AP Physics 2 · Unit 10 · Topic 10.2
Tracking Charge During Contact and Induction
Follow electrons through friction, contact, polarization, grounding, and induction without losing sight of charge conservation. The goal is to predict the sign and amount of charge on every object—not merely memorize a list of charging methods.
Learning Goals
- Use charge conservation and quantization to calculate transferred charge or electron count.
- Distinguish conductors, insulators, polarization, contact charging, and induction.
- Track electron motion during friction, conduction, grounding, and two-conductor induction.
- Predict final charge signs from the order in which a ground and an inducing object are removed.
- Interpret an electroscope without assuming that leaf separation alone reveals charge sign.
1. Start with a System Boundary
Charge accounting depends on which objects are inside the chosen system. For an isolated system,
Charge can move from one object to another inside the boundary, but the algebraic total does not change. When Earth is connected by a conducting path, include Earth in the system or explicitly count the charge crossing the boundary.
2. What Actually Moves?
In ordinary solid materials, atomic nuclei remain bound in place while electrons can be transferred or redistributed. An object becomes negative by gaining electrons and positive by losing electrons.
The minus sign connects electron number to charge: gaining \(N_e\) electrons makes \(\Delta Q\) negative. Saying “positive charge moved” may be a useful circuit convention later, but it is not the microscopic story for charging ordinary solids.
3. Conductors and Insulators
| Material model | Response to excess charge | Useful examples |
|---|---|---|
| Conductor | Some electrons move through the material and redistribute until electrostatic equilibrium is reached. | Metals, graphite, salt water, the human body |
| Insulator | Transferred charge tends to remain localized, although molecules can still polarize. | Dry glass, rubber, plastic, ceramic |
These are models, not perfect categories. Moist air or a damp surface creates leakage paths, so static charge often disappears faster on humid days.
4. Electrostatic Equilibrium in a Conductor
After charge motion settles, the electric field inside the conducting material is zero. Otherwise, mobile charges would continue accelerating. Excess net charge resides on the surface and spreads according to geometry and nearby charges.
Important: “field inside the material is zero” does not mean the conductor has no net charge or that the field outside is zero.
5. Charging by Friction: Separate, Do Not Create
Rubbing increases the number of microscopic contacts between unlike materials. Their different electron-binding tendencies can transfer electrons from one surface to the other. If two initially neutral objects form an isolated pair,
The material that loses electrons becomes positive; the material that gains the same electrons becomes negative. Friction does not manufacture charge. It separates charge that was already present in the atoms.
A Small Charge Represents Many Electrons
A plastic bead has charge \(-4.80\,\mathrm{nC}\). How many excess electrons are on it?
Solution. The negative sign identifies excess electrons. Use the magnitude to find their number:
The bead has approximately \(3.00\times10^{10}\) excess electrons.
Track Both Objects
Object A loses \(2.50\times10^{12}\) electrons to initially neutral object B. Find both final charges.
A lost electrons, so \(q_A=+4.01\times10^{-7}\,\mathrm C\). B gained them, so \(q_B=-4.01\times10^{-7}\,\mathrm C\). Their sum remains zero.
6. Charging by Contact, or Conduction
When conductors touch, they form one conducting object temporarily. Electrons move because the initial charge distribution is not at equilibrium. After the connected system reaches a common electric potential, separating the objects traps the new charge on each one.
For two identical, isolated conducting spheres, symmetry gives equal final charges:
Do not apply this equal-sharing shortcut to unequal conductors. Unequal objects reach equal potential, not necessarily equal charge.
Opposite Initial Signs
Identical isolated metal spheres carry \(+8.0\,\mathrm{nC}\) and \(-2.0\,\mathrm{nC}\). They touch, reach equilibrium, and separate.
Each sphere ends at \(+3.0\,\mathrm{nC}\). Electrons moved from the initially negative sphere toward the more positive sphere.
Recalculate After Every Touch
Identical spheres A, B, and C begin with \(+12\,\mathrm{nC}\), \(0\), and \(0\). A touches B and separates. Then B touches C and separates.
