We propose a variational method to solve Maxwell’s equations in singular axisym- metric domains with arbitrary data. Considering the equations written in (r, θ, z), we use a Fourier transform in θ to reduce 3D equations to a series of 2D equations, depending on the Fourier variable k. We then consider the case k = 0, corresponding to the full axisymmetric case, and focus on the computation of the magnetic field. The non stationary variational formu- lation to compute the solution is derived, and solved with a finite element approach. Numerical examples are shown.