Energy density: Each plate of an air-filled parallel-plate air capacitor has an area of 0.0040 m², and the separation of the plates is 0.080 mm. An electric field of 5.3 × 10⁶ V/m is present between the plates. What is the energy density between the plates? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Question

Quizplus · Accepted Answer

The energy density (u) in the electric field of a capacitor is given by the formula $u = \frac{1}{2} \epsilon_0 E^2$, where $\epsilon_0$ is the permittivity of free space (8.85 × 10^-12 C^2/N·m^2) and $E$ is the electric field strength (5.3 × 10^6 V/m). Plugging in the values, $u = \frac{1}{2} \times 8.85 \times 10^{-12} \times (5.3 \times 10^6)^2 = 124.7$ J/m^3, which rounds to 124 J/m^3, making option A correct.

Energy Density: Each Plate of an Air-Filled Parallel-Plate Air Capacitor