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If you’re working on AP Physics 2 Unit 10 Progress Check FRQ 1, this guide helps you master electric force, electric field, and electric potential -key Unit 10 topics.
You’ll learn the FRQ format, important formulas, derivation methods, force diagrams, scoring criteria, common mistakes, and see original practice questions with model answers aligned to College Board standards.
Official AP Classroom Progress Check questions are secure and not publicly released, so this guide uses original practice material to prepare you with confidence.
AP Physics 2: Algebra-Based is a college-level course covering fluids, thermodynamics, electricity, magnetism, optics, and modern physics. Unit 10 – Electric Force, Field, and Potential introduces electrostatics and is one of the most heavily tested units on the exam.
| Unit title | Unit 10: Electric Force, Field, and Potential |
| AP exam weight | 15–18% of the total AP Physics 2 exam score (one of the highest) |
| Progress Check FRQs | 4 free-response questions total; FRQ 1 is typically the highest-stakes multi-part question |
| Progress Check MCQs | ~24 multiple-choice questions covering all Unit 10 topics |
| Science practices tested | Mathematical Routines, Translation Between Representations, Experimental Design and Analysis, Qualitative/Quantitative Translation |
| Key CED topics | 10.1 Electric Charge and Force; 10.2 Electric Field; 10.3 Electric Potential; 10.4 Electric Potential Energy; 10.5 Capacitors |
| Prerequisite concepts | Vector addition, work-energy theorem, gravitational field analogy (from earlier physics) |
| Calculator use on FRQ | Calculator is permitted on most FRQ components; derivations require symbolic manipulation |
| Resource Type | Description | Access |
| Unit 10 Progress Check FRQ 1 AP Physics 2 Guide | Complete guide covering electric force, electric field, electric potential, formulas, and scoring tips | Download |
| AP Physics 2 Unit 10 Formula Sheet | One-page formula sheet for Coulomb’s Law, electric field, electric potential, and electric potential energy | Download |
| Electric Force Practice Questions | Practice questions on Coulomb’s Law, charge interaction, force direction, and magnitude comparison | Download |
| Electric Field Derivation Practice | Step-by-step practice for electric field magnitude, direction, components, and vector superposition | Download |
| Electric Potential Practice Set | Questions on scalar potential, potential due to multiple charges, and algebraic superposition | Download |
| Force Diagram Worksheet | Practice sheet for drawing and labeling forces on test charges near charged spheres | Download |
| Unit 10 FRQ Model Answers | Original FRQ-style questions with detailed model answers and scoring breakdowns | Download |
| AP Physics 2 Unit 10 Mock FRQ | Timed long-response practice based on Unit 10 Progress Check difficulty and format | Download |
| Common Mistakes Checklist | Quick checklist covering sign errors, vector mistakes, missing work, and incorrect force diagrams | Download |
Unit 10 appears frequently in AP Physics 2: Algebra-Based FRQs. Electric field and potential questions showed up on many recent exams. Since force, field, and potential are closely linked, weakness in one concept can lower performance across the whole FRQ.
The Unit 10 Progress Check FRQ 1 is a multi-part, long free-response question. Based on College Board’s official AP Classroom documentation for Unit 10, here is the exact structure:
| FRQ type | Long free-response question (highest point value in the Progress Check) |
| Typical point value | 10–12 points across 3–4 labeled sub-parts |
| Time suggested | ~20 minutes (similar to AP exam long FRQ allocation) |
| Format | Stimulus-based: a figure or diagram of charged objects is provided; sub-parts build on the same scenario |
| Typical scenario | Two or more charged spheres or point charges at fixed positions near a reference point |
| Sub-parts typically cover | (a) Derivation of electric potential at a point; (b) Derivation of electric field magnitude and direction; (c) Force diagram for a test charge; (d) Work or energy analysis |
| Calculator permitted? | Yes – but derivations must be symbolic; numerical answers require supporting work |
| Notation requirement | Physics notation required: vector notation for E and F, scalar notation for V; must show equation, substitution, and result |
Download AP Physics 2 Study Material
A common Unit 10 FRQ 1 setup uses two fixed charged spheres placed near Point P. Charges may be positive, negative, or mixed.
