Contents 
We consider a magnetic operator of AharonovBohm type with Dirichlet boundary conditions in a planar, bounded and simply connected domain $\Omega$
\begin{equation}
(i \nabla + A_{a})^2 u = \Delta u + 2 i A_{a} \cdot \nabla u + i \nabla \cdot A_{a} u + A_{a}^2 u,
\end{equation}
where for each $a \in \Omega$ the magnetic potential is given by
\begin{equation}
A_{a}(x_{1}, x_{2}) = \alpha (  \frac{x_{2}  a_{2}}{xa^2}, \frac{x_{1}  a_{1}}{xa^2} ).
\end{equation}
We analyse the behavior of its eigenvalues as the singular pole $a$ moves in the domain. For any value of the circulation $\alpha$ of the potential, we prove that the kth magnetic eigenvalue converges to the kth eigenvalue of the Laplacian as the pole approaches the boundary. We show that the magnetic eigenvalues depend in a smooth way on the position of the pole, as long as they remain simple. In case of halfinteger circulation, we show that the rate of convergence depends on the number of nodal lines of the corresponding magnetic eigenfunction. In addition, we provide several numerical simulations both on the circular sector and on the square, which find a perfect theoretical justification within our main results. 
