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Volume I · MMXXVI AP Physics C: Electricity and Magnetism
Library AP Physics C: Electricity and Magnetism Unit 10: Conductors and Capacitors
⁂   AP Physics C: Electricity and Magnetism · Unit 10

10. Conductors and Capacitors

10–15% of the AP exam. 8 key topics. 4 common errors analyzed.

10–15% exam weight

Unit 10: Conductors and Capacitors

Unit 10 (Conductors and Capacitors) is part of the calculus-based AP Physics C: E&M curriculum. Gauss's Law, line integrals, and differential equations appear throughout — set up integrals carefully before evaluating.

Key topics in this unit

  1. Properties of conductors in electrostatic equilibrium (E = 0 inside, field perpendicular to surface, charge on surface)
  2. Capacitance definition: C = Q/V
  3. Parallel-plate capacitor: C = ε₀A/d, derived from Gauss's Law and potential difference
  4. Cylindrical and spherical capacitor derivations using Gauss's Law
  5. Dielectric materials: dielectric constant κ, effect on C, E, and V at constant charge vs. constant voltage
  6. Energy stored in a capacitor: U = Q²/2C = CV²/2 = QV/2
  7. Capacitors in series and parallel: equivalent capacitance
  8. Cavity shielding: field and potential inside a conductor enclosure

Common errors — what the rubric penalizes

These are the most frequently penalized mistakes on AP exam FRQs and MCQs. Review each before your next practice session.

Common error

Confusing the behavior of a capacitor when a dielectric is inserted at constant charge vs. constant voltage — students often apply the same formula regardless of which quantity is held fixed, leading to incorrect conclusions about how E, V, and U change.

Common error

Incorrectly deriving capacitance for non-parallel-plate geometries — forgetting to use Gauss's Law to find E first, then integrate E·dr to find V, before computing C = Q/V; instead plugging C = ε₀A/d in spherical or cylindrical cases.

Common error

Adding capacitances in series using the parallel rule (and vice versa) — the reciprocal rule for series capacitors is the opposite of the resistor convention and is frequently inverted.

Common error

Neglecting to account for the energy change when a dielectric is inserted — students compute the new capacitance correctly but forget that inserting a dielectric at constant voltage requires the battery to do work, changing the stored energy.

Study checklist

  • Can you list all key topics from memory without this page?
  • Have you worked through at least one FRQ-style question per topic?
  • Can you explain each common error above — and why the correct answer differs?
  • Have you reviewed the relevant College Board CED section and formula sheet entries?
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