What's an ideal wire?

I'm not talking about an ideal wire in a circuit (a wire with infinite conductance).

I'm talking about an ideal wire in the case of the magnetic field of an infinite current carrying wire. What dimensions must an ideal wire have to better approximate an infinite current carrying wire in terms of its magnetic field?

For example, for a parallel plate capacitor, the field better approximates two infinite plates as $$A >> d$$ where $A$ is the area and $d$ is the length.

Or for a solenoid, the field better approximates an infinite solenoid as

$$L>> d$$ where $L$ is the length and $d$ is the diameter.

For a current carrying wire, what dimensions must it have to better approximate an infinite wire?

• I believe the process is to take the expression for a finite wire, then send one or more parameters to whatever they need to be in order to extract the infinite wire case.
– BMS
Mar 13, 2014 at 14:59
• by "infinite current carrying wire" do you mean the current is infinite or the length of the wire is infinite? If you mean the length of the wire is infinite, then L>>d for a straight wire. If the wire isn't straight, but is an infinitely repeating pattern, repeating with respect to a particular direction, say an infinite sine wave pattern or an infinite helix, the length of the pattern should be large compare to the width of the pattern. Mar 13, 2014 at 15:01
• @DavePhD I mean the length in infinite, not the current. Is $d$ the diameter of the wire?
– user41086
Mar 13, 2014 at 15:10
• yes (12 characters required) Mar 13, 2014 at 15:16