---
title: "AP Physics C: E&M Representations FRQ Practice"
description: "29 Translation Between Representations questions written in the AP format, each scored part by part."
canonical: "https://fiveable.me/ap-physics-c-e-m/frqs/translation-between-representations"
type: "frq-type-practice"
subject: "AP Physics C: E&M"
---

# AP Physics C: E&M Representations FRQ Practice

## What the Representations FRQ asks

The Translation Between Representations (TBR) question is FRQ 2 on the AP Physics C: E&M exam. You represent one electricity and magnetism scenario as a bar chart, a derived equation, and a sketched graph, then justify a claim that ties them together.

- **25–30 min**: suggested on the exam
- **12 points**: across parts A to D
- **95 min**: for all four FRQs

| Part | What it asks | Points |
| --- | --- | --- |
| A: Bar chart | Draw bars for quantities such as energy, field strength, or current | 3 |
| B: Derivation | Derive an expression for a key quantity, starting from a fundamental principle | 4 |
| C: Graph | Sketch a graph of a related quantity, such as potential versus position | 3 |
| D: Claim | Indicate a result, often whether two parts agree, and justify it | 2 |

## How Representations FRQ practice works

1. **Read the full question.** The scenario, its figures, and parts A through D, laid out the way the exam shows them.
2. **Write on a 27-minute timer.** Inside the 25 to 30 minutes the exam suggests for this question. Pause it or turn it off, and your response saves as you go.
3. **Submit for a score out of 12.** Your response is scored against the scoring guidelines written for that question. Your first score is included.

## All 29 questions

### Unit 8: Electric Charges, Fields, and Gauss's Law (1)
- [Electric field and flux in charged spherical shell](/ap-physics-c-e-m/frq-practice?id=698acbd04eb20800e308517e&type=frq-2-translation-between-representations)

### Unit 9: Electric Potential (5)
- [Particle energy and motion in uniform electric field](/ap-physics-c-e-m/frq-practice?id=6977ce3f6d7ee03370aa0a56&type=frq-2-translation-between-representations)
- [Electric potential from two fixed point charges](/ap-physics-c-e-m/frq-practice?id=698ac1754eb20800e3085140&type=frq-2-translation-between-representations)
- [Electric potential from two fixed point charges](/ap-physics-c-e-m/frq-practice?id=698ac2c74eb20800e3085149&type=frq-2-translation-between-representations)
- [Electric potential and field from fixed point charges](/ap-physics-c-e-m/frq-practice?id=698acfef4eb20800e3085197&type=frq-2-translation-between-representations)
- [Electric potential and field from opposite point charges](/ap-physics-c-e-m/frq-practice?id=698ad1e74eb20800e30851a0&type=frq-2-translation-between-representations)

### Unit 10: Conductors and Capacitors (8)
- [Concentric conducting spheres with dielectric material](/ap-physics-c-e-m/frq-practice?id=698abea64eb20800e308512d&type=frq-2-translation-between-representations)
- [Coaxial cable electric field and flux distribution](/ap-physics-c-e-m/frq-practice?id=698ac3bc4eb20800e3085150&type=frq-2-translation-between-representations)
- [Parallel-plate capacitor with conducting sphere and dielectric](/ap-physics-c-e-m/frq-practice?id=698ac5f94eb20800e308515b&type=frq-2-translation-between-representations)
- [Charge redistribution between conducting spheres](/ap-physics-c-e-m/frq-practice?id=698ac7054eb20800e3085161&type=frq-2-translation-between-representations)
- [Charge redistribution and capacitor electric field](/ap-physics-c-e-m/frq-practice?id=698accb54eb20800e3085184&type=frq-2-translation-between-representations)
- [Charge redistribution through conducting sphere contact and capacitor](/ap-physics-c-e-m/frq-practice?id=698ad58d4eb20800e30851b0&type=frq-2-translation-between-representations)
- [Charge redistribution on connected conducting spheres](/ap-physics-c-e-m/frq-practice?id=698ad8124eb20800e30851b7&type=frq-2-translation-between-representations)
- [Charge redistribution between connected conducting spheres](/ap-physics-c-e-m/frq-practice?id=698ad99e4eb20800e30851ba&type=frq-2-translation-between-representations)

