## 4 Discussion
A more accurate calculation of the electric field arising during magnetic stimulation with a microcoil was performed by [PERSON] and [PERSON], and they found the electric field to be about 0.026 mV/m [19] at a distance just outside the coil insulation surface (0.3 \(\upmu\)m from the coil). How could one distinguish experimentally a model based on capacitive coupling from one based on magnetic stimulation? (1) Both predict an electric field that is proportional to the frequency and the amplitude of the applied coil current and that is out of phase with the coil current. (2) Increasing the thickness of the insulation should decrease the capacitance, thereby increasing the diffusion constant and making capacitive stimulation even more difficult. Magnetic stimulation, on the other hand, should not be affected by the thickness of the insulation. (3) The electric field produced by capacitive stimulation is sensitive to the tissue resistance (Figure 7), but the electric field induced by magnetic stimulation is not. (4) If the wire were made from silver instead of copper, then \(r_{i}\) would be smaller. This would decrease the electric field via capacitive stimulation, but (assuming a current source) this would not affect magnetic stimulation. (5) Increasing the wire gauge and thus decreasing the wire radius would increase \(r_{i}\), which would increase the electric field caused by capacitive stimulation. There would be no effect of wire gauge during magnetic stimulation (again, assuming a current source). (6) The coil could be wound using more turns. This would have a complicated influence during capacitive stimulation because it would couple the individual windings capacitively. For magnetic stimulation, increasing the number of windings would increase the magnetic field (assuming a current source, so any changes in coil resistance or inductance do not affect the current). (7) Finally, the length of the coil leads (_L_) would play a major role in capacitive stimulation, but less or no role during magnetic stimulation. To examine some of these effects in more detail, if we make the wire thinner (decrease _a_), we will increase \(r_{\rm i}\). But assuming that \(r_{\rm i}\) is still much smaller than \(r_{\rm e}\) and that we are driving the coil with a current source, increasing \(r_{\rm i}\) should increase the magnitude of the tissue electric field, making it easier to stimulate. (Essentially, we increase the voltage drop along the wire.) For instance, when the resistance \(r_{\rm i}\) becomes equal to the resistance of the tissue \(r_{\rm e}\), the peak of the electric field will be huge, about 1,500,000 mV/m. Note, however, that as we increase \(r_{\rm i}\) while using a current source, the voltage produced by the source will grow. The current source must be powerful enough to produce such a voltage, otherwise letting \(r_{\rm i}\) become large in our calculation is unrealistic. Nevertheless, the best way to stimulate neurons in the brain may be to use two electrodes, an anode and a cathode, with a gap (\(r_{\rm i}=\infty\)), as is often used in traditional electric stimulation [26]. Increasing the resistance of the tissue space, \(r_{\rm e}\), would decrease \(D\) and increase the electric field in the tissue (Figure 7). For instance, making \(r_{\rm e}\) ten times larger, \(r_{e}=3200\) M\(\Omega\)/m, would increase the electric field in the tissue to 40 mV/m. The radius of the cylinder of tissue, \(b\), is the least well-known parameter in our model. A more accurate calculation would treat the tissue as a volume conductor and determine the distribution of the tissue voltage and electric field as a function of position. In this case, the average electric field in the tissue may be smaller than value we calculate, but its peak value adjacent to the insulation may be larger. Our calculation only approximates the physical situation examined by [PERSON] et al. [18]. Their coil was not a straight wire, but bent into a hairpin loop.