The standard explanation is that the magnetic field stores the energy but when I start considering different sizes of a single loop inductor with a current flowing in it things start to get a bit vague. As the loop diameter is increased the inductance goes up so the single loop can store more energy. At small diameters the magnetic field across the loop is a reasonable value but if the loop was 1 mile across or 100 miles it is difficult to see how any part of the loop is any different to a straight piece of wire that doesn't have inductance. Is it the case that a straight piece of wire stores energy in its magnetic field when current flows?
Yes, a straight length of wire has inductance, because it is surrounded by a magnetic field and the magnetic field stores energy. You can calculate the inductance per unit length by calculating the B-field around the wire and integrating it over all space. Here's a paper that does the calculation: www.g3ynh.info/zdocs/refs/NBS/Rosa1908.pdf
Straight pieces of wire do have inductance, but in practice it is often small enough to ignore. Also the current through a straight wire can't just appear and disappear "by magic" at the ends of the wire, and the complete electrical circuit might behave more like a loop even if part of it is a "straight wire". http://www.ee.scu.edu/eefac/healy/indwire.html
When you calculate inductance on a straight wire, if one wire is X miles long and another wire with the same diameter is 2X miles long, does the total inductance simply double? I was thinking about power transmission lines which can be a thousand miles long, is inductance causing an extra vector of power loss? Over and above ohmic losses? Or is such inductance just too low a value to effect long distance power lines? In that regard it would seem lower frequencies would produce lower losses. I wonder if that is what Edison was thinking about when he was touting DC as a power carrier?
Yes the wire has inductance but as Alephzero says the inductance of the wire in a very large loop doesn't account for the inductance. What I am getting at is if the loop is very large like 1000 miles the inductance is very large but the field across the loop decreases at a squared rate so at some point that too will become negligible so how can the inductance be large since no field would be measured across the loop of a large inductor.
Your reasoning seems to be based on a 0/0 argument. When you are trying to 'reason out' the limits of what happens as one quantity increases and another decreases, you can't be sure of your conclusions. The simple formula for inductance of a coil implies dimensions much less than the wavelength involved so it is not reasonable to consider the diameter to be more. You have to consider the radiative effect, once the structure is a significant fraction of a wavelength and the energy is no longer just 'stored'.
The same laws of physics apply to a loop of wire you can hold in your hand and one that circles the solar system. If you could string such a long wire, and overcome losses (or use superconducting metal), you would need to spend a huge amount of energy to get 1 amp of DC flowing through it, energy which would be ultimately stored in the static magnetic field around that long wire. First, consider that a lot if the magnetic field energy is very close to the wire. Decreasing the wire diameter by half has the same effect as doubling the size of the loop. Second, it is true that the magnetic field decreases rapidly with distance, but you are integrating it over three dimensional space whose volume is increasing rapidly.
A straight wire has an inductance per unit length, which varies very slowly with L/d, more or less like its Log - hence you can take 500 to 700nH/m in most cases. Doubling L or halving d has the same little effect per unit length, but in addition, doubling the length about doubles the self-inductance. Parallel wires add their induction and this increases the inductance, while opposing currents subtract their effects and reduce the inductance. That's why a loop gives a bit less nH/m than a straight wire, as the return current reduces the induction. As well, wires sum less than 2* the induction of a single wire, even if close to an other, so the induced voltage and the self-inductance is less than N^{2} times the self-inductance of a single turn, at identical wire diameter. If an annular coil is small and thick, you can multiply some 400nH/m by N^{2}. If the coil has a different shape, for instance a solenoid or a toroid, the smaller interaction between the turns farther apart gives a smaller inductance per unit length - but the losses may decrease even faster.
Thanks for your explanations guys. I was under the impression that coils had greater inductance than straight wires but if it is the other way around then size of loop and the magnetic coupling across them is irrelevant to my original question. The answer is that the magnetic field around the wire can be viewed as a tension of space that springs back when the current stops. A bit like a bow wave on a zero mass boat where if the boat engine is cut the boat would be pushed backwards by the bow wave levelling out if you get my drift.