---
title: "AP Physics C: E&M Unit 9 Review: Electric Potential"
description: "AP Physics C: E&M Unit 9 covers Electric Potential Energy and Electric Potential. Study guides, practice questions, and key terms for every topic."
canonical: "https://fiveable.me/ap-physics-c-e-m/unit-9"
type: "unit"
subject: "AP Physics C: E&M"
unit: "Unit 9 – Electric Potential"
---

# AP Physics C: E&M Unit 9 Review: Electric Potential

## Overview

Unit 9 covers three tightly linked ideas: the potential energy stored in charge configurations (U_E = kq1q2/r), the scalar electric potential at a point in space (V = kq/r and its integral form), and how potential differences drive energy exchange when charges move (delta U_E = q delta V). The unit rewards careful attention to signs and to the distinction between the scalar potential and the vector electric field.

## AP CED Alignment

This unit hub is organized around AP Course and Exam Description topics, skills, and exam task types when they are available in the source data.
- Topic 9.1: Electric Potential Energy
- Topic 9.2: Electric Potential
- Topic 9.3: Conservation of Electric Energy
- Topic 9.2: Electric Potential and Its Relationship to the Electric Field
- Practice 3: Scientific Questioning and Argumentation
- Practice 2: Mathematical Routines
- FRQ 4 – Qualitative/Quantitative Translation
- FRQ 2 – Translation Between Representations
- FRQ 1 – Mathematical Routines

## Topics

- [Topic 9.1: Electric Potential Energy](/ap-physics-c-e-m/unit-9/1-electric-potential-energy/study-guide/InqS68GlgFXEOpRi): Defines U_E = kq1q2/r for two point charges, establishes the zero-reference at infinity, explains the sign convention, and extends to multi-charge systems via pairwise summation.
- [Topic 9.2: Electric Potential](/ap-physics-c-e-m/unit-9/2-electric-potential/study-guide/NRfC3T6m1ZWgp69A): Introduces V as a scalar field (J/C), covers point-charge and continuous-distribution formulas, scalar superposition, the relationship E_x = -dV/dx and delta V = -integral E dot dr, and equipotential maps.
- [Topic 9.3: Conservation of Electric Energy](/ap-physics-c-e-m/unit-9/3-conservation-of-electric-energy/study-guide/UJ3tt1NL0NomtBVo): Applies delta U_E = q delta V and conservation of energy to predict kinetic energy changes when charged particles move through potential differences, including sign-convention analysis and the electron-volt unit.

## Hardest Topics And Analytics

Snapshot: practice snapshot
This snapshot uses Fiveable practice activity to show where students tend to miss questions and which review moves are worth prioritizing first.
- **57% average MCQ accuracy** (Across 760 multiple-choice practice attempts for this unit.)
- **760 MCQ attempts** (Practice activity included in this snapshot.)
- **38% average FRQ score** (Across 4 scored free-response attempts for this unit.)
- **Topic 9.1: Electric Potential Energy**: 42% MCQ miss rate across 376 attempts. Review Electric Potential Energy with attention to how the concept appears in AP-style source and evidence questions.
- **Topic 9.3: Conservation of Electric Energy**: 36% MCQ miss rate across 241 attempts. Review Conservation of Electric Energy with attention to how the concept appears in AP-style source and evidence questions.

## Review Notes

### Topic 9.1: Electric Potential Energy

The electric potential energy of two point charges equals the work an external agent must do to assemble the configuration from infinite separation. The reference point is U_E = 0 at r = infinity. For any pair, U_E = kq1q2/r. For a system of three charges, add the three unique pairwise terms: U_12 + U_13 + U_23. The sign of U_E tells you whether the configuration is bound (negative, opposite charges) or requires stored energy to maintain (positive, like charges).

- **U_E = kq1q2/r**: Potential energy of two point charges; k = 1/(4pi*epsilon_0) = 9x10^9 N*m^2/C^2; r is the separation distance.
- **Sign of U_E**: Positive when q1*q2 > 0 (like charges repel, energy stored); negative when q1*q2 < 0 (opposite charges attract, energy released on assembly).
- **Pairwise superposition**: Total U_E for N charges = sum of U_E for every unique pair; for three charges that is three terms.
- **Work-energy connection**: Work done by the electric field on a charge equals -delta U_E; work done by an external force to move a charge quasi-statically equals +delta U_E.

