Electrostatic Potential and Capacitance
How energy is stored in electric fields and the devices that store charge
Table of Contents
2.1 Introduction
In previous chapters, we studied the notion of potential energy and the work-energy theorem. In this chapter, we extend these ideas to electric charges. The concept of electric potential energy and electric potential helps us understand how energy is stored in electric fields and how capacitors work.
2.2 Electric Potential
The electric potential at a point is the work done per unit positive charge in bringing a test charge from infinity to that point without acceleration:
2.3 Potential due to a Point Charge
2.4 Potential due to a Dipole
For an electric dipole with charges ±q separated by distance 2a:
2.5 Equipotential Surfaces
Surfaces where the potential is the same at every point. Key properties:
- Electric field is always perpendicular to equipotential surfaces
- No work is done in moving a charge along an equipotential surface
- For a point charge, equipotential surfaces are concentric spheres
- For a uniform field, equipotential surfaces are parallel planes
2.6 Capacitance
Capacitance is the ability of a system to store charge per unit potential difference:
2.7 Parallel Plate Capacitor
The most common capacitor: two parallel conducting plates separated by distance d:
Inserting a dielectric (insulator) between plates increases capacitance by factor κ. The dielectric gets polarized, creating an internal field that opposes the external field, reducing net field and allowing more charge storage.
2.8 Capacitors in Series and Parallel
Series Combination
1/C = 1/C₁ + 1/C₂ + ...
Total capacitance is less than smallest. Same charge on each, voltages add.
Parallel Combination
C = C₁ + C₂ + ...
Total capacitance is sum of all. Same voltage across each, charges add.
2.9 Energy Stored in a Capacitor
The energy is not stored on the plates but in the electric field between them. The energy density (energy per unit volume) is u = ½ε₀E², showing that stronger fields store more energy.