Nykytiheys

Nykytiheys, the Finnish term for current density, is a vector field that describes the flow of electric current per unit area within a material or space. Its magnitude indicates how much current passes through a unit area, and its direction follows the conventional flow of positive charge. The SI unit is ampere per square meter (A/m^2).

For a conductor with a uniform cross-sectional area A carrying a current I, the current density magnitude is J = I/A, and the vector J points along the direction of current flow. The total current crossing a surface S is I = ∫_S J·dA. In isotropic, homogeneous media, Ohm’s law relates current density to the electric field E by J = σE, where σ is the conductivity; in anisotropic materials, J = σ·E with a conductivity tensor σ.

The conservation of charge is expressed by the continuity equation ∇·J + ∂ρ/∂t = 0, where ρ is the charge density. Under steady-state conditions, ∂ρ/∂t = 0 and ∇·J = 0. Boundary conditions involve the surface current density K = J·n, the component of J flowing through a boundary with normal vector n.

Nykytiheys is central to the design and analysis of electrical systems, influencing wire and trace cross-sections, thermal management, and reliability considerations such as electromigration. It also plays a role in plasma and astrophysical contexts, where current density describes net charge transport through ionized media.