Hello ,This image represents surface charges in a circuit caused by the battery's electric field, if you were to place an other electric field source of the same magnitude (but not connecting it to the circuit (on top of the battery or under it)) and placing so it has the same direction of the battery's electric field for me it would do 2 things :
First, since they are in the same direction their power will add up resulting in a doubled potential difference (e.g voltage) (well not totally since the distance at least a bit more), this will translate to the surfaces charges as a double of their density everywhere to maintain the same electric field inside the wire.
Second, The battery will get used more quickly due to the higher current.
However I know that this is wrong because :
This requires if I place the other electric field source to counter act the electric field of the battery, or if the other electric field is stronger will imply many weird reactions(after thinking about it you need a really strong second battery) .
The evenements I describe don't seem to really happen in the real life,
So if someone could show me the error in my reasoning,Thanks. TLDR: In a circuit why dosen't the electric field of other external things even help a tiny bit when stacking with the battery's electric field.