Final answer:
The extension of a wire of a fixed volume subjected to a constant force is inversely proportional to the cross-sectional area and directly proportional to the length. Therefore, it is proportional to the length of the wire itself.
Step-by-step explanation:
The question relates to the extension produced in a wire drawn to a certain length and subjected to a constant force in the context of magnetic fields. The provided formula for magnetic force, F = IIB sin θ, where I is the current, B is the magnetic field, and θ is the angle between the wire and the direction of the magnetic field, indicates that the magnetic force on a section of the wire is directly proportional to the length of the wire, l. However, for calculating the extension produced in the wire, Hooke's law and the concept of Young's modulus would be more applicable rather than the magnetic force formula.
Typically, the extension is inversely proportional to the cross-sectional area and directly proportional to the force and the length of the wire when considering a uniform material and cross-section. Since the volume is constant and equals the product of cross-sectional area and length (A × l), the longer the wire, the smaller the cross-sectional area, thereby, the greater the extension for a given force. Consequently, for a fixed volume of iron, the extension would be proportional to the length, so the correct answer would be D. I.