You are usually asked to:
College Board Unit 10 Progress Check questions are secure and not publicly released. This guide uses original practice questions with similar format, content, and difficulty to help you prepare confidently for FRQ 1.
To answer Unit 10 FRQ 1 with full credit, you need mastery of four interconnected physical concepts. Each concept appears in one or more sub-parts, and they are linked – a misunderstanding of one propagates through all connected sub-parts.
| Concept | What It Describes | FRQ Sub-Part Where It Appears | Key Equation |
| Electric Charge | The fundamental property causing electromagnetic interactions; conserved, quantized; comes in + and − | Setup and all sub-parts | q = ne (charge quantization); F_E = k|q₁||q₂|/r² |
| Electric Force | The Coulomb force between two charges; attractive for opposite, repulsive for same sign; follows inverse square law | Force diagrams; net force calculations | F_E = k|q₁q₂|/r² (Coulomb’s Law) |
| Electric Field | Force per unit positive test charge; vector quantity; points away from positive, toward negative | Magnitude derivation; direction drawing | E = F_E/q₀ = kq/r² (point charge) |
| Electric Potential | Electric potential energy per unit charge; scalar quantity; due to point charge V = kq/r | Potential derivation; potential energy calculations | V = kq/r (point charge); V_total = Σ kqᵢ/rᵢ |
| Electric Potential Energy | Energy stored in a charge configuration; work done against electric force; connects to kinetic energy via conservation | Work-energy calculations; energy change analysis | U_E = qV = kq₁q₂/r |
| Relationship E and V | Electric field is the negative gradient of potential; points from high to low potential; magnitude |E| = −ΔV/Δd | Justification questions; graph interpretation | |E| = −dV/dx (1D); E points from high to low V |
Download AP Physics 2 Formula Sheet
Coulomb’s Law is the starting point for almost every Unit 10 FRQ calculation. You must be able to apply it correctly — with sign conventions, vector directions, and units — in multi-charge configurations.
F_E = k|q₁||q₂| / r²
Where: k = Coulomb’s constant = 8.99 × 10⁹ N·m²/C² (often given as 9 × 10⁹ for AP calculations)
q₁, q₂ = magnitudes of the two charges (in Coulombs)
r = distance between the centers of the charges (in meters)
The force is directed along the line connecting the two charges: attractive if opposite signs, repulsive if same sign.
| Question Type | What to Write | Points Typically Awarded For |
| Find the magnitude of force between two charges | Write F_E = k|q₁||q₂|/r²; substitute values; state result with units (Newtons) | 1 pt: correct equation; 1 pt: correct substitution; 1 pt: correct answer with units |
| Derive expression for force in terms of variables | Write symbolic equation; show substitution of variables; simplify if requested | 1–2 pts: correct symbolic derivation; 0 pts if numerical only when symbolic required |
| Find net force on a charge due to multiple charges | Apply Coulomb’s Law for each pair; use vector addition; state direction explicitly | 1 pt per correct force calculation; 1 pt for correct vector sum |
| Determine direction of force using principles | State whether same-sign (repulsive) or opposite-sign (attractive); draw vector in correct direction | 1 pt for correct direction; 0 pts for direction without justification |
Sphere A has charge +q at distance d above Point P.
Sphere B has charge +2q at distance 2d right of Point P.
A positive test charge q₀ is placed at Point P.
Electric field is one of the most tested ideas in AP Physics 2 Unit 10 FRQ 1. It must be treated as a vector, so both magnitude and direction matter.
