Question

A parallel plate capacitor has uniform electric field \( E \) in the space between the plates. If the distance between plates is \( d \) and area of each plate is \( A \), the energy stored in the capacitor is \( \epsilon_0 \) = permittivity of free space

• A. \( \frac{1}{2} \epsilon_0 \frac{EA}{d} \)
• B. \( \frac{1}{2} \epsilon_0 E^2 A d \)
• C. \( \frac{1}{2} \epsilon_0 \frac{A d}{E^2} \)
• D. \( \frac{1}{2} \epsilon_0 E^2 A \)

Hint:

In capacitor problems, the energy stored is related to the electric field, the area of the plates, and the distance between them.

Answer 1

The Correct Option is B

Step 1: Understanding the formula for energy stored in a capacitor.
The energy stored in a parallel plate capacitor is given by: \[ U = \frac{1}{2} \epsilon_0 E^2 A d \] Where: - \( E \) is the electric field, - \( A \) is the area of each plate, - \( d \) is the distance between the plates, - \( \epsilon_0 \) is the permittivity of free space. Thus, the correct answer is (B) \( \frac{1}{2} \epsilon_0 E^2 A d \).