Because vn, Be, and FL are orthogonal (8 = 90°), FL = q vn By uz forces the moving electrons toward the outer cell membrane, creating a space charge that acts to depolarize the cell. Note that uz is a unit vector with the direction of the Lorentz force, i.e., |uz| = 1. Figure 2.4-1 illustrates schematically this process for the orthogonal case. Note that By is the vector component of Be that by definition is orthogonal to vn in the x-y plane of the membrane. If the cell orientation is such that Be is parallel with vn , 8 = 0°, and there will be zero Lorentz force and no change in the cell resting potential. The Hall-induced electric field across the current-carrying volume of thickness t can be shown to be Ez = vx By V/m in the direction shown. The induced Hall potential is simply VH = t Ez = t vx By = Jx By/(q n). q is the electron charge, and n is the average density of electrons moving in the volume. (Note that if By or vn changes sign, the cell will be hyperpolarized, and will fire at a lower rate or will be inhibited.) In closing, note that the parallel current density need not be carried by electrons; any anion or cation with good mobility (and thus high vx) will do.
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