AP Physics 2 · Topic 10.2

Topic 10.2: Conservation of Electric Charge and the Process of Charging

Unit 10: Electric Force, Field, and Potential15-18% of the multiple-choice section

Topic 10.2 says charge is never created or destroyed, only moved. A system's net charge stays constant unless charge crosses its boundary, and what crosses is almost always electrons. Friction, contact, induced charge separation and grounding are the mechanisms the CED names for moving it.

AP Physics: Unit 10 (topics 10.2 Conservation of Electric Charge and the Process of Charging). AP Physics 2 Unit 10, Topic 10.2. One learning objective, 10.2.A, asks students to describe the behavior of a system using conservation of charge. Three essential knowledge statements support it. 10.2.A.1 states that the net charge or charge distribution of a system can change in response to the presence of, or changes in, the net charge or charge distribution of other systems, with sub-statements that the net charge of a system can change due to friction or contact between systems (10.2.A.1.i), that induced charge separation occurs when the electrostatic force between two systems alters the distribution of charges within the systems, resulting in the polarization of one or both systems (10.2.A.1.ii), and that induced charge separation can occur in neutral systems (10.2.A.1.iii). 10.2.A.2 states that any change to a system's net charge is due to a transfer of charge between the system and its surroundings, with sub-statements that charging typically involves the transfer of electrons to and from the system (10.2.A.2.i) and that the net charge of a system will be constant unless there is a transfer of charge to or from the system (10.2.A.2.ii). 10.2.A.3 states that grounding involves electrically connecting a charged system to a much larger and approximately neutral system, such as Earth. The topic prints no boundary statement and no relevant equation. The CED's suggested skills here are 1.A, 2.C, 3.B and 3.C. Unit 10 carries 15 to 18 percent of the multiple-choice section and a suggested 14 to 21 class periods.

What Topic 10.2 actually requires

Topic 10.2 fits on a single printed page of the CED, which makes it easy to underestimate. It carries a single learning objective, 10.2.A: describe the behavior of a system using conservation of charge. Three essential knowledge statements sit under it, two of them with sub-statements, and the CED prints no boundary statement and no relevant equation for this topic at all.

That absence is a signal, not an oversight. With no formula to practice, the questions have to be descriptions, comparisons and justifications, and the suggested skills say the same thing.

Skill	CED wording
1.A	Create diagrams, tables, charts, or schematics to represent physical situations.
2.C	Compare physical quantities between two or more scenarios or at different times and locations in a single scenario.
3.B	Apply an appropriate law, definition, theoretical relationship, or model to make a claim.
3.C	Justify or support a claim using evidence from experimental data, physical representations, or physical principles or laws.

Two of the four are argument skills. Unit 10 as a whole is weighted at 15 to 18 percent of the multiple-choice section with roughly 14 to 21 class periods suggested, and this topic is where you learn to say why a charge ended up where it did.

The essential knowledge breaks down like this:

10.2.A.1 and its three sub-statements: how one system's charge responds to another system.
10.2.A.2 and its two sub-statements: conservation itself, and the fact that electrons are what move.
10.2.A.3: grounding.

Conservation of charge, in the CED's words

Start with 10.2.A.2, because it is the law. Any change to a system's net charge is due to a transfer of charge between the system and its surroundings. Sub-statement 10.2.A.2.ii turns that into the version you will quote in a justification: the net charge of a system will be constant unless there is a transfer of charge to or from the system.

Read those two together and the pattern is the one every AP conservation law follows. Draw a boundary, then ask what crosses it. Nothing crossing means the total inside cannot change. It is the same discipline you used for systems and center of mass and for conservation of linear momentum, and charge is the strictest member of the family: there is no charge equivalent of friction quietly draining the total away.

Statement 10.2.A.1 is the one that makes the topic interesting, because it names two different things that can change. The net charge or charge distribution of a system can change in response to the presence of, or changes in, the net charge or charge distribution of other systems.

Net charge is the signed total. It changes only when charge crosses the boundary.
Charge distribution is where that total sits inside the object. It can change with nothing crossing the boundary at all.

Those two columns are where the topic's traps live. A polarized balloon has a different distribution and the same net charge. A grounded sphere has a different net charge. Keep a two-column tally, before and after, and the accounting becomes mechanical.

The choice of system is yours, and it changes the answer. Take a rod alone and its charge changes when you rub it. Take the rod plus the cloth and the total sits at whatever it was before you started.

Electrons move; protons do not

Sub-statement 10.2.A.2.i is short and does a lot of work: the charging of a system typically involves the transfer of electrons to and from the system.

Three consequences follow, and all three are testable.