**Checkpoint:** A +2 micro-C charge and a -3 micro-C charge are 0.10 m apart. Is U_E positive or negative, and what does that sign mean physically?

Charge product q1*q2 | Sign of U_E | Physical meaning
--- | --- | ---
Positive (like charges) | Positive | Energy must be added to hold them at distance r
Negative (opposite charges) | Negative | System releases energy as charges approach from infinity

### Topic 9.2: Electric Potential and Its Relationship to the Electric Field

Electric potential V is a scalar field: it assigns a single number (in volts = J/C) to every point in space. For a point charge, V = kq/r. For multiple point charges, add the individual potentials algebraically (scalar superposition). For a continuous distribution, integrate: V = (1/4pi*epsilon_0) integral dq/r. The potential difference between two points is delta V = -integral_a^b E dot dr. Conversely, the electric field component in any direction is E_x = -dV/dx. Equipotential lines are perpendicular to field lines everywhere; moving along an equipotential requires no work.

- **Scalar superposition**: V_total = sum of kqi/ri for all point charges; no vector addition needed, just algebraic sum with signs.
- **Integral form**: V = (1/4pi*epsilon_0) integral dq/r; used for rings, rods, disks, and other continuous distributions.
- **delta V = -integral E dot dr**: Potential difference found by integrating the dot product of E and the path element; path independence means any path gives the same result.
- **E_x = -dV/dx**: The electric field component in a direction equals the negative rate of change of V in that direction; steeper potential gradient means stronger field.
- **Equipotential lines**: Curves of constant V; always perpendicular to E field vectors; no work is done moving a charge along an equipotential.

**Checkpoint:** A thin ring of charge Q and radius R: write the expression for V at a point on the axis a distance x from the center, and explain why no integration over direction is needed.

Quantity | Type | Superposition rule | Key formula
--- | --- | --- | ---
Electric field E | Vector | Vector sum of components | E = kq/r^2 (direction matters)
Electric potential V | Scalar | Algebraic sum with signs | V = kq/r (no direction)

### Topic 9.3: Conservation of Electric Energy

When a charge q moves between two points with a potential difference delta V, the change in electric potential energy is delta U_E = q delta V. Because the electrostatic force is conservative, the total mechanical energy is conserved when no other forces act: delta K + delta U_E = 0, so delta K = -q delta V. A positive charge moving from high V to low V loses potential energy and gains kinetic energy. A negative charge moving from high V to low V gains potential energy and slows down. The electron-volt (eV) is a convenient energy unit: 1 eV = 1.6x10^-19 J, the energy gained by one elementary charge moving through 1 V.

- **delta U_E = q delta V**: Core equation for this topic; delta V = V_final - V_initial; sign of q and sign of delta V both matter.
- **delta K = -delta U_E**: Conservation of energy with no non-conservative forces; kinetic energy gained equals potential energy lost.
- **Electron-volt (eV)**: Energy unit equal to 1.6x10^-19 J; useful when an elementary charge moves through a potential difference of 1 V.
- **Path independence**: The work done by the electrostatic force depends only on the endpoints, not the path; this is what makes delta U_E = q delta V universally applicable.

**Checkpoint:** An electron (q = -1.6x10^-19 C) is released from rest near a negative plate and moves toward a positive plate where the potential is 50 V higher. Does the electron speed up or slow down? Find its final kinetic energy.

Charge sign | Moves toward higher V | delta U_E | delta K
--- | --- | --- | ---
Positive (+q) | Yes | Positive (increases) | Negative (slows down)
Positive (+q) | No (lower V) | Negative (decreases) | Positive (speeds up)
Negative (-q) | Yes | Negative (decreases) | Positive (speeds up)
Negative (-q) | No (lower V) | Positive (increases) | Negative (slows down)

