  We consider non-Lorentzian expansions, Galilean and Carrollian, of the
Lorentz force equation in which both the particle position and the
electro-magnetic field are expanded. There are two well-known limits in the
case of a constant field, called electric and magnetic, that are studied
separately. We show that the resulting equations of motion follow equivalently
from considering a non-linear realisation of a certain infinite-dimensional
algebras.
