Let $\Omega$ be a $3-D$ bounded domain with a hole of radius $\mathcal{O}(\epsilon)$ and centre $x_0$, say $\Omega_0$, that is removed from the $\Omega$. Define $v_c (y)$ such that it satisfies, \begin{align*} \Delta_y v_c &= 0 \quad y \ne \Omega_0 \\ v_c &= 1 \quad y \in \partial \Omega_0 \\ v_c & \rightarrow 0 \quad \text{as} \quad |y| \to \infty \end{align*} So, $v_c$ must have far field asymptotic behaviour given by, \begin{align*} v_c \sim \dfrac{C}{|y|} + \dfrac{p y}{|y|^3} + \mathcal{O}(|y|^{-3}), \quad \text{as} \quad |y| \to \infty \end{align*} , where $C \ge 0$ is called the electrostatic capacitance of $\Omega_0$, and the vector $p$, is called the dipole moment of $\Omega_0$.
It will be a great help if someone tells how to get such an expression for $v_c$