how many amps can a square inch of copper bar carry at any temperature rise?
There is always some temperature rise, even with a mA of current. You need to define a limit, such as 100 degrees C rise. Also depends on surroundings, open air, in a conduit, etc.
It will depend on the type of insulation. A naked copper bar can carry huge amounts of current, and even turn red hot. If it runs too hot it will oxidize after a while. The amount of amps will depend on the resistance and voltage applied. Use ohm's law and the copper resistivity eqn. to find out exactly how much. The temperature rise will depend on the ambient temperature and the type of cooling, i.e., natural or forced air flow. .
