Review AP Physics 2 Unit 10 to build a complete picture of electrostatics, from Coulomb's law and charge conservation through electric fields, potential energy, voltage, and capacitors. This unit carries 15-18% of the exam and connects directly to circuits in Unit 11.
Use the topic guides, key terms, and available practice questions to work through every concept from electric force to conservation of electric energy.
Unit 10 is the foundation of all electricity content in AP Physics 2. It introduces the electric force as a field force that obeys Newton's laws, then builds upward through field maps, potential energy, voltage, and energy storage in capacitors.
Unit 10 covers electric charge and Coulomb's law, conservation and transfer of charge, electric fields and field maps, electric potential energy, electric potential and equipotential lines, parallel-plate capacitors, and conservation of electric energy for moving charges.
Coulomb's law gives the magnitude of the electrostatic force between two point charges: |F| = k|q1 q2|/r^2. The electric field E = F/q describes the force per unit charge at any point in space, and the net field from multiple charges is found by vector superposition.
Electric potential energy for a pair of point charges is U_E = kq1q2/r. Electric potential V = U_E/q is a scalar, so contributions from multiple charges add directly. Potential difference delta V = delta U_E / q connects energy changes to voltage, and equipotential lines are always perpendicular to field vectors.
A parallel-plate capacitor stores charge according to C = Q/delta V, with capacitance set by C = kappa epsilon_0 A/d. Stored energy is U_C = (1/2)Q delta V. When a charge moves through a potential difference, delta U_E = q delta V, and conservation of energy links that change to a change in kinetic energy.
The deepest thread in Unit 10 is that electric force is conservative, meaning you can track every interaction through potential energy and voltage instead of force vectors alone. Coulomb's law, field maps, equipotential lines, capacitor storage, and particle acceleration are all different windows into the same energy bookkeeping. Understanding that connection prepares you for circuits in Unit 11, where voltage and energy transfer drive every calculation.
Introduces charge as a fundamental property, the elementary charge e, the point charge model, Coulomb's law |F| = k|q1 q2|/r^2, electric permittivity, and the comparison of electric and gravitational forces.
Covers conservation of charge, charging by friction, contact, and induction, induced charge separation in neutral objects, and grounding.
Defines the electric field E = F/q, covers vector superposition of fields from multiple charges, field line maps, and the distinct field behavior inside conductors versus insulators in electrostatic equilibrium.
Defines U_E = kq1q2/r for a pair of point charges, explains the sign convention, and extends to multi-charge systems using pairwise summation.
Introduces electric potential V = kq/r as a scalar, scalar superposition, potential difference delta V = delta U_E / q, equipotential lines, and the relationship |E| = |delta V / delta r|.
Covers parallel-plate capacitor geometry, C = Q/delta V, C = kappa epsilon_0 A/d, the effect of dielectrics, the uniform field between plates, and stored energy U_C = (1/2) Q delta V.
Applies conservation of energy to charged particles moving through potential differences using delta U_E = q delta V and delta K = -delta U_E, with attention to sign conventions for positive and negative charges.
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Review Conservation of Electric Energy with attention to how the concept appears in AP-style source and evidence questions.
Review Electric Charge and Electric Force with attention to how the concept appears in AP-style source and evidence questions.
Review Conservation of Electric Charge and the Process of Charging with attention to how the concept appears in AP-style source and evidence questions.
Charge is a fundamental property of matter, quantized in units of the elementary charge e = 1.602 x 10^-19 C. Protons carry +e, electrons carry -e, and neutrons carry no charge. Coulomb's law gives the magnitude of the electrostatic force between two point charges: |F_E| = k|q1 q2|/r^2, where k = 8.99 x 10^9 N m^2/C^2. The force is attractive for opposite signs and repulsive for like signs, and it falls off as 1/r^2. Electric permittivity epsilon_0 appears in the equivalent form |F_E| = |q1 q2| / (4 pi epsilon_0 r^2). For any object with both mass and charge, the gravitational force is almost always negligible compared to the electrostatic force at small scales; gravity dominates at large scales only because macroscopic objects are nearly electrically neutral.
