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.
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.
| 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.
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.
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.
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.
| 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).
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.
Try AP-style multiple-choice questions and written prompts after you review the notes.
A uniformly charged solid insulating cylinder and a solid conducting cylinder of the same radius R and length carry equal total positive charges. The figure shows cross-sectional views of both cylinders with representative electric field vectors drawn at several interior points.
Two identical neutral metal spheres, P and Q, rest on insulating stands and are in contact. A negatively charged rod is brought near sphere P, as shown. While the rod remains in place, the spheres are separated. The rod is then removed.
2. Two large, parallel conducting plates of area are separated by a distance , as shown in Figure 1. The plates are initially uncharged and are connected to a battery that maintains a potential difference of with the top plate at higher potential. The region between the plates is initially air, which can be treated as vacuum with permittivity . A small insulating sphere of mass carrying charge is released from rest midway between the plates. Take .
Figure 1. Parallel-plate capacitor connected to a 480 V battery with a positively charged insulating sphere released midway between the plates.
Figure dot. Force diagram. Dot represents the center of mass of the charged insulating sphere just after release.
On the dot shown in Figure dot, representing the charged sphere just after it is released, draw and label the forces that are exerted on the sphere. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot.
Derive an expression for the magnitude of the electric field between the plates in terms of and . Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Then use your result to derive an expression for the magnitude of the net force on the sphere in terms of , , , , and .
Figure 2. Axes for electric potential V as a function of vertical position y between the plates (y=0 at bottom plate, y=d at top plate).
On the axes provided in Figure 2, sketch the electric potential between the plates as a function of vertical position , where at the bottom plate and at the top plate. Clearly indicate on your sketch the values and , and draw an arrow on your sketch to indicate the direction of the electric field.
Indicate whether each of the following quantities increases, decreases, or remains the same when the dielectric is inserted while the battery stays connected. A dielectric slab of thickness (equal to the plate separation) and relative permittivity is inserted to completely fill the region between the plates while the battery remains connected and maintains . The sphere is again placed midway between the plates and released from rest.
Given values: , , , , , , , .
Briefly justify each answer. Your justification must reference conservation of charge and/or the relationship between , , capacitance, and energy. Then calculate the new energy stored in the capacitor after the dielectric is inserted.
3. In Experiment 1, a student is given a parallel-plate capacitor with square conducting plates. The plates can be separated by an adjustable distance d. The region between the plates can be either air or completely filled with a slab of dielectric material. The student is asked to determine the permittivity of the dielectric material and relate the results to electric field and electric potential in the capacitor.
Describe a procedure for collecting data that would allow the student to determine the permittivity of the dielectric material. In your description, include the measurements to be made. Include any steps necessary to reduce experimental uncertainty.
Describe how the collected data could be analyzed to determine . Include references to appropriate equations and to relationships between measured and known quantities.
Figure 1. Parallel-plate capacitor circuit for measuring charge q and potential difference ΔV with adjustable plate separation d and optional dielectric slab filling the gap.
Figure 2. Blank graphing grid for a straight-line plot used to determine capacitance C from measurements of charge q and potential difference ΔV.
DeltaV (V) | q (x10^-8 C) |
|---|---|
50.0 | 0.46 |
100.0 | 0.91 |
150.0 | 1.36 |
200.0 | 1.82 |
250.0 | 2.27 |
In Experiment 2, the student sets the plate separation to and fully inserts the dielectric so it completely fills the gap between the plates. For each trial, the student charges the capacitor to an absolute potential difference , then disconnects the power supply and uses the electrometer to measure the charge on one plate. Table 1 contains the data collected.
Indicate two quantities, either measured quantities from Table 1 or additional calculated quantities, that could be graphed to produce a straight line that could be used to determine the capacitance of the capacitor.
Vertical axis: Horizontal axis:
On Figure 2, create a graph of the quantities indicated in part C(i) that can be used to determine .
Use Table 2 to record the data points or calculated quantities that you will plot.
Clearly label the axes, including units as appropriate.
Plot the points you recorded in Table 2.
Draw a best-fit line for the data graphed in part C(ii).
Using the best-fit line that you drew in part C(iii), calculate an experimental value for the capacitance . Using the best-fit line from part C(iii), the student determines that the slope of the graph is .
1. Two small conducting spheres, Sphere A and Sphere B, are mounted on insulating stands and can be treated as point charges, as shown in Figure 1. Sphere A has mass and initial charge . Sphere B has mass and initial charge . The centers of the spheres are separated by a distance in air, which may be treated as vacuum with permittivity . The spheres are then touched together and separated again so that the final charges on the two identical conducting spheres are equal. Ignore air breakdown and assume the spheres are small compared with .
Figure 1. Two identical small conducting spheres on insulating stands separated by r = 0.40 m along the +x direction.
Figure 2. Force-direction vectors at Sphere A due to Sphere B (electric and gravitational).
Figure 3. Direction of the net electric field at the midpoint P between two spheres.
Complete the following tasks in Figures 2 and 3.
Indicate the direction of the electric force exerted on Sphere A by Sphere B in Figure 2.
Indicate the direction of the gravitational force exerted on Sphere A by Sphere B in Figure 2.
Indicate the direction of the net electric field at the midpoint point P between the spheres in Figure 3.
After the spheres are touched together and separated, the final charges on the identical conducting spheres are equal.
Derive an expression for the magnitude of the net electric field at the midpoint point P after the spheres are separated, in terms of , , and the initial charges and . Begin your derivation by writing a fundamental physics principle or an equation from the reference information.
Figure 4. Parallel-plate capacitor (A = 0.020 m^2, d = 2.0×10^−3 m) connected to a 120 V battery; dielectric slab inserted to fully fill the plate gap.
Indicate whether the magnitude of the electric field between the plates increases, decreases, or remains the same after the dielectric is inserted. A parallel-plate capacitor has plate area and plate separation , as illustrated in Figure 4. The capacitor is connected to a battery that maintains a constant potential difference . The capacitor is initially filled with vacuum (permittivity ). A dielectric slab with dielectric constant is then inserted fully between the plates while the capacitor remains connected to the battery.
Increases
Decreases
Remains the same
Justify your answer.
| 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.
Open the individual guides for Unit 10 when you want a closer review of one topic.
browse guidesUse AP-style practice after you review the notes so you can check what you understand.
start practicePractice free-response reasoning and compare your answer with scoring guidance.
practice FRQsUse unit cheatsheets for a quick visual review after you work through the notes.
open cheatsheetsEstimate your broader AP score goal after you review the course and exam format.
open calculatorAP 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.