Final answer:
The magnetic field strength around a long straight current-carrying wire decreases with increasing distance from the wire, as described by the equation B = µ₀I / (2πr). The right-hand rule is used to determine the direction of this field.
Step-by-step explanation:
The relationship between the distance of a current-carrying wire and a dipole magnet's magnetic field strength is governed by the physical law that describes the intensity of the magnetic field around the wire. The magnetic field strength of a long straight wire carrying an electric current is calculated using the equation B = µ₀I / (2πr), where B is the magnetic field strength, µ₀ is the magnetic permeability of free space (4π x 10-7 T·m/A), I is the current flowing through the wire, and r is the shortest distance from the wire to the point at which the field is being measured.
According to this equation, the magnetic field strength decreases as the distance r from the wire increases, indicating an inverse relationship between the two. Furthermore, using the right-hand rule, one can determine the direction of the magnetic field, which forms concentric circles around the wire. For a significant force comparable to Earth's magnetic field to be observed, the current does not need to be extremely large, as historical experiments by Oersted have shown.