# Superposition of Magnetic Fields

1. Apr 26, 2009

### latentcorpse

this problem relates to finding the on axis field of two coaxial coils of the same radius when they have their currents in the same/opposite directions.
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?