Worked example: A parallel-plate capacitor has plate area 10 cm², separation 1 mm, air-filled C₀ = 8.85 pF. Insert a BaTiO₃ slab (εᵣ = 1200). Find the new capacitance and the energy stored at 100 V. Step 1: C = εᵣ·C₀ = 1200 × 8.85 pF = 10.6 nF. Step 2: Energy U = ½CV² = 0.5 × 10.6×10⁻⁹ × 100² = 5.3×10⁻⁵ J = 53 μJ. Step 3: Without dielectric: U₀ = 0.5 × 8.85×10⁻¹² × 10⁴ = 4.4×10⁻⁸ J — over 1000× less! Step 4: Microscopic picture: the BaTiO₃ polarises so strongly that the field inside drops ~1200×, letting 1200× more charge sit on the plates at the same voltage. Conclusion: high-εᵣ dielectrics are why phone capacitors are microscopic yet effective — polarisation multiplies storage.