- A and B share \(+12\,\mathrm{nC}\): \(q_A=q_B=+6\,\mathrm{nC}\).
- B and C share B's \(+6\,\mathrm{nC}\): \(q_B=q_C=+3\,\mathrm{nC}\).
Final charges are \(q_A=+6\,\mathrm{nC}\), \(q_B=+3\,\mathrm{nC}\), and \(q_C=+3\,\mathrm{nC}\). Their total is still \(+12\,\mathrm{nC}\).
7. Polarization Is Not Net Charging
A nearby charged object exerts forces on charges inside a neutral object. In a conductor, mobile electrons redistribute across the object. In an insulator, electron clouds shift slightly within atoms or molecules.
The near and far regions acquire opposite imbalances, yet their sum can remain zero. This separation is polarization, not necessarily charge transfer.
8. Why a Charged Object Attracts a Neutral One
Polarization places opposite induced charge closer to the external charge and like induced charge farther away. Because electric force decreases with distance, the nearer attraction is stronger than the farther repulsion. Either a positive or a negative charged object can therefore attract a neutral polarizable object.
9. Grounding: Charge Can Enter or Leave
Grounding connects a conductor to Earth through a conducting path. Earth is so large that it can accept or supply a modest number of electrons without an appreciable change in its electric potential.
- Positive inducer nearby: electrons are attracted from Earth into the conductor.
- Negative inducer nearby: electrons are repelled from the conductor into Earth.
Ground does not always “remove charge” and does not always “add electrons.” The external charge determines the direction of electron flow.
10. One-Conductor Induction: The Reliable Sequence
- Bring a charged inducer near a neutral conductor without touching it. The conductor polarizes.
- While the inducer remains, connect the conductor to ground. Electrons flow in or out.
- Remove the ground connection first. The conductor is now isolated with a nonzero net charge.
- Remove the inducer. The remaining excess charge redistributes over the conductor.
The final conductor charge has the sign opposite the inducer. The inducer never touches the conductor and need not lose any of its own charge.
Which Way Do Electrons Move?
A positive rod approaches a neutral metal sphere. The sphere is grounded, then the ground is removed, and finally the rod is taken away.
Reasoning. The positive rod attracts electrons from Earth into the sphere. Disconnecting the ground traps those extra electrons. After the rod leaves, they spread over the sphere. The sphere finishes negative.
Why Ground Must Leave First
The same positive rod polarizes a grounded sphere, but the rod is removed while the ground wire remains attached.
Reasoning. Once the rod leaves, there is no external attraction holding extra electrons on the sphere. They can flow back through the ground connection. The sphere returns approximately to neutral before it is disconnected.
11. Two-Conductor Induction Without Grounding
Start with two neutral metal spheres touching on insulating supports. Bring a positive rod near sphere A. Electrons move from B toward A, leaving B electron-deficient. While the rod is still present, separate A and B; then remove the rod.
A remains negative and B remains positive. No charge entered or left the isolated two-sphere system, so \(q_A+q_B=0\). The spheres acquire net charges without either sphere touching the charged rod.
12. Contact and Induction Compared
| Process | Required contact | Typical final sign |
|---|---|---|
| Conduction | Charged object touches conductor | Often the same sign as the charging object |
| Grounded induction | No contact with inducer; conductor contacts ground | Opposite the inducer |
| Polarization only | No contact required | Net charge remains unchanged |
13. A Charge-Tracking Table
For every stage, record four items:
- Which objects are in the system?
- Which conducting paths exist now?
- What force acts on mobile electrons?
- Did charge merely redistribute, or cross the boundary?
This table prevents sign guessing and exposes whether a conservation equation includes Earth.
14. Reading an Electroscope
A conducting knob, stem, and two leaves form one conductor. Like charge on the two leaves makes them repel and spread apart. Leaf separation shows that charge is distributed on the electroscope, but it does not reveal the sign by itself.
- Touching the knob with a charged object can transfer charge by conduction.
- Bringing a charged object near the knob can redistribute existing charge by polarization.
- If the electroscope already has a known charge, increased divergence usually indicates the nearby object has the same sign; decreased divergence indicates the opposite sign. Geometry and distance should be controlled.