A positively charged object has lost something. It did not gain protons. It is short of electrons, and the object it was rubbed against is holding them.
The carrier is negative. The stuff that physically moves carries a minus sign, so the direction electrons travel is opposite to the direction of conventional positive charge flow. That distinction does no harm here and becomes essential in Topic 11.1.
The hedge is real. The CED wrote typically. In a solid it is electrons; in a solution or a gas, ions move too. For the rubbed rods, touched spheres and grounded conductors in this topic, the carrier is the electron.

Charge also comes in whole units, which is the bridge back to Topic 10.1. EK 10.1.A.1.ii says the elementary charge $e$ can be considered to be the smallest indivisible amount of charge, and the AP Physics 2 equation sheet prints $e = 1.60 \times 10^{-19}\ \text{C}$ in its Constants group. So a transfer is always an integer number of electrons, and you can count them:

n = \frac{|q|}{e}

That relationship is not printed on the equation sheet. It follows from the definition of $e$ , and it is the arithmetic behind the numerical questions in this topic.

Charging by friction and by contact

Sub-statement 10.2.A.1.i names the two mechanisms that change a net charge: the net charge of a system can change due to friction or contact between systems.

Friction. Rub two neutral materials together and electrons move from one to the other. Which way they go depends on the pair of materials, which is not something AP Physics 2 asks you to predict. What it does ask is the bookkeeping. If both objects started neutral and only electrons moved between them, they end with equal and opposite charges. That is not a separate rule to memorize; it is 10.2.A.2.ii applied to the two-object system, whose total never changed.

Contact. Touch a charged conductor to another conductor and charge redistributes across the combined object, then stays split when you separate them. If the two conductors are identical, nothing distinguishes one from the other, so the charge has to end up shared equally and each carries half the total. Note that the CED does not print this equal-sharing result as essential knowledge; it follows from the symmetry of two identical conductors, and the worked example below spells out the reasoning rather than asserting the rule.

A vocabulary note worth keeping straight. Textbooks call these charging by friction and charging by conduction, and they call the next mechanism charging by induction. Unit 10 of the CED uses none of those three phrases. It says friction or contact, and it says induced charge separation. The word induction appears in this CED only in Unit 12, attached to electromagnetic induction and Faraday's law, which is a different phenomenon entirely. Learn both vocabularies, and write the CED's.

Induced charge separation and polarization

Sub-statement 10.2.A.1.ii defines the mechanism: induced charge separation occurs when the electrostatic force between two systems alters the distribution of charges within the systems, resulting in the polarization of one or both systems. Sub-statement 10.2.A.1.iii adds the line that is easiest to miss: induced charge separation can occur in neutral systems.

Nothing crosses a boundary here. This is the charge distribution column of 10.2.A.1, on its own.

Here is why a neutral object still gets pulled in. Bring a negatively charged rod near a neutral object and the object's electrons are pushed to the far side, leaving the near side positive. The near side is attracted and the far side is repelled, and the two do not cancel, because the electric force falls off as the inverse square of distance. The nearer, opposite charge wins. The object is drawn toward the rod even though its net charge is still exactly zero. That is the answer to the unit's own essential question about why a charged rubber balloon sticks to a wall.

Topic 10.1 supplies the microscopic picture. EK 10.1.C.2 models electric polarization as the induced rearrangement of electrons by an external electric field, resulting in a separation of positive and negative charges within a material or medium, and EK 10.1.C.1 defines permittivity as a measurement of the degree to which a material or medium is polarized in the presence of an electric field. So permittivity and induced charge separation are the same physics seen from two topics.

The distinction that gets tested: separation is not charging. An object that has been polarized and nothing else has the same net charge it started with. To convert separation into a net charge you need a path for charge to leave, which is what grounding provides.

Grounding

EK 10.2.A.3 is one sentence: grounding involves electrically connecting a charged system to a much larger and approximately neutral system, for example Earth. Both qualifiers earn their place.

Much larger. Because the ground is enormous compared with the object, charge that flows into it spreads over something vast, and the ground's own condition barely registers the change. That is what makes it an effectively bottomless reservoir: it will take electrons or supply them on demand without pushing back.

Approximately neutral. Not exactly neutral. The CED hedges because Earth is not a perfect zero, and the model is that it is close enough to treat as one.

Also read the "e.g." in that sentence. Earth is the example, not the definition. Any sufficiently large, roughly neutral conductor is a ground, which is why a car body or a metal chassis is called ground in a circuit.

