Solenoid Design -- Answer EITHER this question OR one of the two preceding!

You are given a certain volume V of copper from which to make wire with a square cross section. The wire you make is then used to wind a one-layer solenoid as shown. (Ignore the practical necessity for insulation between the wires and pretend that they can be wound so that the distance between turns is exactly the width of the wire.)

Your goal is to generate the highest possible magnetic field at the centre of the solenoid.

1.

[6 marks] For wire of a given cross section and for a given current I in the wire, should you make the inside diameter of the solenoid large or small? Explain.

2.

[6 marks] For a given inside diameter and for a given voltage ${\cal E}$ applied to the solenoid, should you make the wire long and thin or short and thick? Explain.