### Unit 11: Electric Circuits (5)
- [RC circuit charging with wire resistance](/ap-physics-c-e-m/frq-practice?id=698ac4c94eb20800e3085156&type=frq-2-translation-between-representations)
- [Battery, resistive wire, capacitor charging dynamics](/ap-physics-c-e-m/frq-practice?id=698ac58b4eb20800e3085159&type=frq-2-translation-between-representations)
- [Capacitor charging through resistive circuit with battery](/ap-physics-c-e-m/frq-practice?id=698ac8094eb20800e3085166&type=frq-2-translation-between-representations)
- [RC circuit with capacitor charging and current decay](/ap-physics-c-e-m/frq-practice?id=698ad8084eb20800e30851b5&type=frq-2-translation-between-representations)
- [Capacitor charging in RC circuit with battery](/ap-physics-c-e-m/frq-practice?id=698ada1d4eb20800e30851bb&type=frq-2-translation-between-representations)

### Unit 12: Magnetic Fields and Electromagnetism (2)
- [Magnetic field distribution around current-carrying wire in magnetic material](/ap-physics-c-e-m/frq-practice?id=698acffb4eb20800e3085199&type=frq-2-translation-between-representations)
- [Magnetic field from current-carrying wire in magnetic material](/ap-physics-c-e-m/frq-practice?id=698ad37e4eb20800e30851a8&type=frq-2-translation-between-representations)

### Unit 13: Electromagnetic Induction (8)
- [Magnetic energy density in solenoids with and without cores](/ap-physics-c-e-m/frq-practice?id=6977d6fc670a3c1e96ac1790&type=frq-2-translation-between-representations)
- [Motional EMF and induced current in sliding conductor bar](/ap-physics-c-e-m/frq-practice?id=698ace894eb20800e3085190&type=frq-2-translation-between-representations)
- [Electromagnetic induction in moving conducting loop](/ap-physics-c-e-m/frq-practice?id=698acfbe4eb20800e3085195&type=frq-2-translation-between-representations)
- [Electromagnetic induction in moving conductor rod](/ap-physics-c-e-m/frq-practice?id=698ad0a74eb20800e308519b&type=frq-2-translation-between-representations)
- [Electromagnetic induction in moving conductor circuit](/ap-physics-c-e-m/frq-practice?id=698ad30b4eb20800e30851a6&type=frq-2-translation-between-representations)
- [Electromagnetic induction in moving conductor loop](/ap-physics-c-e-m/frq-practice?id=698ad5144eb20800e30851af&type=frq-2-translation-between-representations)
- [Electromagnetic induction in moving conductor bar](/ap-physics-c-e-m/frq-practice?id=698ad8ff4eb20800e30851b8&type=frq-2-translation-between-representations)
- [Electromagnetic induction in moving conductor bar](/ap-physics-c-e-m/frq-practice?id=698ada264eb20800e30851bc&type=frq-2-translation-between-representations)

## Sample question

**Electric field and flux in charged spherical shell**

A thin, nonconducting spherical shell of inner radius a = 0.10 m and outer radius b = 0.20 m is centered at the origin, as shown in Figure 1. The material of the shell has a uniform volume charge density ρ = +3.0 × 10⁻⁶ C/m³ throughout the region a ≤ r ≤ b. A point charge q = -2.0 μC is fixed at the center of the shell. The space inside and outside the shell is vacuum with permittivity ε₀ = 8.85 × 10⁻¹² F/m. Neglect gravitational interactions unless explicitly stated.

Figures:
  Type: setup_diagram
  Caption: Figure 1. Thin nonconducting spherical shell (inner radius a = 0.10 m, outer radius b = 0.20 m) with a central point charge q = −2.0 μC, showing three spherical Gaussian surfaces at r = 0.05 m, 0.15 m, and 0.30 m.
  URL: https://kcbwzropdukwhmmvdylp.supabase.co/storage/v1/object/public/frq_stimulus/ap-physics-c-e-m/b6116a4e-ff96-4015-873f-600ae8ad4259_fig1.jpg
  Placement: after-background

Figure 2:
  Type: bar_chart
  Caption: Figure 2. Bar chart of electric-field magnitude |E| at three radii (0.05 m, 0.15 m, 0.30 m). The r = 0.30 m bar is provided as the reference; students complete the other bars.
  URL: https://kcbwzropdukwhmmvdylp.supabase.co/storage/v1/object/public/frq_stimulus/ap-physics-c-e-m/b6116a4e-ff96-4015-873f-600ae8ad4259_numfix1_fig2.png
  Placement: before-part
  Part Letter: A

Part A (3 points):
  Prompt: In Figure 2, **draw** bars to represent |E| at r = 0.05 m and r = 0.15 m relative to the bar shown at r = 0.30 m. If |E| = 0, write a "0" in that column.
  Context: The electric field magnitude at a distance r from the center is |E(r)|. The partially completed bar chart in Figure 2 shows a bar that represents |E| at r = 0.30 m.
  Verb: draw

