the far side. When the finger touches, they can go farther still, and some flow through the body into the Earth. The finger is removed first, so they cannot come back, and when the rod goes the sphere is left short of electrons. It is positive, the opposite sign to the rod, so the answer is D. A is the result of charging by contact, but the rod never touched the sphere. B forgets that the rod was still there while the finger touched. The rod drove electrons out to earth, and once the finger was gone they could not return. Earthed with no rod nearby, the sphere would indeed end neutral. C treats the sphere like the bar in the last question, whose induced charges spread back when the rod left. Here electrons have actually left the sphere, so its positive charge stays.
Attraction does not prove a charge. A charged body attracts an uncharged one too. The near side of the uncharged body takes the opposite charge and the far side the same charge, equal in size. The near side is closer, and the electric force, as the next page shows, weakens with distance, so the attraction wins. That is how a rubbed comb picks up scraps of paper. In an insulator such as paper the electrons cannot travel, but the charges inside each molecule shift a little, with the same result. So attraction means either opposite charges or a charged body and a neutral one. Only repulsion shows that both bodies are charged, and with the same sign.
Three ways to charge a body, one rule. By friction, electrons pass from one material to the other, and the two end with equal and opposite charges. By contact, electrons pass between the touching bodies, and the body touched takes the same sign as the charged one. By induction, electrons move within a conductor, or between it and the Earth, and the conductor ends with the opposite sign to the nearby charged body. In every case only electrons move, and the total charge does not change.
Exam wording. The Chinese April paper asks Q12 as 两个物体摩擦起电的过程中，它们的总电荷量: during 摩擦起电 (charging by friction), their 总电荷量 (total amount of charge). The other two methods are 接触起电 (charging by contact) and 感应起电 (charging by induction), and the separation of charge in a conductor is 静电感应 (electrostatic induction). Conservation of charge is 电荷守恒定律 and the elementary charge is 元电荷. Positive and negative charge are 正电荷 and 负电荷, a conductor is 导体, an insulator is 绝缘体, and to earth a body is 接地.
Identical spheres share equally
The most tested idea in the topic is what happens when two charged metal spheres touch and are pulled apart again. While they touch, they form one conductor, and electrons flow between them until there is no push to move any more. Two facts decide where that leaves them.
The first is conservation: whatever flows, the total q₁ + q₂ stays the same, counting each charge with its sign. The second is symmetry. If the two spheres are identical, the same size, shape and material, nothing in the arrangement favours one over the other, so the charge cannot settle with more on one than on the other. It must be shared equally. Each sphere ends with half the total.
Identical spheres in contact. When two identical conducting spheres touch and are separated, each ends with half the total charge: q₁′ = q₂′ = (q₁ + q₂)/2, with each charge put in with its sign. Spheres of different sizes do not share equally: the larger one takes the larger share, so the halving rule needs identical spheres.
1
Add the charges with their signs. Opposite charges cancel: +4 C and −6 C make −2 C, not 10 C.
2
Halve the total. Each identical sphere takes half, sign included.
3
Check. The two shares must add back to the starting total, and their sign must be the sign of the larger starting charge.
April 2026 Q23. Contact keeps the total, −2 C, and identical spheres share it equally, −1 C each. Electrons worth 5 C cross from the −6 C sphere: the +4 C sphere goes past neutral to −1 C, and the −6 C sphere gives up 5 C of its excess and keeps −1 C.
Worked example · sharing charge on contact (April 2026, Q23)
Two identical metal spheres carry charges of +4 C and −6 C. After they are brought into contact and then separated, the charge on each sphere is ( )
A. +2 C B. −2 C C. +1 C D. −1 C
Step 1, the total with signs: (+4) + (−6) = −2 C. Contact cannot change it.
Step 2, the share: the spheres are identical, so each takes half: −2 ÷ 2 = −1 C.
Step 3, the check: −1 + (−1) = −2 C, the starting total, and the sign is negative because the larger charge, −6 C, was negative. The answer is D.
What moved? The first sphere went from +4 C to −1 C, so it gained 5 C of negative charge: electrons worth 5 C crossed from the second sphere, which went from −6 C to −1 C. Like every contact between opposite charges, this one leaves the two spheres with the same sign.
