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AP Course

AP Physics C: Electricity and Magnetism

Updated for the AP Physics C: Electricity and Magnetism framework effective fall 2024, with calculus-based fields, circuits, and induction.

Build calculus-based E&M with original field models, derivations, experiments, quizzes, and practice sets.

Lessons
Electric Charge and Electric ForceConservation of Electric Charge and the Process of ChargingElectric FieldsElectric Fields of Charge DistributionsElectric FluxGauss’s LawElectric Potential EnergyElectric PotentialConservation of Electric EnergyElectrostatics with ConductorsRedistribution of Charge between ConductorsCapacitorsDielectricsElectric CurrentSimple CircuitsResistance, Resistivity, and Ohm’s LawElectric PowerCompound Direct Current CircuitsKirchhoff’s Loop RuleKirchhoff’s Junction RuleResistor Capacitor (RC) CircuitsMagnetic FieldsMagnetism and Moving ChargesMagnetic Fields of Current-Carrying Wires and the Biot-Savart LawAmpère’s LawMagnetic FluxElectromagnetic InductionInduced Currents and Magnetic ForcesInductanceCircuits with Resistors and Inductors (LR Circuits)Circuits with Capacitors and Inductors (LC Circuits)
Quizzes
Practice Problems Formula notes, diagrams, and practice sets will be added here.

AP Physics C: Electricity and Magnetism · Unit 9 · Topic 9.3

Conservation of Electric Energy

Scalar potential and vector field are linked by line integrals and gradients, simplifying energy and distribution problems.

1. Topic Lens

Conservation of Electric Energy is studied through electric potential. Connect the system boundary, interacting parts, and measurable evidence before applying a formula.

\[\Delta V=-\int_i^f\vec E\cdot d\vec\ell\]

2. Why the Formula Works

The relationship is built from definitions and conservation reasoning:

  1. Electric potential change is negative work per unit charge done by the field.
  2. For an infinitesimal displacement, dV=-E·dℓ.
  3. The directional-derivative identity for every direction gives E=-∇V.
\[\vec E=-\nabla V\]

3. Detailed Visual Model

Pixel diagram for Conservation of Electric EnergyOriginal schematic connecting Conservation of Electric Energy to Electric Potential.+
Conservation of Electric Energy: an original pixel-style model. Use it as a schematic, not a literal scale drawing.

4. Worked Example and Lab Link

A charge q=2 C moves through ΔV=-5 V. Find its potential-energy change.

Answer: ΔU=qΔV=(2)(-5)=-10 J.

Investigation idea: Create a numerical potential map for multiple charges and compare gradient arrows with directly summed fields.

Common trap: Potential can be zero where field is not zero; potential reference choice does not change measurable differences.

Checkpoint · Topic 9.3

Explain how conservation of electric energy supports or limits this conclusion: ΔU=qΔV=(2)(-5)=-10 J.

Official curriculum reference: College Board AP Physics C: Electricity and Magnetism course page. The explanation and worked example are independently written for this study site.