= Solution
\b[Why the shape is immaterial far away.] Partition an arbitrary small planar loop into small rectangular loops with the same oriented current. Currents on internal shared edges cancel, leaving only the original boundary. Their <magnetic dipole moments> add to $\mathbf m=I\mathcal A\mathbf n$, with $\mathcal A$ the enclosed area. Far enough away, the leading fields add as dipoles at the same position. The general <magnetic dipole field> is
$$
\boxed{\mathbf B=\frac{\mu_0}{4\pi r^3}
\left[3(\mathbf m\cdot\widehat{\mathbf r})\widehat{\mathbf r}-\mathbf m\right].}
$$
Higher spatial multipoles contain shape-dependent corrections. The axial and transverse results above are the special directions of this expression.
\b[The aligned terrestrial model.] Take the moment to point toward geographic south. At northern latitude $\lambda$, the <magnetic dipole inclination versus latitude> gives local northward and downward components
$$
B_N=B_{\rm eq}\cos\lambda,\qquad B_D=2B_{\rm eq}\sin\lambda.
$$
Using the specified $\lambda=53^\circ$ and $B_{\rm eq}=35\ \mathrm{\mu T}$,
$$
B_N\simeq21.1\ \mathrm{\mu T},\qquad B_D\simeq55.9\ \mathrm{\mu T},
$$
$$
\boxed{|\mathbf B|=B_{\rm eq}\sqrt{1+3\sin^2\lambda}
\simeq59.7\ \mathrm{\mu T},\quad
\iota=\arctan(2\tan\lambda)\simeq69.4^\circ.}
$$
The direction is geographic north and $69.4^\circ$ below horizontal, with no eastward component in this ideal model. These values use the latitude printed in the paper.
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