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In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in coulombs per cubic meter (C⋅m −3), at any point in a volume.
A surface charge is an electric charge present on a two-dimensional surface. These electric charges are constrained on this 2-D surface, and surface charge density , measured in coulombs per square meter (C•m −2 ), is used to describe the charge distribution on the surface.
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.
However, if p(r) exhibits an abrupt step in dipole moment at a boundary between two regions, ∇·p(r) results in a surface charge component of bound charge. This surface charge can be treated through a surface integral, or by using discontinuity conditions at the boundary, as illustrated in the various examples below. As a first example ...
The charge-based BEM solves an integral equation of the potential theory [1] written in terms of the induced surface charge density. This formulation is naturally combined with fast multipole method (FMM) acceleration, and the entire method is known as charge-based BEM-FMM.
The method of image charges (also known as the method of images and method of mirror charges) is a basic problem-solving tool in electrostatics.The name originates from the replacement of certain elements in the original layout with fictitious charges, which replicates the boundary conditions of the problem (see Dirichlet boundary conditions or Neumann boundary conditions).
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.
Gauss's law makes it possible to find the distribution of electric charge: The charge in any given region of the conductor can be deduced by integrating the electric field to find the flux through a small box whose sides are perpendicular to the conductor's surface and by noting that the electric field is perpendicular to the surface, and zero ...