Coil B field strength with different diameters

[girts]

Hi, I have a quick question.

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

 

[mfb]

What exactly do you call "strength of the magnet"? Peak magnetic field flux density? Overall flux? Total energy stored in the magnet?

The current will be lower in the thicker coil, right.

 

[anorlunda]

If you Google "transformer design calculator" you'll find a number of resources like this one
http://www.dicks-website.eu/coilcalculator/index.html

They allow you to play with all the parameters and dimensions and will calculate the results.

 

[girts]

Ok I'll try to make myself more clear, imagine that my rod is a rod at the middle and has plates of certain diameter at the ends, now the goal here is to have a higher flux density at those plates at the ends, now the plates are the same diameter for both rods but the two rods themselves are physically different as one has a smaller diameter while the other one has a larger diameter.
assuming I wrap the same gauge copper wire with the same number of turns around each one and apply the same Voltage aka PD across those two coils which one will have a higher current and so a higher flux density at the ends? My reasoning is the one which is wound around the rod with the smaller diameter because for the same number of turns the length of wire is less so less resistance and higher current?

I hope you understood my idea?thanks.

 

[mfb]

The smaller coil has a larger expansion ratio between coil part and disk part, that will reduce the magnetic field more. I don't see how you could get even remotely uniform magnetic fields at the disks however, assuming an expansion ratio that is not too close to 1.