Abstract
In order to understand a possible decay modes of a neutron star magnetic field, we used electron-magnetohydrodynamics equations to calculate the evolution of a specific configuration in a solid sphere. Assuming a high conductivity, we found that the evolution of a purely toroidal field can be written in terms of the dissipationaless Burger equation, which has a family of stationary solutions. Introducing a small perturbation in the stationary toroidal field, we found that the poloidal component of the perturbation grows with time. Therefore, a toroidal magnetic field is unstable to poloidal perturbations under Hall effect. This instability under Hall effect was found numerically in the works of Urpin and Shalybkov and Reinhardt and Geppert.