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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.
Rosser's Equation is given by the following: + = = where: is the conduction-current density, is the transverse current density, is time, and is the scalar potential.. To understand Selvan's quotation we need the following terms: is charge density, is the magnetic vector potential, and is the displacement field.
The two most significant results of the Drude model are an electronic equation of motion, = (+ ) , and a linear relationship between current density J and electric field E, =. Here t is the time, p is the average momentum per electron and q, n, m , and τ are respectively the electron charge, number density, mass, and mean free time between ...
The carrier density is important for semiconductors, where it is an important quantity for the process of chemical doping.Using band theory, the electron density, is number of electrons per unit volume in the conduction band.
Then the electric field and current density are constant and parallel, and by the general definition of resistivity, we obtain ρ = E J , {\displaystyle \rho ={\frac {E}{J}},} Since the electric field is constant, it is given by the total voltage V across the conductor divided by the length ℓ of the conductor:
where current density J D is the displacement current, and J is the current density contribution actually due to movement of charges, both free and bound. Because ∇ ⋅ D = ρ , the charge continuity issue with Ampère's original formulation is no longer a problem. [ 22 ]
The Hall coefficient is defined as the ratio of the induced electric field to the product of the current density and the applied magnetic field. It is a characteristic of the material from which the conductor is made, since its value depends on the type, number, and properties of the charge carriers that constitute the current.
For negative charges, the sign of the current density is opposite to the velocity of the charges. [2]: 749 In SI units, current density (symbol: j) is expressed in the SI base units of amperes per square metre. [4]: 22 In linear materials such as metals, and under low frequencies, the current density across the conductor surface is uniform.