Part B (4 points):
  Prompt: **Derive** an expression for the electric field E(r) (including sign/direction using the radial unit vector r) for the region a < r < b in terms of ρ, q, a, r, ε₀, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.
  Verb: derive

Figure 3:
  Type: graph_axes
  Caption: Figure 3. Axes for electric flux Φ_E through a spherical Gaussian surface versus radius r for 0 ≤ r ≤ 0.35 m; sketch must show sign and slope changes at r = a and r = b.
  URL: https://kcbwzropdukwhmmvdylp.supabase.co/storage/v1/object/public/frq_stimulus/ap-physics-c-e-m/b6116a4e-ff96-4015-873f-600ae8ad4259_fig3.jpg
  Placement: before-part
  Part Letter: C

Part C (3 points):
  Prompt: On the axes shown in Figure 3, **sketch** a graph of the electric flux Φ_E(r) through a spherical Gaussian surface of radius r, for 0 ≤ r ≤ 0.35 m. Your graph must indicate the sign of Φ_E and any changes in curvature or slope at r = a and r = b.
  Verb: sketch

Part D (2 points):
  Prompt: **Indicate** whether the magnitude of the particle's initial acceleration is greater than, less than, or equal to g. Briefly justify your answer by comparing the magnitudes of the electric and gravitational forces at r₀ using Fₑ = |Q| |E(r₀)| and F_g = mg.
  Context: A small test particle of mass m = 1.0 × 10⁻⁶ kg and charge Q = +1.0 × 10⁻⁹ C is released from rest at r₀ = 0.30 m and moves radially under the influence of the electric force from the charge distribution and the gravitational force from Earth. Take g = 9.8 m/s² downward. At the release point, the radial direction is horizontal, so the gravitational force is perpendicular to the radial electric force. Use the electric field at r₀ due to the total enclosed charge at that radius.
  Verb: indicate and briefly justify

Image URLs (3):
  - https://kcbwzropdukwhmmvdylp.supabase.co/storage/v1/object/public/frq_stimulus/ap-physics-c-e-m/b6116a4e-ff96-4015-873f-600ae8ad4259_fig1.jpg
  - https://kcbwzropdukwhmmvdylp.supabase.co/storage/v1/object/public/frq_stimulus/ap-physics-c-e-m/b6116a4e-ff96-4015-873f-600ae8ad4259_numfix1_fig2.png
  - https://kcbwzropdukwhmmvdylp.supabase.co/storage/v1/object/public/frq_stimulus/ap-physics-c-e-m/b6116a4e-ff96-4015-873f-600ae8ad4259_fig3.jpg

## Questions

**How many responses can I get scored?**

You can read every question without a plan. Your first scored response is included. A plan unlocks unlimited scoring.

**What representations does the TBR ask for?**

A bar chart for quantities such as energy, field strength, or current, a derivation, a graph of a related quantity, and a justified claim, often about whether your representations agree.

**How is the TBR different from the Mathematical Routines question?**

Both include derivations. The TBR is built around linking a bar chart, an equation, and a graph of the same scenario, and it is worth 12 points instead of 10.

**How do I draw the bar chart or graph?**

Use the drawing tool to draw on the question’s figure or on a blank graph. Your drawing is scored with the rest of your response. You can also switch to handwrite and add a photo of your page.

**Are these real College Board questions?**

No. We wrote them in the AP format, with the same four parts, and wrote scoring guidelines for each one.

## Related

- [Representations FRQ exam guide](/ap-physics-c-e-m/ap-physics-c-electricity-magnetism-exam/ap-physics-c-e-m-ap-phys-em-frq-translation-between-representations/study-guide/ap-physics-c-e-m-ap-phys-em-frq-translation-between-representations)
- [AP Physics C: E&M Mathematical Routines FRQ practice](/ap-physics-c-e-m/frqs/mathematical-routines)
- [AP Physics C: E&M Experimental Design FRQ practice](/ap-physics-c-e-m/frqs/experimental-design)
- [AP Physics C: E&M Qualitative/Quantitative FRQ practice](/ap-physics-c-e-m/frqs/qualitative-quantitative-translation)
- [AP Physics C: E&M FRQs](/ap-physics-c-e-m/frqs)
- Any question by id: the `get_frq` tool on the [Fiveable MCP server](/mcp/docs)

## About This Document

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