Use a Known Reference Charge
A positively charged electroscope has separated leaves. A rod approaches the knob without touching, and the leaves move closer together.
Reasoning. A negative rod would repel electrons toward the leaves, partially neutralizing their positive charge and reducing their repulsion. Under the stated ideal conditions, the rod is negative.
15. Evidence and Model Limits
Electroscope motion identifies qualitative redistribution, not an exact charge value. Leakage, humidity, hand position, nearby conductors, and inconsistent distance can change the observation. A quantitative claim needs calibration and repeated trials.
16. Conservation with an Open Boundary
Suppose a sphere begins neutral and finishes with \(-6.4\,\mathrm{nC}\) after grounded induction. The sphere alone is an open system while grounded:
Earth loses \(6.4\,\mathrm{nC}\) of negative charge, so \(\Delta Q_{\text{Earth}}=+6.4\,\mathrm{nC}\). For the combined sphere–Earth system, the changes add to zero.
17. A Fast Problem-Solving Workflow
- Draw every object and mark initial net charge.
- Circle the system used for conservation.
- Mark every temporary conducting connection.
- Track electrons, not vague “charge fluid.”
- Apply symmetry only after checking identical geometry.
- Verify that final algebraic charge equals initial charge plus any boundary transfer.
18. Common Traps
- Claiming that friction creates charge.
- Treating neutral as “contains no charged particles.”
- Confusing polarization with a change in net charge.
- Assuming ground always supplies electrons.
- Removing the inducer before disconnecting ground.
- Giving unequal conductors equal final charge after contact.
- Using leaf separation alone to identify sign.
- Assuming charge spreads freely through an insulator.
1. A neutral object loses \(5.0\times10^{10}\) electrons. What sign and approximate charge does it acquire?
Show reasoning and answer
Losing negative particles leaves the object positive. \(q=N_e e=(5.0\times10^{10})(1.602\times10^{-19})\approx+8.0\times10^{-9}\,\mathrm C=+8.0\,\mathrm{nC}\).
2. Identical metal spheres have charges \(-10\,\mathrm{nC}\) and \(+4\,\mathrm{nC}\). They touch and separate. Find each final charge.
Show reasoning and answer
Total charge is \(-6\,\mathrm{nC}\). Identical spheres share it equally, so each finishes at \(-3\,\mathrm{nC}\).
3. A negative rod is brought near a neutral grounded conductor. Which way do electrons move, and what sign remains if the ground is removed first?
Show reasoning and answer
The negative rod repels electrons from the conductor into Earth. Removing the ground traps an electron deficit, so after the rod leaves the conductor is positive.
4. A charged rod attracts a neutral paper scrap. Does attraction prove the rod and paper have opposite net charges?
Show reasoning and answer
No. The paper can remain net neutral while polarization places opposite induced charge closer to the rod, producing a stronger attraction than the farther repulsion.
5. During induction, why does removing the rod before the ground usually fail to leave a net charge?
Show reasoning and answer
With the ground still connected, removing the rod removes the force that maintained the electron imbalance. Electrons can flow between Earth and the conductor until it returns approximately to neutral.
6. The leaves of an initially neutral electroscope diverge when a rod approaches without contact. Has the electroscope necessarily gained net charge?
Show reasoning and answer
No. The nearby rod can polarize the electroscope, sending like charge to both leaves while the electroscope's total charge remains zero.
Investigation: Separate Transfer from Polarization
Use two strips of transparent tape, small neutral paper pieces, and a low-charge classroom electroscope. First compare attraction and repulsion after peeling matched tape strips. Then approach the electroscope knob without touching, withdraw the object, and repeat with brief contact. Record whether leaf divergence persists after the charged object is removed. Keep approach distance, contact time, and humidity as controlled as possible. Persistent divergence after contact is evidence of transfer; temporary divergence during approach can be explained by polarization.
Safety: use only everyday static-charge sources. Keep charged objects away from outlets, electronics, flammable vapors, and anyone with implanted medical devices.
Official curriculum reference: College Board AP Physics 2 course page. The explanation and worked example are independently written for this study site.