Energy Density of a Capacitor – Rankers Physics

Parallel Plate Capacitor: Practice Problem & Solution

Energy per unit volume for a capacitor having area A and separation d kept at potential difference V is given by:
\( \frac{1}{2} \varepsilon_0 \frac{V^2}{d^2} \)
\( \frac{1}{2 \varepsilon_0} \frac{V^2}{d^2} \)
\( \frac{\varepsilon_0 V^2 A^2}{2d^2} \)
\( \frac{1}{2} \frac{V^2 A^2}{\varepsilon_0 d^2} \)

Solution Explained:

To solve this problem, we apply the core principles of Parallel Plate Capacitor. Understanding the underlying formula is key to arriving at the correct answer below:

Energy density (energy per unit volume) of a capacitor is given by the formula \( u = \frac{1}{2} \varepsilon_0 E^2 \). Substituting electric field \( E = \frac{V}{d} \) gives \( u = \frac{1}{2} \varepsilon_0 \frac{V^2}{d^2} \).

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