Grounding is the third step in the sequence that leaves a conductor with a net charge without ever touching it with the charged object, and the order of operations is the whole trick:

Bring the charged rod near the neutral conductor. Induced charge separation, net charge still zero.
Ground the conductor while the rod stays in place. The charge the rod repels now has somewhere to go, so it leaves.
Disconnect the ground. By 10.2.A.2.ii the conductor's net charge is now locked in.
Remove the rod. The remaining charge spreads out, and the total is unchanged.

Swap steps 3 and 4 and you get nothing: with the ground still attached, removing the rod simply lets the charge flow back and the conductor ends neutral. The conductor's final charge is always opposite in sign to the rod that charged it, which is the giveaway that grounding was involved.

The unit's lightning-storm essential question runs on the same idea. The CED does not answer its own essential questions, but the ingredient it hands you is EK 10.1.C.4.ii: a car's metal shell is a conductor, so charge travels through the shell rather than through the people inside it. The rubber tires are not what is doing the work.

Conductors, insulators, and where that definition lives

Which mechanism works on an object depends entirely on whether its charge carriers can move, and the CED files that definition under Topic 10.1 rather than here. EK 10.1.C.4.ii: conductors are made from electrically conducting materials in which charge carriers move easily; insulators are made from electrically nonconducting materials in which charge carriers cannot move easily. EK 10.1.C.4.i connects it to permittivity, which in a given material is determined by the ease with which electrons can change configurations within the material.

If you are revising charging and cannot find the conductor definition in Topic 10.2, that is why. It is one topic earlier.

Situation	Conductor	Insulator
Charge deposited at one spot	Spreads over the object	Stays roughly where it was put
Grounded while charged	Drains almost completely	Barely drains
Charged by contact	Shares readily	Shares poorly
Polarized by a nearby charge	Whole electrons shift across the object	Charge shifts slightly within each molecule

Both columns polarize, and that is the row to read twice. An insulator cannot pass charge from one end to the other, but its molecules can still stretch, and the aggregate of those small separations is exactly what EK 10.1.C.2 describes. That is why a rubber balloon, an insulator through and through, still sticks to a wall.

What the questions actually ask

With no equation in the topic, Topic 10.2 questions live in the skills. Match your answer to the skill being tested.

Skill 2.C, comparing. Compare physical quantities between two or more scenarios or at different times and locations in a single scenario. In this topic that means before against after: net charge before touching against net charge after, force before against force after, charge on sphere A against charge on sphere B. Write both values down and say which changed.

Skill 3.C, justifying. Justify or support a claim using evidence from experimental data, physical representations, or physical principles or laws. A justification here names the principle, conservation of charge, and then tracks the electrons: where they were, where they went, and what stopped them. "Charge is conserved" alone is a claim, not a justification.

Skill 1.A, drawing. Create diagrams, tables, charts, or schematics to represent physical situations. When you draw a polarized object, put signs on both ends. A diagram showing only the near-side charge implies the object gained charge, which is the error the question is checking for.

Skill 3.B, applying. Apply an appropriate law, definition, theoretical relationship, or model to make a claim. Usually this means naming the mechanism that actually applies and saying why the others do not.

Unit 10 as a whole is flagged in the CED as strong practice for the second free-response question, the Translation Between Representations question, which asks for graphical and verbal models of a scenario compared against a mathematical representation of the same situation. The CED is explicit that content from any unit may appear in that question, so treat Unit 10 as good preparation rather than a prediction.

Where Topic 10.2 goes wrong

Saying the protons moved. 10.2.A.2.i says charging typically transfers electrons. A positive object is one that lost electrons, and the protons in its nuclei never went anywhere.
Calling a polarized object charged. Induced charge separation changes the distribution, not the total. A neutral object that has been polarized still has a net charge of zero, and saying otherwise loses the point the question was testing.
Forgetting the second object. Rubbing produces two charged objects, not one. If a question gives you the rod, the cloth is part of the answer.
Removing the rod before the ground. In the induction sequence, disconnecting the ground has to come first. Reverse the two and the conductor ends up neutral.
Assuming touching spheres always split charge evenly. That result depends on the two conductors being identical. Different sizes share unequally, and AP Physics 2 will not ask you to compute that split.
Reading conservation as immobility. Conservation of charge does not say charge cannot move. It says the total in a system with no transfers across its boundary does not change. Charge moves constantly; it just never appears or disappears.
Assuming insulators do not respond. They cannot conduct, but they polarize, and the attraction that follows is real.

Counting the electrons that actually moved

A glass rod is rubbed with a silk cloth. Both were neutral beforehand. Afterward the rod carries a net charge of $-4.8\ \text{nC}$ . (a) How many electrons moved, and in which direction? (b) What is the net charge on the cloth? (c) What is the net charge of the rod and cloth taken together?

