My aim of this design is to use a coil energized by a small current to generate a magnetic field that is equivalent to the one generated by a larger current flowing in a wire. For example, the magnetic flux at the centre point of the coil with 10A DC current is equivalent to that at 10cm away from a 100A current carrying wire. It is an open design so the "current gain" can be chosen by myself.

Here is the formula I am using: B=(1/2)*n*I*μ*(1/sqrt( r^2 + (l^2)/4 )) where r is radius, l is total length, n is turn number. From the formula, we can see that radius, total length of the coil and turn numbers are parameters that we need to determine. Here are my ideas:

Since we need to put a small sensor at the centre point for magnetic flux, I decided to take 10cm radius and 20cm length so that the small sensor can be considered as a point. Therefore, the magnetic flux there can be perfectly uniform to avoid any potential error. The turn number was randomly chosen as 10. With parameter decided, I can collect data and establish a datasheet to get final "current gain".

I want to ask whether idea is correct? Is there any other aspects that need to be considered in terms of engineering design? Please give me some ideas or suggestions to build this coil.

Thank you all