AP Physics C: Electricity and Magnetism Free Response QuestionsFRQ Archive & Practice (2021 to 2025)

What do AP Physics C: Electricity and Magnetism FRQs test?

Setting up and evaluating the right law from first principles, not recalling a formula.

The free response section is half of the AP Physics C: Electricity and Magnetism score, and it is fundamentally different from the multiple choice section in what it rewards. Where Section I tests recognition of correct setups and answers, Section II requires students to derive expressions step by step: selecting the correct Gaussian surface or Amperian loop, writing the surface or line integral explicitly, applying boundary conditions to the differential equation for an RC or RL circuit, and calculating the rate of change of magnetic flux for Faraday's law. Per the AP Physics C: Electricity and Magnetism Course and Exam Description published by College Board, students who state a numerical answer without showing the integral or derivative setup receive no credit for that part. This is the defining feature of a calculus based physics FRQ: the work is the answer.

How are the three AP Physics C: Electricity and Magnetism FRQs structured?

Three comparable multi part questions, each drawing from a different major unit of the course.

Unlike AP Biology, AP Physics C: Electricity and Magnetism does not have a formal long versus short FRQ distinction. All three Section II questions are roughly equal in depth and point value. Each question is multi part, and the parts follow a consistent pattern: a field or potential derivation using Gauss's law or Biot Savart, a circuit analysis using Kirchhoff's laws or a time constant calculation, a flux or EMF calculation using Faraday's law, and a qualitative justification of sign or direction using Lenz's law or field line reasoning. The three questions together cover the full sweep of the five course units, which means every major topic, electrostatics, capacitors and circuits, magnetic fields, and electromagnetic induction, is tested in Section II.

How are AP Physics C: Electricity and Magnetism FRQs scored?

Analytic point rubrics, awarded part by part, with calculus setup as a required element.

Each of the three FRQs carries a scoring guideline that College Board's trained Readers apply part by part. A point is awarded only when the response meets the exact rubric requirement for that part, so partial credit accumulates independently across parts: answering part (a) correctly and part (b) incorrectly still earns the part (a) points. There is no penalty for an incorrect attempt, so students should write something for every part. The calculus requirement makes AP Physics C: E&M rubrics more demanding than those for algebra based exams: a part that requires integrating a field expression awards the point only to a response that shows the integral setup, the substitution of limits, and the algebraic simplification, not to one that states the correct final formula from memory. The scoring guidelines for each year are on the AP Physics C: Electricity and Magnetism scoring guidelines page.

Worked example: how a real AP Physics C E&M FRQ is scored

Gauss's law question: selecting the Gaussian surface, evaluating the integral, and finding potential.

The following worked example illustrates the rubric mechanics for a standard electrostatics FRQ, the question type that appears most reliably on AP Physics C: E&M and the type most commonly lost to incomplete integral setup. The scenario mirrors the structure of real College Board questions: a conducting spherical shell with a charge, asking for the electric field in three regions, the electric potential as a function of r, and the work done assembling the charge. Each part below pairs the rubric requirement with a response that earns the point and a response that loses it, exactly as scoring guidelines document them.

1. (a) Find the electric field for r less than the inner radius of the shell

   Rubric: Point earned only if the response explicitly states that the Gaussian surface is a sphere of radius r less than the inner radius, writes the surface integral of E dot dA equals Q enclosed over epsilon zero, identifies Q enclosed as zero for a region inside a conductor, and concludes E equals zero. Stating the conclusion without the Gaussian surface setup and the Q enclosed argument earns no credit.

   Earns the point: Choose a spherical Gaussian surface of radius r inside the shell. By Gauss's law, the surface integral of E dot dA equals Q enclosed divided by epsilon zero. No charge is enclosed by this surface (the shell is a conductor and any enclosed region contains no free charge), so Q enclosed equals zero, therefore E equals zero everywhere inside.

   Loses the point: E equals zero inside a conductor. (States the correct conclusion but provides no Gaussian surface selection, no integral statement, and no Q enclosed argument. The rubric requires the derivation, not the result.)

2. (b) Find the electric field for r greater than the outer radius of the shell

   Rubric: Point earned only if the response selects a spherical Gaussian surface of radius r outside the shell, writes the flux integral as E times 4 pi r squared (justifying by symmetry that E is uniform and radial over the sphere), sets it equal to Q total over epsilon zero, and solves to E equals Q over (4 pi epsilon zero r squared). The symmetry justification, that E is constant in magnitude and perpendicular to the surface, must appear before E is factored out.

