Final answer:
The greatest self-inductance in a wire is achieved by coiling it tightly, creating a solenoid, which maximizes the magnetic field lines intersection per unit current. The least self-inductance is attained by stretching the wire straight, minimizing the overlapping of magnetic field lines.
Step-by-step explanation:
The shape of the wire significantly affects its self-inductance, which is a measure of how well a conductor opposes the change of electric current passing through it. Due to the properties of magnetic fields and induction, the greatest self-inductance is achieved when the wire is coiled into a tightly wound solenoid. This is because the coiling of the wire increases the number of magnetic field lines that intersect the loop per unit current, thus enhancing the inductive effect. On the other hand, the least self-inductance occurs when the wire is stretched out straight, as this configuration minimizes the overlapping of magnetic field lines and thus reduces the inductive effect.
Answer a) Coil the wire tightly for the greatest self-inductance, stretch it straight for the least, is correct. The shape does indeed affect self-inductance contrary to option c), and thickness is not directly related to self-inductance as suggested by d).