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What gauge wire should I use?

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At those current levels, you should be using Triax cables with a guard. Triax has 2 shields and a center conductor. The outer shield is ground and the inner shield is driven at the same potential as the inner conductor. Triax cables look like BNC cables. There are two, three and 4 lug triax cables. 3 lug is common on newer instrumentation. A 1 meter cable with connector will run you about $150 USD.
 
Why the run length matters?

Intrigued
 
All these responses so far are interesting especially considering there is no way to answer the question without knowing what kind of signal will be transferred over the wire... Every suggestion so far is at best a wild incomplete guess.

dist1nct needs to qualify the frequency and the acceptable voltage drop and possible noise issues, as he mentioned pico amp currents which require special considerations.
 
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