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\section{Motivating the Derivation}  In pursuit of an empirically determined value for the electron charge-to-mass $e/m$ ratio we must guide electrons in a variable circular path using a homogeneous magnetic field. The Helmholtz configuration of two current-carrying coils with radius \textit{R} separated by a distance \textit{d} as shown in Figure\ref{fig1} Figure \ref{fig1}  provides the necessary field. To determine the magnetic field \textit{B} we will first find the magnetic field due to a single current-carrying loop using the Biot-Savaart Law.