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In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. [1] The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point.
This ongoing current in both directions is called the exchange current density. When the potential is set more negative than the formal potential, the cathodic current is greater than the anodic current. Written as a reduction, cathodic current is positive. The net current density is the difference between the cathodic and anodic current density.
The exchange current is the current at equilibrium, i.e. the rate at which oxidized and reduced species transfer electrons with the electrode. In other words, the exchange current density is the rate of reaction at the reversible potential (when the overpotential is zero by definition).
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
The upper graph shows the current density as function of the overpotential η . The anodic and cathodic current densities are shown as j a and j c, respectively for α=α a =α c =0.5 and j 0 =1mAcm −2 (close to values for platinum and palladium). The lower graph shows the logarithmic plot for different values of α (Tafel plot).
The current carried by each electron must be , so that the total current density due to electrons is given by: = = Using the expression for gives = A similar set of equations applies to the holes, (noting that the charge on a hole is positive).
Probability currents are analogous to mass currents in hydrodynamics and electric currents in electromagnetism. As in those fields, the probability current (i.e. the probability current density) is related to the probability density function via a continuity equation. The probability current is invariant under gauge transformation.
The charge density appears in the continuity equation for electric current, and also in Maxwell's Equations. It is the principal source term of the electromagnetic field; when the charge distribution moves, this corresponds to a current density. The charge density of molecules impacts chemical and separation processes.