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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 10 · Topic 10.3

Capacitors

Boundary conditions, geometry, dielectrics, and circuit connections determine capacitance and stored field energy.

1. Topic Lens

Capacitors is studied through conductors and capacitors. Connect the system boundary, interacting parts, and measurable evidence before applying a formula.

\[C=\frac{Q}{V}\]

2. Why the Formula Works

The relationship is built from definitions and conservation reasoning:

  1. During charging, the instantaneous potential is V(q)=q/C.
  2. Incremental work is dW=V(q)dq.
  3. Integrate from zero to Q and substitute Q=CV for equivalent forms.
\[U=\int_0^Q\frac{q}{C}\,dq=\frac{Q^2}{2C}=\frac12CV^2\]

3. Detailed Visual Model

Pixel diagram for CapacitorsOriginal schematic connecting Capacitors to Conductors and Capacitors.
Capacitors: an original pixel-style model. Use it as a schematic, not a literal scale drawing.

4. Worked Example and Lab Link

A 2 F capacitor is charged to 3 V. Find stored energy.

Answer: U=½(2)(3²)=9 J.

Investigation idea: Measure voltage during safe low-voltage charging and infer capacitance from charge or time data.

Common trap: Capacitance is primarily geometric; changing Q does not by itself change an ideal capacitor's C.

Checkpoint · Topic 10.3

Explain how capacitors supports or limits this conclusion: U=½(2)(3²)=9 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.