(A) : A light beam or a radio beam of same intensity will have same values of `vecE` and `vecB` (R) : A light beam or a radio beam of same intensity will have different values of `vecE` and `vecB`

Options

A. Both 'A' and 'R' are true and 'R' is the correct explanation of 'A'.
B. Both 'A' and ’R' are true and 'R' is not the correct explanation of 'A
C. A' is true and 'R' is false
D. 'A' is false and R' is true

Answer

To analyze the statements given in the question, we need to understand the relationship between the electric field (\( \vec{E} \)) and magnetic field (\( \vec{B} \)) in electromagnetic waves, particularly in light and radio waves.

### Step-by-Step Solution:

1. **Understanding the Intensity of Electromagnetic Waves**:
The intensity \( I \) of an electromagnetic wave is related to the electric field \( \vec{E} \) and magnetic field \( \vec{B} \) by the formula:
\[ I = \frac{1}{2} \epsilon_0 c E^2 = \frac{1}{2} \frac{B^2}{\mu_0} c \]
where \( \epsilon_0 \) is the permittivity of free space, \( \mu_0 \) is the permeability of free space, and \( c \) is the speed of light in vacuum.

2. **Relating \( \vec{E} \) and \( \vec{B} \)**:
In electromagnetic waves, the relationship between the electric field and magnetic field is given by:
\[ c = \frac{E}{B} \]
This means that for a given intensity, the values of \( \vec{E} \) and \( \vec{B} \) are not independent; they are related through the speed of light.

3. **Comparing Light and Radio Waves**:
Both light and radio waves are forms of electromagnetic radiation, but they differ in frequency and wavelength. However, if they have the same intensity, the relationship between \( \vec{E} \) and \( \vec{B} \) will still hold true.

4. **Analyzing the Statements**:
- **Statement (A)**: "A light beam or a radio beam of same intensity will have same values of \( \vec{E} \) and \( \vec{B} \)" is **incorrect**. While the intensity is the same, the actual values of \( \vec{E} \) and \( \vec{B} \) can differ due to their dependence on frequency.
- **Statement (R)**: "A light beam or a radio beam of same intensity will have different values of \( \vec{E} \) and \( \vec{B} \)" is **correct**. The values of \( \vec{E} \) and \( \vec{B} \) can vary based on the specific characteristics of the wave, even if the intensity is the same.

5. **Conclusion**:
The correct conclusion is that (A) is false and (R) is true. Therefore, the answer to the question is that (R) is correct while (A) is incorrect.