C

To determine the relationship between the electric field (E) and electric potential (V) of a dipole, we can use the formulas for an electric dipole.
The electric dipole moment is defined as \( p = q \cdot d \), where \( q \) is the charge and \( d \) is the separation between the two charges. The electric field due to a dipole at a point in space can be expressed as:
\( E = \frac{1}{4\pi \epsilon_0} \cdot \frac{2p \cdot cos(\theta)}{r^3} \)
where \( r \) is the distance from the dipole center and \( \theta \) is the angle with respect to the dipole axis.
The potential due to a dipole is given by:
\( V = \frac{1}{4\pi \epsilon_0} \cdot \frac{p \cdot cos(\theta)}{r^2} \)
Therefore, comparing the dependency of E and V with respect to r, we find that the correct option is C, which shows these relationships accurately.