Question

An air-filled parallel plate capacitor has a uniform electric field \( E \) in the space between the plates. If the distance between the plates is \( d \) and area of each plate is \( A \), the energy stored in the capacitor is (\( \varepsilon_0 \) = permittivity of free space)

• A. \( \dfrac{1}{2}\varepsilon_0 E^2 A d \)
• B. \( \dfrac{E^2 A d}{\varepsilon_0} \)
• C. \( \dfrac{1}{2}\varepsilon_0 E^2 \)
• D. \( \varepsilon_0 E A d \)

Hint:

Capacitor energy can be found directly using electric field energy density when field is uniform.

Answer 1

The Correct Option is A

Step 1: Write energy density of electric field.
Energy density in an electric field is \[ u = \frac{1}{2}\varepsilon_0 E^2 \]
Step 2: Find volume between capacitor plates.
\[ V = A d \]
Step 3: Calculate total energy stored.
\[ U = u \times V = \frac{1}{2}\varepsilon_0 E^2 \cdot A d \]
Step 4: Conclusion.
The energy stored in the capacitor is \( \dfrac{1}{2}\varepsilon_0 E^2 A d \).