Conservation of charge

Rub a plastic scale with a woollen cloth and the scale suddenly attracts bits of paper — charge has appeared, as if from nowhere. It hasn't. Nothing in friction, contact, or induction manufactures a single unit of charge; every charging trick you meet in this chapter is really charge moving house from one object to another. The principle of conservation of charge says the total charge in an isolated system never changes — only its distribution does. This article extends the friction and contact examples you already know into a general rule you can use to check any charging scenario, and into a real quantitative tool: predicting exactly how much charge ends up on each object after two conductors touch.

The core insight

Charge is never created or destroyed during friction, conduction, or induction — it only transfers between objects, so the total charge of an isolated system stays constant before and after.

The core idea

Every charging method on the ICSE Class 8 syllabus — friction, conduction (contact), and induction — rearranges existing charge rather than making new charge.

Friction. When a glass rod is rubbed with silk, electrons move from the glass to the silk. The glass, having lost negative charge, is left positively charged; the silk, having gained exactly that negative charge, becomes negatively charged by the same amount. Add the two charges together and the sum is the same as before rubbing: zero.

Conduction (contact). When a charged conductor touches an uncharged (or differently charged) conductor, charge flows across the contact until the two reach a shared state. Nothing is added to or removed from the pair as a whole — the total is simply shared out differently.

Induction. Here the two bodies never even touch. The nearby charge only pulls the free charges inside the uncharged body apart, piling opposite charge on the near side and like charge on the far side. No charge crosses between the bodies at all, so the total stays exactly as it was. Putting this in one statement, for any isolated group of objects with charges q1,q2,…,qnq_1, q_2, \ldots, q_n:

Qtotal=q1+q2+⋯+qn=constant.(1)Q_{\text{total}} = q_1 + q_2 + \cdots + q_n = \text{constant}. \qquad (1)

where: QtotalQ_{\text{total}} is the sum of all the charges in the system (measured in the same units throughout, with sign), and "constant" means this sum has the same value before and after any charging process — friction, contact, or induction — carried out entirely within that system. Individual qiq_i values can change a great deal; their sum cannot.

Figure
Two spheres before and after contact showing charge redistributing while the total charge stays the same
Contact redistributes charge — the total is unchanged before contact +8 sphere A 0 sphere B total = +8 units touch after contact +4 sphere A +4 sphere B total = +8 units, still Charge moved from A to B, but nothing was created or destroyed.

Conservation of charge is not just a description — it is a checking tool. If a written explanation of a charging scenario implies that positive charge appeared without an equal amount of negative charge showing up somewhere else, that explanation is wrong.

Derivation AEqual charge sharing between identical conducting spheres in contact

The goal is to show, using nothing but the conservation law and the idea that identical conductors touching share charge equally between them, that when two identical metal spheres carrying charges q1q_1 and q2q_2 are brought into contact and separated, each ends up with exactly the average of the two starting charges — a result you can use directly for any pair of identical conductors, not only the specific numbers in a textbook example.

Step 1. Write down the total charge before contact. By conservation of charge, the total charge of the two-sphere system is fixed at Qtotal=q1+q2Q_{\text{total}} = q_1 + q_2, and this value cannot change while the spheres remain isolated from everything else, whether they are touching or not.

Step 2. Use the symmetry of identical spheres. Because the two spheres are identical in size and material, once they touch and form a single connected conductor, there is no physical reason for the shared charge to prefer one sphere over the other — both spheres are, in every respect that matters for charge, indistinguishable. So the charge divides equally between them the instant they are in contact.

Step 3. Combine the two facts. Let q′q' be the (equal) charge on each sphere just after contact. Conservation of charge requires q′+q′=q1+q2q' + q' = q_1 + q_2, so 2q′=q1+q22q' = q_1 + q_2, which gives

q′=q1+q22.(2)q' = \frac{q_1 + q_2}{2}. \qquad (2)

where: q′q' is the final charge on each of the two identical spheres after contact and separation, and q1,q2q_1, q_2 are their charges before contact. Each sphere's final charge is simply the average of the two starting charges, and separating the spheres afterward locks in that value on each one.

