Local field potentials are important indicators of in vivo neural activity. Sustained, phase-locked, sound-evoked extracellular fields in the mammalian auditory brainstem, known as the auditory neurophonic, reflect the activity of neurons in the medial superior olive (MSO). We develop a biophysically based model of the neurophonic that accounts for features of in vivo extracellular recordings in the cat auditory brainstem. By making plausible idealizations regarding the spatial symmetry of MSO neurons and the temporal synchrony of their afferent inputs, we reduce the challenging problem of computing extracellular potentials in a 3D volume conductor to a onedimensional problem. We find that postsynaptic currents in bipolar MSO neuron models generate extracellular voltage responses that strikingly resemble in vivo recordings. Simulations reproduce distinctive spatiotemporal features of the in vivo neurophonic response to monaural pure tones: large oscillations (hundreds of microvolts to millivolts), broad spatial reach (millimeter scale), and a dipole-like spatial profile. We also explain how somatic inhibition and the relative timing of bilateral excitation may shape the spatial profile of the neurophonic. We observe in simulations, and find supporting evidence in in vivo data, that coincident excitatory inputs on both dendrites lead to a drastically reduced spatial reach of the neurophonic. This outcome surprises because coincident inputs are thought to evoke maximal firing rates in MSO neurons, and it reconciles previously puzzling evoked potential results in humans and animals. The success of our model, which has no axon or spike-generating sodium currents, suggests that MSO spikes do not contribute appreciably to the neurophonic.