Conservation of Electric Charge and the Process of Charging
Use system boundaries to distinguish transferred net charge from redistributed charge.
AP Physics 2 Topic 10.2 · College Board CED printed p. 46 / PDF p. 53 · See this topic in the course outline
Charging is bookkeeping. Decide whether charge crossed the boundary or merely moved to another place inside it.
For another explanation, read Conductors and Insulators. Use the corrected charge-mobility discussion to explain contact, polarization, and grounding with a system boundary.
Before you start
- Elementary charge and the signs of electrons and protons
- Conductors, insulators, and polarization
A conserved quantity, three different charging stories
For a selected system, , with signed charge transfers. If no charge crosses its boundary, its net charge stays fixed. Friction and contact can transfer electrons between materials; they do not create charge. A rod that becomes negative has gained electrons, and the other object in the isolated pair has lost the same charge. Ordinary solids usually exchange electrons; the protons remain bound in nuclei.
Contact with a charged conductor can transfer electrons until the connected conductors reach a common potential. Equal sharing follows for identical isolated spheres in a symmetric environment, not for arbitrary shapes. A nearby charge can also change a system’s distribution without changing its net charge: electrons in a neutral conductor move toward a positive rod, leaving a positive region farther away. A neutral insulator may polarize through small bound-charge displacements. In both cases opposite regions can exist in a net-neutral system.
Grounding makes the boundary matter
Grounding connects an object electrically to a much larger, approximately neutral reservoir, usually Earth. Earth can supply or accept a small amount of charge while changing its own potential negligibly. It does not always “remove electrons”: the transfer direction depends on the object and nearby sources.
- Bring a positive rod near a neutral isolated metal sphere. Electrons move toward the rod; net sphere charge is still zero.
- With the rod held in place, ground the sphere. Electrons can enter from Earth.
- Disconnect the ground first. The extra electrons are now trapped on the isolated sphere.
- Remove the rod. Excess negative charge redistributes over the surface.
The sphere becomes negative although the rod never touched it. Its charge changed during grounding, when electrons crossed its boundary. For the larger system sphere + rod + Earth, total charge was conserved throughout. Removing the rod before disconnecting ground allows redistribution and transfer that can leave the sphere neutral.
Identical spheres and an explicit ledger
Two identical isolated metal spheres, initially +8.0 nC and −2.0 nC, touch and separate. Find the final charges and electron transfer.
Select both spheres as one system: total charge is +6.0 nC before and after contact.
Why this step? No charge crosses the combined isolated boundary.
Symmetry and common potential give Q₁ = Q₂ = +3.0 nC after separation.
Why this step? Identical spheres in the same environment share equally; charge conservation alone would not establish this.
Sphere 1 changes by −5.0 nC, so it gains electrons from sphere 2.
Why this step? A decrease in positive net charge corresponds to incoming electrons.
Answer and check
Each ends at +3.0 nC; about 3.1 × 10¹⁰ electrons move from the initially −2.0 nC sphere to the initially +8.0 nC sphere.
Try it from memory
Write your answer and reason before opening the worked answer. Your self-assessment is a study decision; it is not an automatically graded score.
Question 1
A charged rod approaches an insulated neutral metal can without touching. Can its near face become charged? Can the can acquire nonzero net charge?
Worked answer and reason
The near face can develop induced charge as electrons redistribute. Without transfer through contact, ground, or another path, the whole can remains neutral.
Distribution and net charge are different; apply the conservation statement to the selected can boundary.
Question 2
Repeat the grounding sequence with a negative rod. What charge remains after disconnecting ground and then removing the rod?
Worked answer and reason
Positive. The negative rod drives electrons to Earth while grounded; disconnecting ground traps an electron deficit.
The rod’s force determines transfer direction; Earth is an approximately fixed-potential reservoir.
JavaScript enables saved drafts and self-assessment. You can always work on paper.
Catch the tempting mistake
- Rubbing creates negative charge.
- Electrons transfer between objects; the combined system’s charge is conserved.