If the distance between two charges doubles, by what factor does the electrostatic force change? (Answer: it decreases by a factor of 4, since force is proportional to 1/r^2.)
| Property | Gravitational Force | Electrostatic Force |
|---|---|---|
| Source | Mass | Electric charge |
| Direction | Always attractive | Attractive or repulsive |
| Law | F = Gm1m2/r^2 | F = k|q1 q2|/r^2 |
| Dominates at | Large (astronomical) scales | Small (atomic/molecular) scales |
The net charge of an isolated system never changes; any change in a system's charge requires a transfer of charge to or from its surroundings. Charging by friction transfers electrons between materials based on their positions in the triboelectric series. Charging by contact (conduction) transfers electrons when objects touch. Charging by induction redistributes charge within a neutral object without direct contact, and grounding allows excess charge to flow to or from Earth, leaving the object with a net charge. Induced charge separation can occur in neutral objects and does not change their net charge.
A neutral metal sphere is brought near a positively charged rod without touching. The near side of the sphere becomes negative. If the sphere is then grounded while the rod is still nearby, what is the sphere's net charge after the ground connection is removed and the rod is taken away? (Answer: the sphere is left with a net negative charge.)
The electric field at a point is defined as E = F_E / q, where q is a small positive test charge that does not disturb the field. Fields point away from positive source charges and toward negative source charges. For a single point charge, E = kq/r^2. The net field from multiple charges is the vector sum of individual fields (superposition). In electrostatic equilibrium, the field inside a solid conductor is zero and the field at the surface is perpendicular to the surface; all excess charge resides on the surface. Inside an insulator, the field can be nonzero. Electric field line maps show direction and relative magnitude: denser lines indicate stronger fields.
Two equal positive charges are placed 0.2 m apart. Where along the line connecting them is the net electric field zero? (Answer: at the midpoint, by symmetry, since the two equal fields point in opposite directions and cancel.)
The electric potential energy of a two-charge system equals the work an external agent must do to bring the charges from infinitely far apart to their current separation: U_E = kq1q2/r. The sign of U_E depends on the product q1q2: positive for like charges (energy stored in repulsion) and negative for opposite charges (energy released in attraction). For a system of more than two charges, sum the potential energy of every unique pair: U_total = sum of k qi qj / r_ij for all i < j. The reference point is U_E = 0 at infinite separation.
Three charges +q, +q, and -q are placed at the corners of an equilateral triangle with side length d. What is the sign of the total electric potential energy of the system? (Hint: identify the three pairs and their signs, then sum.)
Electric potential V is the electric potential energy per unit charge at a point: V = U_E / q. For a point charge, V = kq/r. Because potential is a scalar, contributions from multiple charges add algebraically: V = k sum(qi/ri). Potential difference delta V = delta U_E / q tells how much energy per coulomb changes when a charge moves between two points. The average electric field magnitude between two points is |E| = |delta V / delta r|, so field vectors point from high to low potential. Equipotential lines (isolines) connect points of equal V and are always perpendicular to field vectors. No work is done moving a charge along an equipotential. Conductors in electrostatic equilibrium are equipotential surfaces.
A positive charge moves from a region of high potential to low potential. Does its electric potential energy increase or decrease? Does it speed up or slow down? (Answer: U_E decreases; kinetic energy increases; the charge speeds up.)
| Feature | Electric Field | Electric Potential |
|---|---|---|
| Type | Vector | Scalar |
| Formula (point charge) | E = kq/r^2 | V = kq/r |
| Superposition | Vector sum | Algebraic sum |
| Relationship | Points from high to low V | Decreases in direction of E |
| Equipotentials | Perpendicular to field lines | Lines/surfaces of constant V |
A parallel-plate capacitor consists of two conducting plates that store equal and opposite charge Q separated by a gap d. Capacitance is defined as C = Q / delta V and depends only on geometry and material: C = kappa epsilon_0 A / d, where kappa is the dielectric constant of the material between the plates, A is the plate area, and d is the separation. The uniform electric field between the plates is E = Q / (kappa epsilon_0 A). Inserting a dielectric increases capacitance by reducing the effective field through induced polarization. Energy stored in a capacitor is U_C = (1/2) Q delta V = (1/2) C (delta V)^2 = Q^2 / (2C).
A capacitor is charged to voltage delta V and then disconnected from the battery. If the plate separation is doubled, what happens to the capacitance, the voltage, and the stored energy? (Answer: C halves, delta V doubles since Q is fixed, and U_C doubles.)
