A current carrying wire will produce its own magnetic field, which means that if a wire is placed between the north and south poles of two magnets, the two magnetic fields will interact, resulting in a force on the wire.
The strength of the force can be calculated using the equation F = B * I * L, where F stands for force, B stands for magnetic flux density, L stands for length and I stands for current.
If a 10 centimeter piece of wire with a 5 amp current flowing through it is placed at 90 degrees into a magnetic field that has a magnetic flux density of 0.4 teslas, it will experience a force of 0.2 newtons.