## Study Guides

- [9.1 Electric Potential Energy](/ap-physics-c-e-m/unit-9/1-electric-potential-energy/study-guide/InqS68GlgFXEOpRi)
- [9.2 Electric Potential](/ap-physics-c-e-m/unit-9/2-electric-potential/study-guide/NRfC3T6m1ZWgp69A)
- [9.3 Conservation of Electric Energy](/ap-physics-c-e-m/unit-9/3-conservation-of-electric-energy/study-guide/UJ3tt1NL0NomtBVo)

## Practice Preview

### Multiple-choice practice

- **AP-style practice question**: Practice 3: Scientific Questioning and Argumentation | A student wants to determine the dielectric constant $$\kappa$$ of a plastic slab. The student charges an isolated parallel-plate capacitor to potential $$V_0$$ and then disconnects the battery. Which procedure yields $$\kappa$$?
- **AP-style practice question**: Practice 2: Mathematical Routines | The electric potential along the x-axis is given by the function $$V(x) = ax^2 - b$$, where $$a$$ and $$b$$ are positive constants. Which of the following correctly compares the magnitude of the electric field at $$x = d$$ to the magnitude of the electric field at $$x = 2d$$?
- **AP-style practice question**: Practice 2: Mathematical Routines | A thin ring of radius $$R$$ carries a uniformly distributed positive charge $$Q$$. Compare the electric field magnitude $$E$$ and electric potential $$V$$ at the center of the ring to their values at a point on the axis at distance $$x = R$$. (Assume $$V = 0$$ at infinity).
- **AP-style practice question**: Practice 2: Mathematical Routines | The electric potential in a region is given by $$V(x, y) = Cxy$$, where $$C$$ is a positive constant. Compare the magnitude of the electric field at point $$P_1(L, 0)$$ to the magnitude of the electric field at point $$P_2(L, L)$$.
- **AP-style practice question**: Practice 2: Mathematical Routines | In a region of space, equipotential lines are spaced $$1.0$$ cm apart. In Region A, the potential difference between adjacent lines is $$5$$ V. In Region B, the potential difference between adjacent lines is $$10$$ V. Compare the magnitude of the electric field $$E_A$$ in Region A to the magnitude $$E_B$$ in Region B.
- **AP-style practice question**: Practice 2: Mathematical Routines | Two large, parallel conducting plates are separated by a distance $$d$$ and maintained at a potential difference $$\Delta V$$. If the distance is increased to $$2d$$ while the potential difference is maintained at $$\Delta V$$, how does the magnitude of the electric field $$E$$ between the plates change?

### FRQ practice

- **Electric potential and field from opposite charges**: FRQ 4 – Qualitative/Quantitative Translation | Electric potential and field from opposite charges
- **Electric potential and field from fixed point charges**: FRQ 2 – Translation Between Representations | Electric potential and field from fixed point charges
- **Electric potential energy and charged particle motion**: FRQ 1 – Mathematical Routines | Electric potential energy and charged particle motion

## Key Terms

- **ΔU_{E}=q ΔV**: The change in electric potential energy of a charged object equals its charge times the potential difference between the two locations; both the sign of q and the sign of delta V determine whether energy increases or decreases.
- **scalar field**: A field that assigns a single scalar value to every point in space; electric potential V is a scalar field, which is why contributions from multiple charges are added algebraically rather than as vectors.
- **superposition principle**: For electric potential, the total V at a point equals the algebraic sum of kqi/ri from each charge; no vector components are needed because V is a scalar.
- **equipotential line**: A curve along which V is constant; the electric field is always perpendicular to equipotential lines, and no work is done moving a charge along one.
- **line integral**: Used in delta V = -integral_a^b E dot dr to find the potential difference between two points by integrating the electric field along any path connecting them; path independence means the result is the same for all paths.
- **Potential from continuous charge distribution**: V = (1/4pi*epsilon_0) integral dq/r; each infinitesimal charge element dq contributes kq/r to the total potential, and the contributions are summed by integration.
- **integration**: The calculus technique used to sum infinitesimal dq contributions when finding V for a ring, rod, disk, or other continuous charge distribution.
- **dot product**: In the relation delta V = -integral E dot dr, the dot product selects the component of E along the path direction; only the component of E parallel to displacement contributes to the potential difference.
- **voltage**: The electric potential difference between two points, measured in volts (V = J/C); in Unit 9 it appears as delta V in both the field-integral relation and the energy equation delta U_E = q delta V.

