Intensity of an electric field (E) depends on distance r due to a dipole, is related as

Options

A. `Eprop (1)/(r)`
B. `E prop (1)/(r^(2))`
C. `E prop (1)/(r^(3))`
D. `E prop (1)/(r^(4))`

Answer

To solve the question regarding how the intensity of an electric field (E) depends on the distance (r) due to an electric dipole, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Electric Field Intensity due to a Dipole**:
The electric field intensity (E) due to an electric dipole can be expressed in two different positions: axial and equatorial.

2. **Identify the Formulas**:
- For the **axial position**, the formula for electric field intensity is:
\[ E_{\text{axial}} = \frac{1}{4 \pi \epsilon_0} \cdot \frac{2P}{r^3} \]
- For the **equatorial position**, the formula is:
\[ E_{\text{equatorial}} = \frac{1}{4 \pi \epsilon_0} \cdot \frac{P}{r^3} \]
Here, \( P \) is the dipole moment and \( r \) is the distance from the dipole.

3. **Analyze the Dependence on Distance (r)**:
- In both formulas, we can see that the electric field intensity \( E \) is inversely proportional to \( r^3 \).
- This means that as the distance \( r \) increases, the intensity of the electric field \( E \) decreases with the cube of the distance.

4. **Conclusion**:
Therefore, we conclude that the intensity of the electric field \( E \) due to an electric dipole is inversely proportional to the cube of the distance \( r \):
\[ E \propto \frac{1}{r^3} \]

5. **Select the Correct Option**:
Based on the analysis, the correct option that matches our conclusion is:
- **Option C**: \( E \) is inversely proportional to \( r^3 \).