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\section*{Appendix: Helmholtz coils}
-The term Helmholtz coils refers to a device for producing a region of nearly uniform magnetic field. It is named in honor of the German physicist Hermann von Helmholtz. A Helmholtz pair consists of two identical coils with electrical current running in the same direction that are placed symmetrically along a common axis, and separated by a distance equal to the radius of the coil $a$. The magnetic field in the central region may be calculated using the Bio-Savart law:
+The term Helmholtz coils refers to a device for producing a region of
+nearly uniform magnetic field. It is named in honor of the German physicist
+Hermann von Helmholtz. A Helmholtz pair consists of two identical coils
+with electrical current running in the same direction that are placed
+symmetrically along a common axis, and separated by a distance equal to
+the radius of the coil $a$. The magnetic field in the central region may be
+calculated using the Biot-Savart law:
\begin{equation}\label{emeq_apx}
B_0=\frac{\mu_0Ia^2}{(a^2+(a/2)^2)^{3/2}},
\end{equation}