Local field potentials (LFPs) are routinely measured experimentally in brain tissue, and exhibit strong low-pass frequency filtering properties, with high frequencies (such as action potentials) being visible only at very short distances (approximately 10 microm) from the recording electrode. Understanding this filtering is crucial to relate LFP signals with neuronal activity, but not much is known about the exact mechanisms underlying this low-pass filtering. In this paper, we investigate a possible biophysical mechanism for the low-pass filtering properties of LFPs. We investigate the propagation of electric fields and its frequency dependence close to the current source, i.e., at length scales in the order of average interneuronal distances. We take into account the presence of a high density of cellular membranes around current sources, such as glial cells. By considering them as passive cells, we show that under the influence of the electric source field, they respond by polarization. Because of the finite velocity of ionic charge movements, this polarization will not be instantaneous. Consequently, the induced electric field will be frequency-dependent, and much reduced for high frequencies. Our model establishes that this situation is analogous to an equivalent RC circuit, or better yet a system of coupled RC circuits. We present a number of numerical simulations of an induced electric field for biologically realistic values of parameters, and show the frequency filtering effect as well as the attenuation of extracellular potentials with distance. We suggest that induced electric fields in passive cells surrounding neurons are the physical origin of frequency filtering properties of LFPs. Experimentally testable predictions are provided allowing us to verify the validity of this model.