1. Recall the formula for potential due to an electric dipole

At a point far from an electric dipole, the electrostatic potential is

$V = \frac{1}{4\pi\varepsilon_0}\frac{p\cos\theta}{r^2}$

where:

• $p$ is the dipole moment,
• $r$ is the distance from the dipole center,
• $\theta$ is the angle with the dipole axis.

2. Identify the dependence on $r$

From the formula,

$V \propto \frac{1}{r^2}$

So the electrostatic potential due to a dipole varies inversely as the square of distance.

3. Check the options

• A: $\dfrac{1}{r^3}$ → incorrect
• B: $\dfrac{1}{r}$ → incorrect
• C: $\dfrac{1}{r^2}$ → correct
• D: $r$ → incorrect

4. Final answer

The correct option is:

$\boxed{C\;:\;\frac{1}{r^2}}$

5. Comparison with stored answer

Stored correct answer: C

This matches the derived answer.