## Common Mistakes

- **Confusing U_E (energy) with V (potential)**: U_E is the energy of a charge configuration in joules; V is energy per unit charge in volts. The relation is U_E = qV only when V is the potential at the location of charge q due to all other charges. Mixing up the two leads to incorrect setup of energy-conservation equations.
- **Getting the sign of delta U_E wrong**: delta U_E = q delta V requires both the sign of q and the sign of delta V = V_f - V_i. A negative charge moving to higher potential has a negative delta U_E (it gains kinetic energy), which is the opposite of what many students expect.
- **Treating V like a vector when superposing**: Electric potential is a scalar. When finding V due to multiple charges, add the individual kqi/ri values algebraically, including their signs. Do not add them as vectors the way you would for electric field components.
- **Forgetting to count all unique pairs in multi-charge systems**: For three charges, there are three unique pairs (1-2, 1-3, 2-3). Students often miss one pair or double-count. Systematically list every pair before summing.
- **Misapplying E_x = -dV/dx direction**: The electric field points in the direction of decreasing potential, not increasing potential. If V increases in the +x direction, E_x is negative (field points in -x). Sketch V vs. x and take the negative slope to avoid sign errors.

## Exam Connections

- **Deriving V from a charge distribution using integration**: Free-response questions in AP Physics C: E&M frequently ask you to set up and evaluate the integral V = (1/4pi*epsilon_0) integral dq/r for a specific geometry such as a ring, arc, or rod. You are expected to identify the correct expression for dq, write r in terms of the geometry, and carry out or simplify the integral. Showing the setup clearly earns method credit even if the algebra is complex.
- **Connecting V and E through derivatives and integrals**: Exam tasks often give you a potential function V(x) and ask for the electric field, or give you E and ask for delta V. You need to apply E_x = -dV/dx in one direction and delta V = -integral E dot dr in the other. Equipotential diagrams may also appear, requiring you to sketch field lines or determine the direction and relative magnitude of E from the spacing of isolines.
- **Energy conservation with sign-convention reasoning**: Multi-part problems commonly combine delta U_E = q delta V with the work-energy theorem to find the speed of a charged particle after it moves through a potential difference. You must handle the sign of q (positive or negative charge) and the sign of delta V correctly to determine whether the particle speeds up or slows down. Justifying your sign reasoning in words is a common written-response expectation.

## Final Review Checklist

- **Unit 9 final review checklist**: Use this list to confirm you can handle every major skill in the unit before exam day.
- **Calculate U_E for charge pairs and systems**: Apply U_E = kq1q2/r with correct signs; sum all unique pairs for three or more charges; identify whether the total energy is positive or negative and explain what that means.
- **Find V for point charges and distributions**: Use V = kq/r for a single point charge; use scalar superposition for multiple charges; set up and evaluate V = (1/4pi*epsilon_0) integral dq/r for a ring, rod, or arc.
- **Move between V and E**: Derive E from V using E_x = -dV/dx; find delta V from a known E field using delta V = -integral E dot dr; sketch or interpret equipotential maps and confirm they are perpendicular to field lines.
- **Apply delta U_E = q delta V with correct signs**: Identify q (including sign), identify delta V = V_f - V_i, compute delta U_E, and use delta K = -delta U_E to find speed changes; handle both positive and negative charges moving in both directions.
- **Use the electron-volt unit**: Convert between eV and joules (1 eV = 1.6x10^-19 J); apply it when an elementary charge moves through a known potential difference.

## Study Plan

- **Step 1: Electric potential energy (Topic 9.1)**: Read the Topic 9.1 guide and practice U_E = kq1q2/r with both like and opposite charge pairs. Then build a three-charge system, list all unique pairs, and compute the total U_E. Confirm you can explain the sign of each term physically.
- **Step 2: Electric potential as a scalar field (Topic 9.2, part 1)**: Work through V = kq/r for single point charges and scalar superposition for two or three charges. Then set up the integral V = (1/4pi*epsilon_0) integral dq/r for a uniformly charged ring on its axis and evaluate it. Compare the effort to the equivalent electric field calculation to see why scalar methods are faster.
- **Step 3: V-to-E relationships and equipotentials (Topic 9.2, part 2)**: Practice deriving E from a given V(x) using E_x = -dV/dx. Then reverse: integrate a known uniform field to find delta V. Sketch an equipotential map for a dipole and verify that field lines cross equipotentials at right angles.
- **Step 4: Conservation of electric energy (Topic 9.3)**: Apply delta U_E = q delta V and delta K = -delta U_E to at least four scenarios: positive charge speeding up, positive charge slowing down, negative charge speeding up, and negative charge slowing down. Use the comparison table in the review notes to check your sign reasoning, then convert one answer to electron-volts.

