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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 12 · Topic 12.1

Magnetic Fields

Vector products, superposition, and symmetry determine magnetic fields and their forces on charges, wires, and loops.

1. Topic Lens

Magnetic Fields is studied through magnetic fields and electromagnetism. Connect the system boundary, interacting parts, and measurable evidence before applying a formula.

\[d\vec B=\frac{\mu_0}{4\pi}\frac{I\,d\vec\ell\times\hat r}{r^2}\]

2. Why the Formula Works

The relationship is built from definitions and conservation reasoning:

  1. The Biot-Savart law superposes current-element contributions.
  2. For a highly symmetric current, the tangential field has constant magnitude on an Ampèrian loop.
  3. Pulling B outside the line integral gives B times loop length equals μ₀Ienc.
\[\oint\vec B\cdot d\vec\ell=\mu_0I_{\text{enc}}\]

3. Detailed Visual Model

Pixel diagram for Magnetic FieldsOriginal schematic connecting Magnetic Fields to Magnetic Fields and Electromagnetism.+
Magnetic Fields: an original pixel-style model. Use it as a schematic, not a literal scale drawing.

4. Worked Example and Lab Link

For a long straight wire, doubling current while holding radius fixed does what to B?

Answer: Since B=μ₀I/(2πr), the field doubles.

Investigation idea: Map B around a long conductor at several radii and test the predicted inverse-radius pattern.

Common trap: Ampère's law is always valid in magnetostatics, but using it to solve for B requires enough symmetry.

Checkpoint · Topic 12.1

Explain how magnetic fields supports or limits this conclusion: Since B=μ₀I/(2πr), the field doubles.

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.