Can you derive the formula for calculating inductance in a copper coil?
Why is the square of the number of turns used?

Thanks

 

The square shows and tells you the character of the slope, or the rate of affect, or change.......when you vary N.

Did that mean anything?

 

Can you derive the formula for calculating inductance in a copper coil?
Why is the square of the number of turns used?

Thanks

The formulae that I have seen for an air cored coil are all approximations so I guess the answer is no, you can't derive a formula.
For ferrite cores there is an AL figure quoted. The inductance is the number of turns squared times this AL value.

Suppose you have two 1 turn coils with inductance L. When they are connected in series but far enough apart that their fields do not interact the inductance will be 2L. But now if we have a coil with two turns the field from each turn affects the other turn and this generates the square relationship. The two turn coil will have an inductance of 4L.

 

http://www.66pacific.com/calculators/coil-inductance-calculator.aspx

 

Or: https://www.allaboutcircuits.com/tools/coil-inductance-calculator/
Several different formulae for different styles of coil: http://www.teslascientific.com/products/coil-inductance-calculator/

 

The formulae that I have seen for an air cored coil are all approximations so I guess the answer is no, you can't derive a formula.

Agreed. I think I remember reading that Wheeler collected a lot of data and looked at many, many alternative expressions before settling on the formula now bearing his name.