The magnetic field at any point near a permanent magnet is determined by the vector sum of the of each of the fields from all of the atomic dipoles within the magnet. Within another nearby magnet, each atomic dipole is subject to a torque which tends to align it with the field from magnet one, and a net force which depends of the gradient of the field from magnet one (at its location). A reasonable approximation for the net force and torque acting on each magnet may achieved by treating each magnet as a current carrying solenoid of the same size, shape, and dipole moment. Either of these would require a massive numeric simulation (for each relative position).

The magnetic field at any point near a permanent magnet is determined by the vector sum of the of each of the fields from all of the atomic dipoles within the magnet. Within another nearby magnet, each atomic dipole is subject to a torque which tends to align it with the field from magnet one, and a net force which depends of the gradient of the field from magnet one (at its location). A reasonable approximation for the net force and torque acting on each magnet may achieved by treating each magnet as a current carrying solenoid of the same size, shape, and dipole moment. Either of these would require a massive numeric simulation (for each relative position). For a rough approximation (which improves with distance) treat each magnet like an electric dipole. Find the “pole strength” and treat a “north pole” like a positive point charge.