The electrostatic potential due to an electric dipole at a distance 'r' varies as

Options

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

Answer

To solve the question regarding the variation of the electrostatic potential due to an electric dipole at a distance 'r', we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Electric Dipole**:
An electric dipole consists of two equal and opposite charges separated by a distance. The dipole moment (P) is defined as the product of the charge (q) and the separation distance (d):
\[ P = q \cdot d \]

2. **Recall the Formula for Electric Potential (V)**:
The electric potential \( V \) due to an electric dipole at a point in space is given by the formula:
\[ V = \frac{1}{4 \pi \epsilon_0} \cdot \frac{P \cos \theta}{r^2} \]
where:
- \( P \) is the dipole moment,
- \( \theta \) is the angle between the dipole moment and the line joining the dipole to the point of interest,
- \( r \) is the distance from the dipole to the point where the potential is being calculated,
- \( \epsilon_0 \) is the permittivity of free space.

3. **Analyze the Dependence on Distance (r)**:
From the formula, we can see that the potential \( V \) varies inversely with the square of the distance \( r \). This means:
\[ V \propto \frac{1}{r^2} \]

4. **Identify the Correct Option**:
Given the options:
- Option 1: \( r \)
- Option 2: \( \frac{1}{r} \)
- Option 3: \( \frac{1}{r^2} \)
- Option 4: \( \frac{1}{r^3} \)

Since we have established that the potential varies as \( \frac{1}{r^2} \), the correct answer is:
\[ \text{Option 3: } \frac{1}{r^2} \]

### Final Answer:
The electrostatic potential due to an electric dipole at a distance 'r' varies as \( \frac{1}{r^2} \).

---