- Any grounded object must become neutral immediately.
- A nearby charged source can maintain an induced net charge while the object is at ground potential.
Put it to work
Give the physical reason as well as the calculation. The worked solutions are on a separate page.
- Problem 3 · conservation ledger
- Problem 4 · ordered procedure and reasoning
- Problem 16 · capacitance experiment and controlled comparison
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For the teacher
- Have students draw a boundary for object-only and object-plus-Earth systems.
- Ask which step crosses that boundary and which merely changes distribution.
- Use identical spheres only when claiming equal final charge.
Source objectives and scope
- 10.2.A — Describe the behavior of a system using conservation of charge.
Suggested skills are teaching guidance. The course applies all science practices across its objectives.
Science references for this teaching
- College Board AP Physics 2 Course and Exam Description, Unit 10 (PDF pages 50–61) — Official topic order, learning objectives, all essential-knowledge clauses, algebra-based scope boundaries; equations visually inspected in local source pages 50,54,56–61.
- OpenStax University Physics Volume 2, 8.5 Molecular Model of a Dielectric — Independent verification that bound polarization leaves a dielectric net neutral and its induced field opposes the free-charge field. All lesson prose and problems are original.
- Corrected original reading: Charge and Matter — Use the corrected charge and Coulomb-law explanations to compare signed charges and pair forces.
- Corrected original reading: Conductors and Insulators — Use the corrected charge-mobility discussion to explain contact, polarization, and grounding with a system boundary.
- Corrected original reading: The Electric Field — Use the corrected point-source and vector-superposition discussion to practice fields and forces. General quantitative fields within insulators are outside the AP core.
- Corrected original reading: The Electric Potential and Potential Energy — Use the corrected algebraic point-charge energy discussion to connect configuration changes with external and electric work.
- Corrected original reading: Calculating Potentials — Use the corrected point-charge scalar sums to practice potential.
- Corrected original reading: Equipotentials, Field lines, and Gradients — Use the corrected contour maps and algebraic field estimates here; calculus-gradient material is an optional extension beyond the AP core.
- Corrected original reading: Capacitors — Use the corrected parallel-plate geometry discussion to compare C, Q, and voltage.
- Corrected original reading: Stored Energy and Dielectrics — Use the corrected energy and dielectric discussion with an explicit fixed-Q or fixed-voltage constraint.
Glossary and deeper reading · 6 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Electric charge
Electric charge is a conserved property that determines electric interactions. It can be positive or negative and is measured in coulombs; ordinary net charges arise from an imbalance of charged particles. For example, transferring electrons between initially neutral objects leaves one negatively charged and the other positively charged.
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Electric polarization
Electric polarization is a separation or rearrangement of positive and negative charge within otherwise neutral matter. It can create induced dipoles without requiring a net charge to cross the object’s boundary. For example, a nearby charged rod can slightly shift bound charges in an insulating object and produce attraction.
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Elementary charge
The elementary charge is the magnitude of the charge carried by a proton or electron, approximately 1.60 × 10⁻¹⁹ coulomb. A proton carries positive elementary charge and an electron carries negative elementary charge. For example, removing one electron from a neutral atom leaves it with a net charge of one positive elementary charge.
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Electrical insulator
An electrical insulator strongly restricts the movement of charge carriers through its bulk. Its bound charges can still rearrange slightly to polarize in an applied electric field. For example, a plastic rod can retain localized excess charge even though it does not conduct current like a metal wire.
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Electrical conductor
An electrical conductor contains charge carriers that can move through the material. In electrostatic equilibrium, mobile charges redistribute until the electric field within the conducting material is zero. For example, excess charge on an isolated metal object resides on its surface after the charges settle.
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Grounding
Grounding connects a conductor to a large charge reservoir that can receive or supply charge. The connection lets charge redistribute to satisfy the potential conditions; it does not always make an object neutral in the presence of nearby sources. For example, a grounded sphere near a charged rod can acquire net charge from the reservoir.