We study the stability of a ferrofluid cylinder placed in a non-magnetic fluid and immersed in an azimuthal magnetic field. The field is created by a rectilinear wire traversed by a current and located at the cylinder centre. The studied case is represented on figure 1a. After formulating the problem of ferrohydrodynamics, we conduct linear stability analysis. The developed model is then compared with experimental data taken from the literature for the unstable and stable cases delimited by a magnetic Bond number (Bom) equalling unity. A good agreement with the data is found concerning the values of the wavelength and the growth rate of the instability1,2. However, in the experiment, the growth rate is observed to be higher for the thinner layers of ferrofluid, in disagreement with the theoretical predictions. In order to solve this issue and further explore the comparison we have conducted a new campaign of experiments, using one cuvette, one pair of ferrofluid and surrounding fluid with the same density, two copper wires of different radii (Rw), various thicknesses of ferrofluid layers (R0) and various current intensities (I). Figure 1b shows the drop-on-wire structure obtained at the end of the experiment consisting in decreasing the current intensity from a stable case (Bom>1) to an unstable case (Bom<1). The results from image analysis provide more insight into the wire effect on the drop formation on wire and at the same time solve the issue raised by the previous experiments. In addition, they bring new insight into the first nonlinear effects, thanks to measurements of the growth and the spacing of the satellite drops on wire, that will be also theoretically investigated though a weakly nonlinear stability analysis. The aim of this work on ferrofluid cylinders is to identify new possibilities of controlling drops formed by liquid jet breakup for applications in the printing domain and medical field. 1 Canu and Renoult, J. Fluid Mech. 915, 137 (2021). 2 Canu and Renoult, J. Fluid Mech. 927, 36 (2021).