i do not think you provided enough information
you have specified a magnetic field in 3 space.
in mechanics, we talk about the state of an object, including things like position, velocity, acceleration, momentum, angular momentum, etc
and use state variable analysis systems (Hamiltonian mechanics, Lagrangian mechanics) to determine the behavior in the future (or the past).
similar things are done in circuits.
what do you want the state of?
how does this thing interact with the magnetic field?
you need to provide more information so maybe some help can be provided