Electric field intensity (E) due to an electric dipole varies with distance (r) of the point from the center of dipole as :

Options

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

Explanation

To determine how the electric field intensity (E) due to an electric dipole varies with the distance (r) from the center of the dipole, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Electric Dipole**:
An electric dipole consists of two equal and opposite charges (+q and -q) separated by a distance (d). The dipole moment (p) is defined as:
\[ p = q \cdot d \]

2. **Distance Consideration**:
We need to analyze the electric field at a point that is very far away from the dipole, specifically when the distance (r) is much greater than the separation distance (d) of the dipole. This is expressed as \( r \gg d \).

3. **Electric Field on the Axis of the Dipole**:
The electric field intensity (E) at a point on the axis of the dipole can be calculated using the formula:
\[ E = \frac{2kp}{r^3} \]
where \( k \) is Coulomb's constant.

4. **Electric Field on the Equatorial Line**:
For a point on the equatorial line (the line perpendicular to the dipole moment), the electric field intensity can be expressed as:
\[ E = \frac{kp}{r^3} \]

5. **Conclusion on the Variation of Electric Field**:
In both cases (on the axis and on the equatorial line), we observe that the electric field intensity (E) is inversely proportional to the cube of the distance (r):
\[ E \propto \frac{1}{r^3} \]

6. **Final Answer**:
Therefore, the correct statement regarding the variation of electric field intensity (E) due to an electric dipole with distance (r) is:
\[ E \text{ is inversely proportional to } r^3 \]