Key Formula:
E = kq / r²
Direction Rules:
| Step | What to Do |
| 1 | Find electric field from each charge using E = kq / r² |
| 2 | Determine direction of each field |
| 3 | Break fields into x- and y-components |
| 4 | Add components separately |
| 5 | Find net field using E_net = √(E_x² + E_y²) |
| Step | Calculation / Result |
| Sphere A field | E_A = kq / d², downward |
| Sphere B field | E_B = k(2q) / (2d)² = kq / 2d², leftward |
| Component setup | E_A is vertical, E_B is horizontal |
| Net field | E_net = √[(kq/d²)² + (kq/2d²)²] |
| Final answer | E_net = kq√5 / 2d² |
Electric potential is a key Unit 10 FRQ 1 topic. Unlike electric field, potential is a scalar, so it has no direction and is easier to combine for multiple charges.
Total Potential:
V_total = Σ(kq / r)
Drawing correct, labeled force diagrams is one of the most consistently tested skills on Unit 10 FRQ 1 – and one of the most commonly done incorrectly. College Board’s rubric for force diagrams has very specific requirements.
| Requirement | What It Means | Common Error |
| Arrows must start at the dot | The dot in the figure represents the charge. Arrows must begin at the dot, not near it or above it. | Drawing arrows that start near but not on the dot – loses the ‘correctly drawn’ point |
| Arrows must point away from the dot | Each force is represented by an arrow starting on the dot and pointing in the direction of the force. | Drawing arrows that start away from the dot – loses the point |
| Label each arrow | Label each force distinctly: F_A for force from Sphere A, F_B for force from Sphere B, etc. | Unlabeled arrows – may lose the label point even if direction is correct |
| Relative lengths must reflect relative magnitudes | If F_A > F_B, the arrow for F_A must be noticeably longer than for F_B. | Equal-length arrows when forces are unequal – loses the relative magnitude point |
| No components drawn unless requested | Draw the actual force (not its x or y component) unless asked to show components. | Drawing component vectors instead of the actual force vectors – loses the point |
| Do not include net force unless asked | Draw individual forces only. The net force arrow is separate and only drawn if explicitly requested. | Adding a net force arrow when not requested – may indicate a misunderstanding |
The AP Physics 2 exam provides a reference sheet with equations and constants. However, knowing which equation to apply, how to set it up for a derivation, and what each variable means is entirely your responsibility. The following tables cover everything tested in FRQ 1.
| Formula | Variables | When to Apply on FRQ 1 |
| F_E = k|q₁||q₂|/r² | k = 8.99×10⁹ N·m²/C²; q₁,q₂ in C; r in m; F_E in N | Force between two point charges; finding force on test charge from each source charge |
| E = F_E/q₀ = kq/r² | E in N/C; q = source charge magnitude in C; r = distance in m | Electric field from a single point charge; checking field direction separately |
| V = kq/r | V in Volts (J/C); q = source charge WITH sign (+/−); r = distance in m | Electric potential from a single point charge – INCLUDE SIGN of q |
| V_total = Σ(kqᵢ/rᵢ) | Sum over all source charges; each qᵢ includes sign | Total electric potential at a point due to multiple charges (scalar sum) |
| U_E = qV = kq₁q₂/r | U_E in Joules; q = charge of particle in the field; V = potential at that point | Electric potential energy of a charge at a potential, or interaction energy of two charges |
| W = qΔV = q(V_i − V_f) | W = work done by electric force; q = charge; ΔV = potential difference | Work done by electric force when a charge moves between two potentials |
| ΔKE = −ΔU_E | Conservation of energy: KE gained = PE lost | Finding final kinetic energy when a charge is released from rest in an electric field |
| |E| = |ΔV/Δd| | E in N/C; ΔV in V; Δd = displacement in m (in direction of E) | Finding field magnitude from potential difference across a distance (uniform field or 1D) |
| Constant | Symbol | Value | Usage |
| Coulomb’s constant | k | 8.99 × 10⁹ N·m²/C² | All Coulomb force and field calculations |
| Elementary charge | e | 1.60 × 10⁻¹⁹ C | When charge is given as multiples of e |
