Based upon the membrane currents generated by an action potential in a
biologically realistic model of a pyramidal, hippocampal cell within rat CA1,
we perform a moment expansion of the extracellular field potential. We
decompose the potential into both inverse and classical moments and show that
this method is a rapid and efficient way to calculate the extracellular field
both near and far from the cell body. The action potential gives rise to a
large quadrupole moment that contributes to the extracellular field up to
distances of almost 1 cm. This method will serve as a starting point in
connecting the microscopic generation of electric fields at the level of
neurons to macroscopic observables such as the local field potential
