Final answer:
The magnetic force in a static magnetic field is non-conservative and does not have a scalar potential function; instead, its behavior is described by Ampère's law and magnetic vector potential.
Step-by-step explanation:
You've asked about the potential function for the magnetic force when the magnetic field is static. It's important to clarify that, contrary to the electrostatic force, which is conservative and has a well-defined potential energy, the magnetic force is intrinsically non-conservative when dealing with static fields. The characteristic of a conservative force is that the work done by the force on a charged particle is independent of the path taken and only depends on the initial and final positions. In magnetic fields, however, there is no scalar potential function that can describe the potential energy for magnetic forces as there is with the electrostatic force. Instead, the behavior of a static magnetic field is better understood in terms of magnetic vector potential and through Ampère's law.