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Say I have two metal rods or tubes and I want to make an electromagnet, one rod is with a diameter x and the other rod has a diameter of x2 (two times larger)

Now I take the same gauge copper wire and wrap an equal amount of turns around each of the two rods.

Then I take the same voltage and apply to both coils on both rods, the question is which will be a stronger magnet?

My reasoning here behind the question is this, if I'm not mistaken the strength of an electromagnet with a coil is determined by the current in the coil times the number of turns that coil has around a given area (rod), now in my case the number of turns is the same for both coils and the voltage applied to both coils is also the same but since one rod has a smaller diameter it means that overall to make the same number of turns requires a shorter copper wire than making the same number of turns on a larger diameter which would need a longer copper wire overall, so given both copper wires have the same "gauge" the longer wire will have a higher ohmic resistance so applying the same voltage will result in a lower current and a lower current times the same number of turns results in a weaker B field right?

So would I be correct in saying that given all other properties are the same , smaller diameter coils with the same gauge and turn count wire will have a stronger B field?

thanks