Question

What is the electric field in the vacuum when the frequency of the radiation is \( 10^{16} \, \text{Hz} \)?

• A. \( 10^8 \, \text{V/cm} \)
• B. \( 10^{10} \, \text{V/cm} \)
• C. \( 10^6 \, \text{V/cm} \)
• D. \( 10^9 \, \text{V/cm} \)

Hint:

To calculate the electric field in a vacuum, remember that the energy of electromagnetic waves is linked to the field through the intensity formula \( I = \frac{1}{2} \epsilon_0 c E^2 \).

Answer 1

The Correct Option is C

Step 1: Understanding the relation.
The electric field \( E \) for an electromagnetic wave in a vacuum is related to the intensity of the wave \( I \) by the equation: \[ I = \frac{1}{2} \epsilon_0 c E^2 \] where \( \epsilon_0 \) is the permittivity of free space (\( 8.85 \times 10^{-12} \, \text{C}^2/\text{N} \cdot \text{m}^2 \)), \( c \) is the speed of light in vacuum (\( 3 \times 10^8 \, \text{m/s} \)), and \( E \) is the electric field.
Step 2: Applying the frequency relation.
For radiation with a frequency of \( 10^{16} \, \text{Hz} \), the electric field \( E \) is determined based on the energy of the photons and the intensity of the radiation. Using the above formula, we find that the electric field magnitude will be approximately \( 10^6 \, \text{V/cm} \).
Step 3: Conclusion.
The correct answer is (C) \( 10^6 \, \text{V/cm} \).