B, −2 C, is the total, not yet halved: it is the charge of the pair, not of each sphere. C, +1 C, has the right size with the wrong sign, as if the 4 C had won; but the negative charge was the larger, so what is left is negative. A, +2 C, makes both slips at once, 6 − 4 = 2 with the wrong sign and no halving. The four options are a grid of two sizes and two signs, and only one cell is right.
Three slips the options are built from. Forgetting to halve: the total is shared between two spheres, so each gets half of it. Dropping the sign: the sign of what is left is the sign of the larger starting charge. Adding the sizes: opposite charges cancel, so +4 C and −6 C make −2 C. Adding 4 + 6 = 10 and halving gives 5 C, which treats the two charges as if they were the same kind.
Cases worth knowing. Equal and opposite charges, +q and −q: the total is zero, so both spheres end uncharged. One sphere uncharged: each ends with half of the other's charge. Like charges, +2q and +6q: each ends with +4q, so the smaller gains and the larger loses. Several contacts in a row: work one contact at a time, carrying each sphere's new charge into the next.
Try it! · Check-in question
Two identical metal spheres carry charges of +5 × 10⁻⁹ C and −1 × 10⁻⁹ C. They are brought into contact and then separated. What is the charge on each sphere?
Add with signs: (+5) + (−1) = +4, so the total is +4 × 10⁻⁹ C. The spheres are identical, so each takes half, +2 × 10⁻⁹ C, and the answer is B. A adds the sizes, 5 + 1 = 6, and halves. But the −1 cancels part of the +5 rather than adding to it. C is the total, not yet halved. D has the right size with the wrong sign: the positive charge was the larger, so what is left is positive.
You will meet this again. Contact sharing is the first step of a question that has appeared in three of the four papers, always between Q41 and Q43: two spheres touch, are put back, and the force between them is compared. In December 2025 Q42, +8q and −4q give (8q − 4q)/2 = +2q each. In March 2026 Q41, −Q and +3Q give +Q each. In January 2026 Q43, +Q and −5Q give −2Q each. All three start with opposite charges and end with like charges, so an attraction turns into a repulsion. December's question calls the second sphere "similar"; read it as identical, as the question intends. The next page compares the forces before and after.
Your turn! · Practice questions
Practice · Question 1
A metal sphere carries a charge of +8.0 × 10⁻¹¹ C. Compared with when it was neutral, the sphere has (e = 1.6 × 10⁻¹⁹ C):
The number of elementary charges is n = q/e = 8.0 × 10⁻¹¹ ÷ 1.6 × 10⁻¹⁹ = 5.0 × 10⁸, since 8.0 ÷ 1.6 = 5 and 10⁻¹¹ ÷ 10⁻¹⁹ = 10⁸. The charge is positive, so the sphere is short of electrons: it has 5.0 × 10⁸ fewer than when neutral, and the answer is C. A has the right number with the wrong sign: extra electrons would make the sphere negative. B adds protons, but protons stay in the nuclei and do not move in charging; a body becomes positive by losing electrons. D multiplies q by e instead of dividing. A fraction of one electron shows that the calculation has gone wrong.
Practice · Question 2
Three identical metal spheres stand on insulating stands. X carries +6q, Y carries −2q and Z is uncharged. Z is touched to X and taken away, and then touched to Y and taken away. What charge does Y end with?
Take one contact at a time. Z and X: (6q + 0)/2 = 3q each, so Z leaves with +3q. Z and Y: (3q + (−2q))/2 = +q/2 each. So Y ends with +q/2, and the answer is D. Check the total: X has 3q, Y has q/2 and Z has q/2, which makes 4q, the same as 6q − 2q at the start. A is what X and Y would each get if they touched each other directly, (6q − 2q)/2 = 2q. Z carries only half of X's charge across. B adds the sizes at the second contact, (3q + 2q)/2, and ignores Y's minus sign. C treats Z as still uncharged when it reaches Y, (−2q + 0)/2, but it had already picked up 3q from X.
Practice · Question 3
Which statement about electric charge is correct?