When a charged object moves between two points with different electric potentials, its electric potential energy changes by delta U_E = q delta V. Because the electrostatic force is conservative, energy is conserved: any decrease in U_E appears as an increase in kinetic energy, and vice versa. For a charge moving freely in an electric field, delta K = -delta U_E. This is the electric analog of conservation of mechanical energy. Sign conventions matter: a positive charge moving from high to low potential loses potential energy and gains kinetic energy; a negative charge moving from high to low potential gains potential energy and loses kinetic energy.
An electron (charge -e) moves from a point at V = 0 V to a point at V = +100 V. Does it speed up or slow down? (Answer: delta U_E = (-e)(+100) < 0, so U_E decreases and K increases; the electron speeds up.)
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A timed, AP-style test built only from unit 10 questions — multiple choice plus free response, scored with AI feedback. Use the standard format or build your own.
| Term | Definition |
|---|---|
| conservation of charge | The net charge of an isolated system remains constant; any change in a system's charge requires a transfer of charge to or from its surroundings. |
| induced charge separation | The redistribution of charges within a system caused by the electrostatic force from a nearby charged object, resulting in polarization without changing the system's net charge. |
| superposition principle | The net electric field or force at a point due to multiple charges is the vector sum of the individual contributions; electric potential adds as a scalar sum. |
| electrostatic equilibrium | A state in which excess charge on a conductor is stationary, the electric field inside the conductor is zero, and all excess charge resides on the outer surface. |
| surface charge distribution on conductors | In electrostatic equilibrium, all excess charge on a solid conductor resides on the outer surface, with none in the interior. |
| equipotential lines | Lines connecting points of equal electric potential; always perpendicular to electric field vectors; no work is done moving a charge along them. |
| equipotential surface | A surface on which every point is at the same electric potential; conductors in electrostatic equilibrium are equipotential surfaces. |
| charge-voltage relationship | C = Q / delta V; defines capacitance as the ratio of stored charge to the potential difference across the capacitor plates. |
| work-energy theorem | In electrostatics, the net work done by the electric force on a charge equals its change in kinetic energy; combined with delta U_E = q delta V, this gives delta K = -delta U_E. |
| Work (W) | Energy transferred by a force; the work done by the electric force on a charge moving through a potential difference is W = q delta V = -delta U_E. |
| Electroscope | A device that detects electric charge; its leaves spread apart when charged and return together when charge is removed or neutralized. |
Electric potential V is a scalar. When finding the total potential from multiple charges, add the values algebraically (with signs), not as vectors. Only electric field and electric force require vector addition.
V = U_E / q is the energy per unit charge at a point in space; it does not depend on a test charge. U_E = qV is the actual energy of a specific charge q at that location. Mixing up the two leads to errors in both calculation and reasoning.
In delta U_E = q delta V, the sign of q matters. A negative charge moving from low to high potential has a negative delta U_E, meaning it gains kinetic energy. Always substitute the signed value of q, not just its magnitude.
The field inside a conductor is zero only in electrostatic equilibrium. Inside an insulator, the field can be nonzero because charge is distributed throughout the volume, not just on the surface.
Coulomb's law in the form F = kq1q2/r^2 applies to point charges or spherically symmetric distributions. For other geometries, use field and potential reasoning rather than direct Coulomb's law calculations.
AP Physics 2 free-response questions frequently ask you to move between field vector maps, equipotential maps, force diagrams, and energy bar charts for the same physical situation. Practice reading a field map and constructing the corresponding equipotential diagram, or using delta U_E = q delta V to fill in an energy bar chart for a charge moving between two labeled equipotentials.
Multiple-choice and free-response items often change one variable in a capacitor or charge configuration and ask you to predict the effect on other quantities. Be ready to reason through how doubling plate separation, inserting a dielectric, or changing the sign of a charge affects C, Q, delta V, E, U_C, and the force on a nearby charge, using the relevant equations as reasoning tools rather than just calculation shortcuts.
A common task type presents a charged particle moving between two points of known potential and asks for its final speed or kinetic energy change. The key skill is correctly applying delta U_E = q delta V with the signed charge value, then using delta K = -delta U_E. Watch for negative charges, which behave opposite to positive charges when moving through the same potential difference.
Use this list to confirm you can handle every major skill in Unit 10 before exam day.
Calculate the magnitude and direction of the electrostatic force between two or more point charges using |F| = k|q1 q2|/r^2, and use vector superposition to find the net force on a charge.
Describe what happens to charge distribution during friction, contact, and induction, and verify that total charge is conserved in each process.