Step 4. Check the special case. If sphere B starts neutral (q2=0q_2 = 0), Step 3 gives q′=q1/2q' = q_1/2 on each sphere — every unit of charge that leaves A is matched by a unit gained by B, so the total q1q_1 is unchanged, only halved between two equal shares. The same reasoning extends to more than two identical spheres: with nn identical spheres all touching at once, the shared charge on each becomes Qtotal/nQ_{\text{total}}/n.

Worked example

Question. Two identical metal spheres, A carrying +8+8 units of charge and B carrying no charge, are brought into contact and then separated. A third identical sphere C, carrying −4-4 units, is then touched to sphere A alone and separated. Find the final charge on each of the three spheres.

Step 1. Apply equation (2) to A and B first. Before their contact, q1=+8q_1 = +8 and q2=0q_2 = 0, so Qtotal=8Q_{\text{total}} = 8 units. By equation (2), each of A and B ends up with q′=8/2=+4q' = 8/2 = +4 units. Sphere C is untouched so far, still at −4-4 units.

Step 2. Apply equation (2) again, now to A and C. Sphere A currently carries +4+4 units (from Step 1) and sphere C carries −4-4 units, so their combined total is Qtotal=4+(−4)=0Q_{\text{total}} = 4 + (-4) = 0 units. By equation (2), each of A and C ends up with q′=0/2=0q' = 0/2 = 0 units after this second contact.

Step 3. Collect the final charges. Sphere A: 00 units (from Step 2). Sphere B: +4+4 units (untouched since Step 1). Sphere C: 00 units (from Step 2). Final answer: A = 0, B = +4 units, C = 0.

Step 4. Sanity-check the grand total. Before anything happened, the three spheres together carried 8+0+(−4)=+48 + 0 + (-4) = +4 units. After both contacts, they carry 0+4+0=+40 + 4 + 0 = +4 units — the same total, exactly as conservation of charge demands, even though it took two separate contacts to get there.

Common traps

  • Thinking friction "creates" charge on the object that becomes charged — it only transfers existing charge, leaving equal and opposite charge on the two objects, never new charge from nowhere.
  • Believing induction transfers charge between the two bodies — during induction no charge crosses over at all; the nearby body's own internal charges merely separate and redistribute.
  • Applying the equal-sharing formula q′=(q1+q2)/2q' = (q_1+q_2)/2 to spheres that are not identical in size or material — unequal conductors do not necessarily split charge equally, only identical ones do.
  • Forgetting to update a sphere's charge before using it in a second contact, as in the worked example — always use the charge a sphere actually carries at that moment, not its original starting value.

Ask the tutor: Want to try a multi-step "spheres touching in sequence" problem, or a mixed friction-and-induction scenario, to practise applying conservation of charge?

If conduction lets charge flow between two objects, how is charge still conserved?

Conservation of charge is not about charge staying put — it is about the total not changing. During conduction, charge genuinely moves from one conductor to the other, so each object's individual charge changes. But if you add up the charge on both objects together, before contact and after contact, you get the same number both times. What looks like a change on each object is really just a redistribution of a fixed total between them.

Why do two identical spheres split charge exactly in half, but I have read that unequal spheres do not?

Splitting charge equally relies on the two spheres being identical in every way that affects how charge settles on a conductor — same size, same shape, same material. When conductors are identical, there is no physical reason for the shared charge to favour one over the other, so symmetry forces an equal split, which is exactly the reasoning behind q′=(q1+q2)/2q' = (q_1+q_2)/2. Spheres of different sizes reach a different, unequal balance instead, because a larger conducting sphere can hold more charge at the same shared condition. That case goes beyond what this article covers, but the total charge is still conserved either way.

Does conservation of charge mean an object can never really become charged?

No — objects genuinely do become charged, and that charge is real and measurable. Conservation of charge only says that whenever an object gains charge, some other object in the system must have lost an equal and opposite amount, so nothing was created from nothing. A rubbed balloon really does pick up charge and really does stick to a wall; the rule simply insists that whatever charge it gained, the cloth that rubbed it lost the exact same amount of the opposite sign.

Before this

Where this leads