An `EM` wave radiates out wards from a dipole antenna with `E_(0)` as the amplitude of its electric filed vector. The electric field `E_(0)` which transports significant energy from the source falls off as

Options

A. `(1)/(r^3)`
B. `(1)/(r^2)`
C. `(1)/(r)`
D. remains constant

Explanation

To solve the problem, we need to determine how the amplitude of the electric field vector \( E_0 \) of an electromagnetic (EM) wave radiating from a dipole antenna falls off with distance \( R \).

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The intensity \( I \) of the electromagnetic wave is related to the electric field \( E \) by the equation:
\[ I \propto E^2 \]
This means that the intensity is proportional to the square of the electric field amplitude.

2. **Intensity from a Dipole**:
For a dipole antenna, the intensity \( I \) at a distance \( R \) from the antenna falls off as:
\[ I \propto \frac{1}{R^2} \]
This indicates that as you move away from the antenna, the intensity decreases with the square of the distance.

3. **Relating Electric Field to Intensity**:
From the relationship \( I \propto E^2 \), we can express the electric field in terms of intensity:
\[ E^2 \propto \frac{1}{R^2} \]
Taking the square root of both sides gives:
\[ E \propto \frac{1}{R} \]
Therefore, the amplitude of the electric field \( E_0 \) falls off as \( \frac{1}{R} \).

4. **Conclusion**:
Based on the above analysis, we conclude that the electric field \( E_0 \) which transports significant energy from the source falls off as:
\[ E_0 \propto \frac{1}{R} \]
Thus, the correct option is **C: \( \frac{1}{R} \)**.