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The more options I have to get the desired results the better chance I have of achieving them. So, thanks for all this info.

I appreciate all the help, I will post my results

Can I use a 15 volt battery with this application? Also, x can be 10.

How much bigger would I have to make electromagnet core, so that the coil would so close to the gap?

Is there a place where I can send them your sketch with figures and they can plug it into there electromagnetic field simulation software to test it.

Yes, 5 inches is maximum length of magnet

Also, what are the dimensions of the pole faces?

I appreciate all your help. Do you know where I can have a core that shaped machined?

The field needs to be uniform across an air gap of 3/4" by 1". It can be up to 5" long

Is there some place I can have this built

A 3 inch by 3 inch area this electromagnet needs to fit. I need the field to be across the c core poles and mostly uniform

I want to build a c frame electromagnet that will be powered with a variable dc source range of 3 to 24 volts. I need to create 200 gauss to 800 gauss in a 3/4" air gap. The c frame made of iron can be 2 inches on each side and maybe tapered down at the pole tops to help concentrate flux in air...