| Electron mass | m_e | 9.11 × 10⁻³¹ kg | Particle motion calculations involving electrons |
| Proton mass | m_p | 1.67 × 10⁻²⁷ kg | Particle motion calculations involving protons |
| Speed of light | c | 3.00 × 10⁸ m/s | Referenced for electromagnetic context but rarely needed in FRQ 1 derivations |
Every point on a College Board AP Physics FRQ rubric follows a predictable pattern. For Unit 10 FRQ 1, here is the point-by-point anatomy of a typical 10–12 point question:
| Sub-Part | Task | Points | What You Must Show |
| (a)(i) – Potential | Derive V at Point P | 3–4 pts | V = kq/r for each charge WITH sign; scalar sum; correct final expression in terms of given variables |
| (a)(ii) – Field | Derive |E| at Point P | 4 pts | E = kq/r² for each charge; vector direction for each; component addition (x and y separately); √(Ex² + Ey²) |
| (b) – Force Diagram | Draw forces on test charge | 3 pts | Correct direction for each force; arrows start and point from the dot; labels (F₁, F₂); correct relative arrow lengths |
| (c) – Paragraph Response | Explain energy/potential change | 3–4 pts | Correct principle cited; correctly applied to scenario; explicit conclusion; coherent paragraph form |
| Notation | Correct physics notation throughout | Up to −1 pt | Missing vector notation on Eor F; missing units on numerical answers; inconsistent signs on potential expressions |
Based on College Board Chief Reader Reports and AP Physics 2 scoring commentary (2019–2025), these are the seven most consistently made errors on Unit 10 FRQ 1:
| Mistake | What Students Do | What Earns Full Credit |
| #1: Treating potential as a vector | Adding V₁ and V₂ as vectors; finding components of V; writing separate x and y components of V | Electric potential is a SCALAR – simply add V₁ + V₂ with appropriate signs: V_total = kq₁/r₁ + kq₂/r₂ |
| #2: Forgetting sign of charge in V = kq/r | Writing V = kQ/r for a charge of −Q (using magnitude only) | Include the sign: V = k(−Q)/r = −kQ/r. Sign in the potential expression is required for full credit. |
| #3: Adding field magnitudes directly | Writing E_total = E₁ + E₂ without vector analysis | Add as vectors using components: E_x = ΣEᵢcos(θᵢ), E_y = ΣEᵢsin(θᵢ), then |E_net| = √(Ex² + Ey²) |
| #4: Wrong electric field direction | Field from a negative charge pointing away from the charge; field from a positive charge pointing toward it | Field points AWAY from positive charges and TOWARD negative charges – at Point P, determine which direction ‘away from +’ or ‘toward −’ points |
| #5: Force diagram arrows not from the dot | Drawing arrows near the dot or starting outside the dot | Every force arrow must start ON the dot and point away from the dot in the direction of the force |
| #6: Missing relative magnitude in force diagram | Drawing F₁ and F₂ as equal-length arrows even when forces are unequal | Calculate relative magnitudes first. If F₂ = 2F₁, draw F₂ arrow noticeably twice as long as F₁. |
| #7: Incomplete paragraph response | Writing correct physics but ending without explicitly answering what was asked | Always end a paragraph response with a direct, explicit conclusion sentence that answers the question: ‘Therefore, the potential energy [increases/decreases] because…’ |
Q: What is Unit 10 Progress Check FRQ 1 about?
A: It tests electric force, electric field, and electric potential. You may derive formulas, draw force diagrams, and analyze charged objects near Point P.
Q: How is electric potential different from electric field?
A: Electric potential is a scalar and values are added directly. Electric field is a vector, so magnitudes and directions must be combined using components.
Q: Why must I show work on FRQ 1?
A: College Board awards points for setup, formulas, reasoning, and steps. Correct answers without work may lose credit.
Q: What does “express in terms of given quantities” mean?
A: Your final answer should use variables given in the problem, such as q, d, r, k, instead of plugging in numbers unless asked.
Q: How important is Unit 10 on the AP Physics 2 exam?
A: Unit 10 is one of the highest-weighted units and commonly appears in FRQs, making it a major scoring opportunity.
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