AP Physics C E&M 70% Sectional Test — Full Electrostatics and Magnetism
Test AP Physics C E&M readiness through Units 8–12 with a sectional covering Biot-Savart integrals, Ampere's law, and integrated electrostatics and magnetism.
What the 70% Sectional Covers
The 70% sectional for AP Physics C: Electricity & Magnetism covers Units 8 through 12, incorporating the complete electrostatics sequence (Units 8–11) alongside the magnetic fields and electromagnetism content of Unit 12. This is the final checkpoint before tackling electromagnetic induction (Unit 13) — the unit that synthesises all of AP Physics C E&M into a unified framework through Faraday's law.
Topics from Earlier Sectionals
All content from the 30% and 50% sectionals remains in scope: Gauss's law and electric field integrals (Unit 8), electric potential line integrals and gradient relationships (Unit 9), capacitance geometry derivations and energy storage (Unit 10), and RC circuit differential equations with Kirchhoff analysis (Unit 11). At the 70% level, these topics may appear as components within multi-part problems that also require magnetism analysis.
New Content: Unit 12 Magnetic Fields and Electromagnetism
Magnetic Force Laws
- Lorentz force F = qv × B: direction from right-hand rule, magnitude F = qvB sinθ
- Circular motion in a magnetic field: radius r = mv/(|q|B)
- Force on current-carrying conductors: F = IL × B; integration for curved conductors
Biot-Savart Law
- Differential field contribution: dB = (μ₀/4π)(I dl × r̂)/r²
- Integration to find B at the centre of a circular loop, on the axis of a loop, and for finite straight wires
- Symmetry arguments to eliminate transverse Biot-Savart contributions
Ampere's Law
- ∮B·dl = μ₀I_enc for symmetric current distributions
- Infinite straight wire, solenoid (B = μ₀nI), and toroid (B = μ₀NI/2πr) derivations
- Finding B inside a conductor with non-uniform current density by integrating J over the Amperian loop cross-section
Cross-Unit Integration Challenges at the 70% Level
The most demanding AP-style problems at this checkpoint integrate electrostatics and magnetism together. Representative examples include:
- A charged particle moving through a region of combined E and B fields — requiring force balance analysis using both field types.
- Comparing the magnetic energy density B²/(2μ₀) with the electric energy density ε₀E²/2 in a problem involving both capacitors and solenoids.
- Deriving the force between two parallel current-carrying wires using Ampere's law to find B from one wire, then applying F = IL × B to the second.
Preparing for Unit 13
Completing this sectional with strong results means you have mastered the two inputs that Faraday's law requires: magnetic field B (from Unit 12) and the time derivative of magnetic flux (which requires both B and the geometry concepts from Units 8–10). If Biot-Savart or Ampere's law integrals are sources of errors, consolidate those skills before Unit 13 — where incorrect B values will propagate into flux and EMF miscalculations.