Inside This Unit: The Full Breakdown
This unit analyzes conductors in electrostatic equilibrium, capacitance, dielectrics, and the energy stored in capacitors and electric fields.
Why it matters
Capacitors appear in both electrostatics and circuits; the field/energy reasoning here connects the two halves of the course.
Key concepts
- Conductors in equilibrium have zero interior field and surface charge only.
- Capacitance C = Q/V; for parallel plates C = ε₀A/d.
- Series capacitors share charge; parallel share voltage.
- Stored energy U = ½CV² = Q²/(2C); field energy density u = ½ε₀E².
Conductors and Capacitance
A conductor in equilibrium has zero internal field, placing all excess charge on its surface and shielding its interior. Capacitance measures stored charge per volt; for parallel plates it follows from the uniform field and V = −∫E·dl, giving C = ε₀A/d.
Dielectrics and Energy
A dielectric increases capacitance by κ. Stored energy is U = ½CV² = Q²/(2C), and equivalently resides in the field with density ½ε₀E². Whether E, V, or U change when a dielectric is inserted depends on whether charge or voltage is held fixed.
AP exam tip
For dielectric problems, state explicitly whether charge or voltage is held constant — the two scenarios give opposite changes in field and energy.
Connections to other units
- Unit 1: Capacitor fields come from Gauss’s law.
- Unit 4: Capacitors store and release energy in RC circuits.