   Earns the point: By symmetry, the field outside a spherically symmetric charge distribution is radial and constant in magnitude over any concentric spherical surface. Choosing a Gaussian sphere of radius r, the surface integral becomes E times 4 pi r squared. Gauss's law gives E times 4 pi r squared equals Q over epsilon zero, so E equals Q divided by (4 pi epsilon zero r squared), directed radially outward.

   Loses the point: E equals kQ over r squared (states the Coulomb formula directly, omitting the Gaussian surface, the symmetry argument, and the explicit surface integral, so the calculus based rubric does not award the point even though the answer is numerically correct).

3. (c) Find the electric potential at the outer surface of the shell

   Rubric: Point earned only if the response derives V by integrating E from infinity to the outer radius R, sets up the integral explicitly as negative the integral from infinity to R of E dot dr, substitutes the expression from part (b), evaluates to V equals Q over (4 pi epsilon zero R), and states that the potential is constant throughout the conductor so V is the same on the inner surface and everywhere inside the shell.

   Earns the point: The potential at radius R is found by integrating the field from infinity: V equals negative the integral from infinity to R of E dr equals negative the integral from infinity to R of Q over (4 pi epsilon zero r squared) dr. Evaluating gives V equals Q divided by (4 pi epsilon zero R). Because the shell is a conductor, this potential is uniform throughout the conducting material and inside the cavity.

   Loses the point: V equals kQ over R (states the result without setting up or evaluating the integral from infinity, so the calculus requirement is unmet and the rubric point is not awarded).

Across all three parts the pattern is identical: the physics conclusion is often roughly right, but the point is lost because the Gaussian surface selection, the symmetry argument, or the integral evaluation is absent. Chief Reader Reports for AP Physics C: E&M consistently note that students who memorize the formula E equals kQ over r squared and V equals kQ over r earn zero or near zero on electrostatics FRQ parts because the rubrics require the derivation pathway, not just the destination. Practicing against official scoring guidelines, writing every integral and every boundary condition explicitly, is the single most effective preparation habit for Section II.

Common AP Physics C: Electricity and Magnetism FRQ mistakes

1. 01

   Choosing the wrong Gaussian surface or skipping the symmetry justification

   The most consistently cited FRQ error in AP Physics C: E&M Chief Reader Reports across 2022 to 2025. Students apply Gauss's law to a charge distribution but either choose a surface that does not exploit the symmetry of the problem (for example, a cube for a spherical distribution) or, more commonly, choose the correct spherical or cylindrical surface but omit the argument that E is constant in magnitude and perpendicular to the surface at every point. Without that justification, factoring E out of the surface integral is mathematically unjustified, and the rubric does not award the point even if the numerical answer is correct. Always state the symmetry argument explicitly before writing E times A.

   AP Physics C: Electricity and Magnetism Chief Reader Reports 2022 to 2025, electrostatics FRQ commentary

2. 02

   Setting up the RC differential equation correctly but applying wrong initial or final conditions

   Chief Reader Reports note that students often write the correct form of the RC differential equation, dQ/dt equals (emf minus Q/C) over R, and correctly separate variables, but then substitute the wrong initial or final conditions when solving for the integration constants. A common version: using Q equals zero as the initial condition for a discharging circuit rather than Q equals Q initial, or using I equals 0 as the final condition for charging when the correct final state has I approaching zero as Q approaches Q max. The result is an exponential that passes through the wrong intercept, earning partial credit only.

   AP Physics C: Electricity and Magnetism Chief Reader Reports 2022 to 2025, circuits FRQ commentary

3. 03

   Computing the magnitude of the induced EMF correctly but omitting or misapplying Lenz's law for direction

   On electromagnetic induction FRQs, most responses correctly differentiate the flux to find the magnitude of the induced EMF. However, a large fraction then state the direction of induced current incorrectly or provide no justification at all. The rubric for direction parts requires an explicit Lenz's law argument: state that the induced current opposes the change in flux, identify whether the flux through the loop is increasing or decreasing, and from that determine the direction of the opposing field and therefore the current direction. Stating the current direction without this three step argument does not earn the direction point.

   AP Physics C: Electricity and Magnetism Chief Reader Reports 2022 to 2024, electromagnetic induction FRQ commentary

4. 04

   Setting up the Biot Savart vector cross product incorrectly in non trivial geometries

   On magnetic field questions requiring a Biot Savart integration, students frequently set up the scalar magnitude of dB correctly but make errors in the vector direction of dL cross r hat, especially when the current element and the field point are not in a simple axis aligned configuration. For a straight wire, the cross product is straightforward; for an arc or a loop where the current element has both x and y components, many responses drop or misdirect the unit vector, producing an integral that points in the wrong direction. Chief Reader Reports flag this as a persistent source of lost points on the magnetic field FRQ.