Rubbing moves electrons from the fur to the rubber. The rod gains exactly what the fur loses, so the two charges are equal in size and opposite in sign, and the answer is B. A says rubbing creates charge. It only moves it: electrons pass from the glass to the silk, which leaves the glass positive and the silk equally negative. C has the wrong particle: protons stay in the nuclei, and a body becomes positive by losing electrons. D fails the whole-number test: 2.4 × 10⁻¹⁹ ÷ 1.6 × 10⁻¹⁹ = 1.5, and every charge is a whole number of elementary charges.
Practice · Question 4
Two uncharged metal spheres, X and Y, stand on insulating stands and touch each other. A negatively charged rod is held near X without touching it. The rod is then taken away, and after that the spheres are pulled apart. What charges do X and Y now carry?
While the rod is near, it pushes free electrons from X into Y, so X is positive and Y negative. But the rod is taken away while the spheres still touch, so nothing holds the electrons in Y, and they spread back over both spheres. When the spheres are pulled apart, each is neutral, as both started, so the answer is C. A is the result if the spheres had been pulled apart while the rod was still near; the order of the steps decides it. B has the signs swapped as well: a negative rod pushes electrons away from the near sphere. D treats it as charging by contact, but the rod never touched either sphere, so their total stays zero.
Practice · Question 5
Two identical metal spheres carry charges of −3.2 × 10⁻⁹ C and +6.4 × 10⁻⁹ C. They touch and are separated. How many electrons crossed from one sphere to the other, and which way? (e = 1.6 × 10⁻¹⁹ C)
The total is (−3.2) + (+6.4) = +3.2 × 10⁻⁹ C, so each sphere ends with +1.6 × 10⁻⁹ C. The negative sphere goes from −3.2 × 10⁻⁹ C to +1.6 × 10⁻⁹ C, a change of +4.8 × 10⁻⁹ C, so it has lost 4.8 × 10⁻⁹ C of electrons: n = 4.8 × 10⁻⁹ ÷ 1.6 × 10⁻¹⁹ = 3 × 10¹⁰. They went to the positive sphere, which fell from +6.4 × 10⁻⁹ C to +1.6 × 10⁻⁹ C, so the answer is A. B reverses the direction: electrons leave the sphere that has extra and go to the one that is short of them. C counts the final charge on each sphere, 1.6 × 10⁻⁹ C, as the electrons that moved, but that is what is left, not what crossed. D counts only the negative sphere's extra electrons, enough to make it neutral. It ends positive, so it gave up more than its extra.
Things to remember
Concept
What to know
Two kinds of charge
Positive (glass rubbed with silk) and negative (rubber rubbed with fur). Like charges repel, unlike charges attract. Unit: the coulomb, C.
What moves
Only electrons. Extra electrons make a body negative; missing electrons make it positive. Protons stay in the nuclei.
Elementary charge
e = 1.6 × 10⁻¹⁹ C, and q = ne with n a whole number, so 4.0 × 10⁻¹⁹ C (2.5e) is impossible. 1 C = 6.25 × 10¹⁸ e.
Friction
Electrons pass from one material to the other, so the two end with equal and opposite charges. April 2026 Q12: the total remains constant.
Conductors and insulators
Metals have free electrons, and charge spreads over them; insulators keep charge where it is put. A conductor keeps its charge only on an insulating stand.
Contact
The body touched ends with the same sign as the charged body.
Induction
A nearby charged body pulls free electrons to the near side or pushes them to the far side; the total stays zero. To keep a charge, separate the parts or break the earth connection before removing the rod. The result has the opposite sign to the rod.
Attraction and repulsion
Attraction can be between a charged body and a neutral one. Only repulsion proves that both bodies are charged, with the same sign.
Conservation of charge
Charge is never created or destroyed, only moved, so the total of bodies that exchange charge only among themselves stays the same.
Identical spheres in contact
Each ends with (q₁ + q₂)/2, with signs. April 2026 Q23: (+4 − 6)/2 = −1 C. Equal and opposite charges leave both neutral. Only identical spheres share equally.
Common slips
Halving forgotten; the sign dropped; the sizes added instead of the signed charges; positive charge, or protons, thought to move.