(a) Direction first. The rod ended up negative, and 10.2.A.2.i says charging typically involves the transfer of electrons, so electrons moved from the silk onto the glass. Nothing positive travelled.
Count them with the elementary charge from the Constants group of the AP Physics 2 sheet, $e = 1.60 \times 10^{-19}\ \text{C}$ : $n = \dfrac{4.8 \times 10^{-9}}{1.60 \times 10^{-19}} = 3.0 \times 10^{10}$ electrons.
(b) The cloth is the only place they could have come from, so by 10.2.A.2 the cloth's net charge changed by exactly the opposite amount. The cloth is left at $+4.8\ \text{nC}$ .
(c) Add the two: $-4.8\ \text{nC} + 4.8\ \text{nC} = 0$ . Choose the rod plus cloth as the system and nothing crossed its boundary, so 10.2.A.2.ii says its net charge could not change, and it did not.
Worth a sanity check on the size of that count. Three times $10^{10}$ electrons have a combined mass of about $2.7 \times 10^{-20}\ \text{kg}$ , using $m_e = 9.11 \times 10^{-31}\ \text{kg}$ from the sheet. No balance would register it, which is why rubbing a rod changes its charge books and not its mass books.

$3.0 \times 10^{10}$ electrons moved from the silk to the glass. The cloth is left at $+4.8\ \text{nC}$ , and the rod-plus-cloth system is still exactly neutral. Net charge changed for each object separately and not at all for the pair.

Two spheres touch, and the force flips sign

Two identical small conducting spheres are held $0.10\ \text{m}$ apart. Sphere A carries $+8.0\ \text{nC}$ and sphere B carries $-2.0\ \text{nC}$ . They are briefly touched together, then returned to their original positions. Compare the electric force before and after.

Before, the signs are opposite, so the force is attractive. Its magnitude, from Topic 10.1: $|\vec{F}| = k\dfrac{|q_A q_B|}{r^2} = (9.0 \times 10^9)\dfrac{(8.0 \times 10^{-9})(2.0 \times 10^{-9})}{(0.10)^2} = 1.44 \times 10^{-5}\ \text{N}$ , or $1.4 \times 10^{-5}\ \text{N}$ to two significant figures.
While the spheres touch they are one conductor, so treat them as one system. Total charge in: $+8.0 + (-2.0) = +6.0\ \text{nC}$ . Nothing else touches them, so 10.2.A.2.ii fixes that total for the whole process.
Split it. The spheres are identical, so nothing physically distinguishes one from the other and the only distribution consistent with that symmetry is an even one: $+3.0\ \text{nC}$ on each. This is a symmetry argument, not a printed CED result, and stating the symmetry is what earns the mark.
After, both spheres are positive, so the force is now repulsive: $|\vec{F}'| = (9.0 \times 10^9)\dfrac{(3.0 \times 10^{-9})^2}{(0.10)^2} = (9.0 \times 10^9)\dfrac{9.0 \times 10^{-18}}{0.010} = 8.1 \times 10^{-6}\ \text{N}$ .
Now the comparison, which is suggested skill 2.C. The direction reverses, from attraction to repulsion. The magnitude falls: $\dfrac{8.1 \times 10^{-6}}{1.44 \times 10^{-5}} = 0.5625$ .
Check that fraction symbolically, since the separation never changed: the ratio is $\dfrac{(3.0)^2}{(8.0)(2.0)} = \dfrac{9}{16}$ , which is $0.5625$ exactly.

Before: $1.4 \times 10^{-5}\ \text{N}$ , attractive. After: each sphere carries $+3.0\ \text{nC}$ and the force is $8.1 \times 10^{-6}\ \text{N}$ , repulsive, exactly $\tfrac{9}{16}$ of the old magnitude. The two spheres' combined charge stayed at $+6.0\ \text{nC}$ throughout.

Charging a sphere without ever touching it

A neutral metal sphere rests on an insulating stand. A negatively charged rod is brought close but never touches it. With the rod still in place, a wire briefly connects the sphere to the ground; the wire is removed, and only after that is the rod taken away. During the grounded moment $1.2 \times 10^{10}$ electrons leave the sphere. Find the sphere's final charge, and explain why the order of the last two steps matters.

