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the field from one coil is

B_z=\frac{\mu_0}{2} I R^2 \frac{R^2}{(z^2+R^2)^{3/2}}

now the field from a coil looks like that of a dipole i.e. it's symmetric above and below the axis. so if the coils have radius R and seperation 2d and i want the field a smaoll distance m from the midpoint and the currents are in the same direction i can get the field from the top as

\frac{\mu_0}{2} I R^2 \frac{R^2}{((z-m)^2+R^2)^{3/2}}

and from the bottom as

\frac{\mu_0}{2} I R^2 \frac{R^2}{((z+m)^2+R^2)^{3/2}}

and then hopefully superimpose.

but this is where im having difficulty making it into all one term (i don't want to leave my final answer as something + something else)

since m is small am i meant to taylor expand or something?