## More Ways To Review

- [Topic study guides](/ap-physics-c-e-m/unit-9#topics)
- [FRQ practice](/ap-physics-c-e-m/frq-practice)
- [Key terms](/ap-physics-c-e-m/key-terms)

## FAQs

### What topics are covered in AP Physics E&M Unit 9?

AP Physics E&M Unit 9 covers three topics: **9.1 Electric Potential Energy**, **9.2 Electric Potential**, and **9.3 Conservation of Electric Energy**. Together they build from the work done by electric forces to the scalar quantity of electric potential, then tie everything together through energy conservation in charged systems. See [Unit 9](/ap-physics-c-e-m/unit-9) for matched resources.

### How much of the AP Physics E&M exam is Unit 9?

Unit 9 makes up 10-20% of the AP Physics E&M exam, making it one of the more heavily weighted single units. It covers electric potential energy, electric potential, and conservation of electric energy. That range means you can expect several multiple-choice questions and at least one free-response component tied to these concepts.

### What's on the AP Physics E&M Unit 9 progress check (MCQ and FRQ)?

The AP Physics E&M Unit 9 progress check includes both MCQ and FRQ parts drawn from all three unit topics: electric potential energy (9.1), electric potential (9.2), and conservation of electric energy (9.3). MCQ questions typically ask you to calculate or compare potential values and energy changes, while the FRQ part asks you to derive relationships and apply conservation principles to charged-particle scenarios. Check [Unit 9](/ap-physics-c-e-m/unit-9) for practice that mirrors the progress check format.

### How do I practice AP Physics E&M Unit 9 FRQs?

The best way to practice AP Physics E&M Unit 9 FRQs is to work through problems that ask you to derive expressions for electric potential energy and electric potential, then apply conservation of electric energy to find final speeds or positions of charged particles. FRQs from this unit often combine a derivation step with a graphical interpretation or a multi-part scenario involving point charges or uniform fields. Start by writing out your energy conservation equation explicitly before solving, since College Board awards method points. Head to [Unit 9](/ap-physics-c-e-m/unit-9) for FRQ practice sets tied to these topics.

### Where can I find AP Physics E&M Unit 9 practice questions?

You can find AP Physics E&M Unit 9 practice questions, including multiple-choice and practice test sets, at [Unit 9](/ap-physics-c-e-m/unit-9). The page organizes MCQ and FRQ practice by topic, covering electric potential energy, electric potential, and conservation of electric energy. Working through topic-by-topic MCQs first, then full practice test sections, is the most efficient way to build confidence across all three topics.

### How should I study AP Physics E&M Unit 9?

Start with electric potential energy (9.1) and make sure you can calculate work done by electric forces before moving to electric potential (9.2), since potential is just potential energy per unit charge. Once those two are solid, conservation of electric energy (9.3) clicks into place naturally. A concrete plan: sketch field diagrams alongside potential diagrams for the same charge configuration so you see how they relate, then practice writing energy conservation equations from scratch without a formula sheet. Prioritize problems where a charged particle moves between two points, since those appear most often on the exam. Use [Unit 9](/ap-physics-c-e-m/unit-9) to find topic-specific practice after each section.

