The local field potential (LFP) is among the most important experimental measures when probing neural population activity, but a proper understanding of the link between the underlying neural activity and the LFP signal is still missing. Here we investigate this link by mathematical modeling of contributions to the LFP from a single layer-5 pyramidal neuron and a single layer-4 stellate neuron receiving synaptic input. An intrinsic dendritic low-pass filtering effect of the LFP signal, previously demonstrated for extracellular signatures of action potentials, is seen to strongly affect the LFP power spectra, even for frequencies as low as 10 Hz for the example pyramidal neuron. Further, the LFP signal is found to depend sensitively on both the recording position and the position of the synaptic input: the LFP power spectra recorded close to the active synapse are typically found to be less low-pass filtered than spectra recorded further away. Some recording positions display striking band-pass characteristics of the LFP. The frequency dependence of the properties of the current dipole moment set up by the synaptic input current is found to qualitatively account for several salient features of the observed LFP. Two approximate schemes for calculating the LFP, the dipole approximation and the two-monopole approximation, are tested and found to be potentially useful for translating results from large-scale neural network models into predictions for results from electroencephalographic (EEG) or electrocorticographic (ECoG) recordings.