A 500 MCM wire with an insulation factor of 90 degrees C is rated at 430.
Most 400 amp services will use parallel wires on each leg to feed the circuit.
A 3/0 wire with an insulation factor of 75 and 90 degrees C is rated at 200 and 225 amps respectively.
The insulation rating of these conductors will be 600 volts.
Typically 400 kcmil in Copper or 600 kcmil in Aluminum.
The wire size depends on how much current it will conduct.
As a service entrance wire you need AWG # 3/0 gauge copper.
#6 bare copper wire.
The size of conductor needed will be a #14. It should be copper and have an insulation factor of 90 degrees C. The fact that it is a three phase load does not enter into the calculation of the wire size.
Presuming that you would like the least expensive installation, the following is calculated on overhead aluminum wire. The wire size needed to hold the voltage drop to 3% would be 3/0 MCM. If the installation could be run on 240 volts then the wire size can be reduced to #2.
4 copper
The wire size depends on how much current it will conduct.
AWG # 10 wire on 30 amp circuit.
If you use 250 or 300 MCM wire you will need a 2 1/2" weather head. If you use 300 MCM wire then you will need a 3" weather head.
you must run the proper size wire based on the ampacity needed, wire must have four conductors including the gound
As a service entrance wire you need AWG # 3/0 gauge copper.
#6 bare copper wire.
If it is a 110 volt light it can safely run on a 20 amp circuit with AWG # 12 wire.
200 amp service in chicago uses 3 aught.
Not in the US of A.
It depends on the length of the run
I would use AWG # 4 copper.