Casimir Force
Quantum Vacuum Fluctuations Between Conducting Plates
Parameters
Plate separation d:
200
nm
Plate area A:
1.0
cm²
Temperature T:
300
K
Casimir Force
Separation d
—
Force F
—
Pressure P
—
Thermal correction
—
Mode cutoff λ_min
—
F vs. Distance (log scale)
Theory
F = −(π²ℏc A)/(240 d⁴)
≈ −(1.3×10⁻²⁷ N·m⁴) × A/d⁴
Only modes fitting nλ/2 = d survive between plates. Outside: full vacuum spectrum → net inward pressure.
Thermal correction (Lifshitz): δF/F ≈ (16π²/3)(k_B T d / ℏc)³