Sketch field vectors and field lines for point charges, dipoles, and parallel plates; identify regions of stronger and weaker fields from line density; state the field inside a conductor in equilibrium.
Use V = k sum(qi/ri) to find potential at a point, U_E = kq1q2/r for a pair, and the pairwise sum for multi-charge systems; correctly apply sign conventions.
Identify that equipotential lines are perpendicular to field vectors, extract the average field magnitude from |E| = |delta V / delta r|, and explain why no work is done along an equipotential.
Apply C = Q/delta V and C = kappa epsilon_0 A/d to predict how changing plate area, separation, or dielectric affects capacitance, voltage, and stored energy.
Use delta U_E = q delta V and delta K = -delta U_E to find the speed or kinetic energy of a charged particle after moving through a potential difference, paying attention to the sign of q.
Read the topic guides for 10.1 and 10.2. Practice applying Coulomb's law to two- and three-charge configurations, paying attention to direction. Then work through examples of charging by friction, contact, and induction, verifying charge conservation in each case. Use the electroscope as a concrete model for detecting charge redistribution.
Read the topic guide for 10.3. Practice sketching field vector maps and field line diagrams for single charges, dipoles, and parallel plates. Confirm you can apply vector superposition to find the net field at a point, and state the field rules for conductors and insulators in equilibrium.
Read the topic guides for 10.4 and 10.5. Work through pairwise U_E calculations for two- and three-charge systems, then practice scalar superposition for V. Draw equipotential maps from field maps and extract average field magnitudes using |E| = |delta V / delta r|. Focus on the sign conventions for both U_E and V.
Read the topic guide for 10.6. Practice using C = Q/delta V and C = kappa epsilon_0 A/d to predict how changing plate area, gap, or dielectric affects C, Q, delta V, and stored energy. Work through at least one problem where the capacitor is disconnected from a battery before a change is made.
Read the topic guide for 10.7. Practice delta U_E = q delta V and delta K = -delta U_E for both positive and negative charges moving through potential differences. Then use the available practice questions to work across all seven topics, and use the AP score calculator to estimate your estimated score range.
Open the individual guides for Unit 10 when you want a closer review of one topic.
Use AP-style practice after you review the notes so you can check what you understand.
Practice free-response reasoning and compare your answer with scoring guidance.
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get printablesAP Physics 2 Unit 10 covers 7 topics: Electric Charge and Electric Force, Conservation of Electric Charge and the Process of Charging, Electric Fields, Electric Potential Energy, Electric Potential, Capacitors, and Conservation of Electric Energy. Together they build from basic charge interactions up through energy storage in electric fields. See the full topic breakdown at AP Physics 2 Unit 10.
AP Physics 2 Unit 10 makes up 15-18% of the AP exam, making it one of the heavier-weighted units. It covers electric charge, electric force, electric fields, electric potential, capacitors, and conservation of electric energy, so strong performance here has a real impact on your overall score.
The AP Physics 2 Unit 10 progress check includes both MCQ and FRQ parts drawn from all 7 unit topics. The MCQ section tests concepts like electric charge, electric force, electric fields, and electric potential. The FRQ part asks you to apply those ideas quantitatively, often involving capacitors or conservation of electric energy. Practice with matched questions at AP Physics 2 Unit 10.
AP Physics 2 Unit 10 FRQs most often pull from electric potential, electric fields, and capacitors. Questions typically ask you to derive or calculate quantities, draw or interpret field diagrams, and explain energy relationships using conservation of electric energy. To practice, work through problems that require you to connect multiple topics, like linking electric potential energy to capacitor charge storage, then check your reasoning step by step. Find practice FRQs at AP Physics 2 Unit 10.
For AP Physics 2 Unit 10 practice questions, including multiple-choice and practice test sets, head to AP Physics 2 Unit 10. You'll find MCQs covering electric charge, electric force, electric fields, electric potential, and capacitors, plus full practice test questions organized by topic so you can target weak spots.
Start with electric charge and electric force so Newton's laws feel familiar in an electrostatics context, then build toward electric potential and capacitors. Sketch field diagrams for every scenario you encounter. Practice moving between force, field, potential energy, and electric potential, since AP Physics 2 Unit 10 FRQs often require all four in one problem. After each topic, do a short set of MCQs to catch gaps early, then revisit conservation of electric energy last since it ties everything together. Organize your review at AP Physics 2 Unit 10.