## Structured Data

```json
{"@context":"https://schema.org","@type":"FAQPage","inLanguage":"en","mainEntity":[{"@type":"Question","@id":"https://fiveable.me/ap-physics-c-e-m/unit-9#what-topics-are-covered-in-ap-physics-e-and-m-unit-9","name":"What topics are covered in AP Physics E&M Unit 9?","acceptedAnswer":{"@type":"Answer","text":"AP Physics E&M Unit 9 covers three topics: **9.1 Electric Potential Energy**, **9.2 Electric Potential**, and **9.3 Conservation of Electric Energy**. Together they build from the work done by electric forces to the scalar quantity of electric potential, then tie everything together through energy conservation in charged systems. See <a href=\"/ap-physics-c-e-m/unit-9\">Unit 9</a> for matched resources."}},{"@type":"Question","@id":"https://fiveable.me/ap-physics-c-e-m/unit-9#how-much-of-the-ap-physics-e-and-m-exam-is-unit-9","name":"How much of the AP Physics E&M exam is Unit 9?","acceptedAnswer":{"@type":"Answer","text":"Unit 9 makes up 10-20% of the AP Physics E&M exam, making it one of the more heavily weighted single units. It covers electric potential energy, electric potential, and conservation of electric energy. That range means you can expect several multiple-choice questions and at least one free-response component tied to these concepts."}},{"@type":"Question","@id":"https://fiveable.me/ap-physics-c-e-m/unit-9#whats-on-the-ap-physics-e-and-m-unit-9-progress-check-mcq-and-frq","name":"What's on the AP Physics E&M Unit 9 progress check (MCQ and FRQ)?","acceptedAnswer":{"@type":"Answer","text":"The AP Physics E&M Unit 9 progress check includes both MCQ and FRQ parts drawn from all three unit topics: electric potential energy (9.1), electric potential (9.2), and conservation of electric energy (9.3). MCQ questions typically ask you to calculate or compare potential values and energy changes, while the FRQ part asks you to derive relationships and apply conservation principles to charged-particle scenarios. Check <a href=\"/ap-physics-c-e-m/unit-9\">Unit 9</a> for practice that mirrors the progress check format."}},{"@type":"Question","@id":"https://fiveable.me/ap-physics-c-e-m/unit-9#how-do-i-practice-ap-physics-e-and-m-unit-9-frqs","name":"How do I practice AP Physics E&M Unit 9 FRQs?","acceptedAnswer":{"@type":"Answer","text":"The best way to practice AP Physics E&M Unit 9 FRQs is to work through problems that ask you to derive expressions for electric potential energy and electric potential, then apply conservation of electric energy to find final speeds or positions of charged particles. FRQs from this unit often combine a derivation step with a graphical interpretation or a multi-part scenario involving point charges or uniform fields. Start by writing out your energy conservation equation explicitly before solving, since College Board awards method points. Head to <a href=\"/ap-physics-c-e-m/unit-9\">Unit 9</a> for FRQ practice sets tied to these topics."}},{"@type":"Question","@id":"https://fiveable.me/ap-physics-c-e-m/unit-9#where-can-i-find-ap-physics-e-and-m-unit-9-practice-questions","name":"Where can I find AP Physics E&M Unit 9 practice questions?","acceptedAnswer":{"@type":"Answer","text":"You can find AP Physics E&M Unit 9 practice questions, including multiple-choice and practice test sets, at <a href=\"/ap-physics-c-e-m/unit-9\">Unit 9</a>. The page organizes MCQ and FRQ practice by topic, covering electric potential energy, electric potential, and conservation of electric energy. Working through topic-by-topic MCQs first, then full practice test sections, is the most efficient way to build confidence across all three topics."}},{"@type":"Question","@id":"https://fiveable.me/ap-physics-c-e-m/unit-9#how-should-i-study-ap-physics-e-and-m-unit-9","name":"How should I study AP Physics E&M Unit 9?","acceptedAnswer":{"@type":"Answer","text":"Start with electric potential energy (9.1) and make sure you can calculate work done by electric forces before moving to electric potential (9.2), since potential is just potential energy per unit charge. Once those two are solid, conservation of electric energy (9.3) clicks into place naturally. A concrete plan: sketch field diagrams alongside potential diagrams for the same charge configuration so you see how they relate, then practice writing energy conservation equations from scratch without a formula sheet. Prioritize problems where a charged particle moves between two points, since those appear most often on the exam. Use <a href=\"/ap-physics-c-e-m/unit-9\">Unit 9</a> to find topic-specific practice after each section."}}]}
```