Parallel-Plate Capacitor: ε₀ from C(1/d)
Air-filled plates of known area. Measure C at several separations and recover ε₀ from a fit of C versus 1/d.
Goal
Determine ε₀ from C = ε₀ A / d (ε_r = 1). The slope of C versus 1/d is ε₀ A.
Equipment
- Parallel plates (known A)
- Micrometer gap
- Capacitance meter
- Air dielectric
Experiment
Theory
Ideal parallel plates ignore fringing: C = ε₀ ε_r A / d. Here the gap is air (ε_r = 1) and A is known. The bench hides C, Q, U and ε₀. You only change d. A capacitance meter reports C after you record.
Procedure
- Plate area A and ε_r = 1 (air) are fixed and known. You only change the gap d.
- Record. A capacitance meter logs C with small noise. There is no live C, Q or ε₀.
- The notebook converts d to metres and C to farads, and computes 1/d. Repeat for at least 6 gaps from about 1.5 mm to 12 mm.
- Fit C versus 1/d; ε₀ = slope / A. Compare with the reference.
Conclusion
The fitted ε₀ agrees with the vacuum permittivity. Main uncertainties: meter noise and neglecting fringing fields.