Rod near, no ground. The rod's negative charge repels the sphere's mobile electrons to the far side, leaving the near side positive. This is induced charge separation, 10.2.A.1.ii, and 10.2.A.1.iii confirms it happens in a neutral system. Net charge so far: still zero, because nothing has crossed the sphere's boundary.
Ground connected. The ground is a much larger and approximately neutral system (10.2.A.3), so it accepts the electrons the rod is pushing away. They leave the sphere through the wire, and now something has crossed the boundary.
Count the transfer: $q = ne = (1.2 \times 10^{10})(1.60 \times 10^{-19}\ \text{C}) = 1.92 \times 10^{-9}\ \text{C}$ of negative charge has left. Losing negative charge leaves the sphere positive, at $+1.92\ \text{nC}$ , which is $+1.9\ \text{nC}$ to two significant figures.
Disconnect the wire first. With no path to the ground, 10.2.A.2.ii locks the sphere's net charge at $+1.9\ \text{nC}$ whatever happens next.
Now remove the rod. The positive charge that is left redistributes itself over the sphere, but the total cannot change, because there is still nothing to transfer through. Final answer $+1.9\ \text{nC}$ .
Why the order matters: reverse the last two steps and you get nothing. Take the rod away while the wire is still attached and the repulsion that drove the electrons out disappears, so they flow straight back from the ground and the sphere ends neutral.

The sphere ends at $+1.9\ \text{nC}$ , opposite in sign to the rod that charged it and never in contact with it. The sequence is the whole method: ground the sphere while the rod is near, disconnect the ground, then remove the rod.

Frequently asked questions

What is the law of conservation of charge?

It is the statement that a system's net charge changes only when charge crosses the system's boundary. AP Physics 2 puts it in two pieces under Topic 10.2: any change to a system's net charge is due to a transfer of charge between the system and its surroundings (10.2.A.2), and the net charge of a system will be constant unless there is a transfer of charge to or from the system (10.2.A.2.ii). Charge is never created or destroyed, only moved, so if one object becomes negative, something else became positive by the same amount.

What are the three ways to charge an object?

Most textbooks list friction, conduction and induction. The AP Physics 2 CED uses different words for the same physics. Essential knowledge 10.2.A.1.i says the net charge of a system can change due to friction or contact between systems, which covers the first two. Statement 10.2.A.1.ii describes induced charge separation, where the electrostatic force between two systems alters the distribution of charge within them and polarizes one or both, and 10.2.A.3 adds grounding, which is what turns that separation into a permanent net charge. Write the CED's vocabulary in a free-response answer.

Why is a neutral object attracted to a charged one?

Because the charged object rearranges the neutral one before pulling on it. This is induced charge separation, and essential knowledge 10.2.A.1.iii says explicitly that it can occur in neutral systems. Bring a negative rod near a neutral object and its electrons are pushed away, leaving the near side positive and the far side negative. The near side is attracted, the far side is repelled, and the attraction wins because the electric force falls off with the square of distance and the attracted charge is closer. The object's net charge is still exactly zero throughout.

What does grounding actually do?

Grounding gives charge somewhere to go. Essential knowledge 10.2.A.3 defines it as electrically connecting a charged system to a much larger and approximately neutral system, such as Earth. Because the ground is so much bigger, it can absorb or supply electrons without becoming noticeably charged itself, so it behaves like an unlimited reservoir. Ground a charged conductor on its own and it ends up neutral. Ground it while a charged object is held nearby, then disconnect the ground before removing that object, and it is left with a net charge opposite in sign to the object that never touched it.

Do protons ever move when an object is charged?

Not in the situations AP Physics 2 asks about. Essential knowledge 10.2.A.2.i says the charging of a system typically involves the transfer of electrons to and from the system. Protons are bound in nuclei and stay put in a solid, so an object that has become positively charged has lost electrons rather than gained protons. The CED's word is typically rather than always, because charge can also be carried by ions in a liquid or a gas, but for a rubbed rod, a touched sphere or a grounded conductor the answer is electrons every time.

What happens when two charged metal spheres touch?

Their charges combine and then redistribute, and the combined total is unchanged. Add the two charges with their signs to get the total, since conservation of charge fixes it while the spheres are isolated. If the two spheres are identical, symmetry means neither can end up with more than the other, so each carries half the total when they are separated. A sphere at plus 8.0 nC touched to one at minus 2.0 nC leaves both at plus 3.0 nC, and a force that was attractive becomes repulsive. Spheres of different sizes share unequally, and AP Physics 2 does not ask you to calculate that split.

Is polarization the same as charging?

No, and the difference is the most tested idea in Topic 10.2. Polarization, which the CED calls induced charge separation, changes where the charge sits inside an object without changing how much it has. A polarized neutral object still has a net charge of exactly zero, because nothing crossed its boundary. Charging changes the net total, and by essential knowledge 10.2.A.2 that requires a transfer of charge between the system and its surroundings. Induced charge separation only becomes charging when you add a path, which is what grounding provides.