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For this question, we'll first define a number, called the "linear density of the coil" which is exactly the one the exercise gives us, in a unit of turns per length. The magnetic field can be calculated as:
[tex]B=\mu_0in[/tex]Where n is the linear density.
In our case, as the coils carry current in opposite directions, the generated magnetic fields will be opposed, and we'll have:
[tex]B=B_{outer}-B_{inner}=\mu_0*(51*10^2*21.68-259*10^2*7.577)[/tex]Please note that we had to multiply by 10^2, in order to convert turns/cm to turns/m
Then, our final magnetic field will be:
[tex]|B|=0.107664T=107664\mu T[/tex]Our final answer is B=107664uT