   AP Physics C: Electricity and Magnetism Chief Reader Reports 2023 to 2024, magnetic fields FRQ commentary

5. 05

   Applying the uniform field formula E equals V over d to non uniform field configurations

   On electrostatics and capacitor FRQs, students frequently use E equals V divided by d as a general relationship between field and potential. This formula is valid only for a uniform field between parallel plates separated by distance d. For spherical or cylindrical geometries, the field is non uniform and the correct relation is E equals negative dV/dr. Substituting E equals V over d into a Gauss's law problem or using it to find the field at a particular radius produces a dimensionally consistent but physically incorrect answer, and the rubric awards no credit for the affected parts.

   AP Physics C: Electricity and Magnetism Chief Reader Reports 2022 to 2025, electrostatics and capacitor FRQ commentary

6. 06

   Stating an answer without showing the integral or derivative setup

   The single most consequential failure mode specific to a calculus based FRQ exam. College Board's rubrics for AP Physics C: Electricity and Magnetism require that any part calling for an integral or a derivative be answered with the explicit setup: the integral expression, the limits of integration, the substitution, and the evaluated result. A response that states E equals kQ over r squared without showing the Gauss's law surface integral, or V equals kQ over r without showing the definite integral from infinity, earns zero for that part regardless of the correctness of the stated result. Chief Reader Reports describe this as the most common reason otherwise capable students earn low Section II scores.

   AP Physics C: Electricity and Magnetism Chief Reader Reports 2022 to 2025, general Section II commentary

How to practice AP Physics C: Electricity and Magnetism FRQs effectively

Timed full solutions written by hand, then scored part by part against the official guideline.

The highest return practice for AP Physics C: E&M is not reading solutions; it is writing complete derivations under time pressure and then grading yourself line by line against the official scoring guideline. The archive above links every released booklet from 2021 to 2025, including the Set 1 and Set 2 variants for 2022 to 2024, which gives a total of nine complete Section II sets to work through. For each session, work one complete three question set in 45 minutes, write every integral and every boundary condition explicitly, then open the scoring guideline and compare your setup to the rubric requirements part by part. Pay specific attention to the parts where you have the right answer but may have skipped the justification: those are the points lost most commonly, per the Chief Reader Reports for 2022 to 2025. After a few practice sessions the specific steps each rubric type requires become automatic, and the time lost to indecision about Gaussian surface choice or integral setup direction drops sharply.

1. 1

   Use the 15 minute reading period to read all three questions, identify which unit each question draws from, and plan your integral or differential equation setup before writing. Committing to the correct Gaussian surface or Amperian loop before you start writing prevents mid solution direction changes.

2. 2

   Write every integral setup in full, including the integral sign, the integrand, and the limits of integration, even when the answer is a formula you know. The rubric awards points for the setup, not the memory of the result.

3. 3

   For every Gauss's law part, write three lines explicitly before factoring E out of the integral: state the chosen Gaussian surface by shape and radius, argue by symmetry that E is constant in magnitude over that surface, and argue by symmetry that E is perpendicular to the surface everywhere. These three lines are what the rubric checks.

4. 4

   On RC and RL circuit parts, write the differential equation first for Q(t) or I(t), separate variables, integrate both sides with explicit limits, apply the initial condition, and then apply the final condition. Each of these is a separate rubric step that can earn a partial credit point independently.

5. 5

   For Faraday's law direction parts, write out the three step Lenz's law argument: identify whether flux is increasing or decreasing, state that the induced current must produce a field opposing the change, and from the right hand rule determine the current direction. A bare arrow on a diagram without this argument does not earn the direction point.

6. 6

   Answer every part of every question. There is no penalty for an incorrect attempt. A partially correct response on a hard part earns more than a blank, and many rubric points are awarded for setup steps that are accessible even when the later algebra goes wrong.

7. 7

   Budget roughly 13 to 15 minutes per question. If a later part in a question depends on a result from an earlier part that you could not derive, use an algebraic placeholder (for example, write let E sub 0 be the field found in part (a), then use E sub 0 in part (b)). College Board rubrics often allow carrying forward an incorrect prior result when the student's subsequent work is internally consistent.

AP Physics C: Electricity and Magnetism FRQ FAQ

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