Question

What is the energy stored per unit volume in vacuum, where the intensity of electric field is \(10^3 \, \text{V m}^{-1}\)?
(Given: \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1}\text{m}^{-2} \))

• A. \( 8.8 \times 10^{-5} \, \text{J m}^{-3} \)
• B. \( 4.425 \times 10^{-8} \, \text{J m}^{-3} \)
• C. \( 8.85 \times 10^{-6} \, \text{J m}^{-3} \)
• D. \( 4.425 \times 10^{-6} \, \text{J m}^{-3} \)

Hint:

Energy density of an electric field depends on the square of electric field strength.

Answer 1

The Correct Option is D

Step 1: Formula for energy density of electric field.
Energy stored per unit volume is given by:
\[ u = \frac{1}{2} \varepsilon_0 E^2 \]
Step 2: Substituting given values.
\[ u = \frac{1}{2} \times 8.85 \times 10^{-12} \times (10^3)^2 \]
Step 3: Simplifying.
\[ u = \frac{1}{2} \times 8.85 \times 10^{-12} \times 10^6 \] \[ u = 4.425 \times 10^{-6} \, \text{J m}^{-3} \]
Step 4: Conclusion.
The energy stored per unit volume is \(4.425 \times 10^{-6} \, \text{J m}^{-3}\).