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Consider a long, thin wire of charge and length .To calculate the average linear charge density, ¯, of this one dimensional object, we can simply divide the total charge, , by the total length, : ¯ = If we describe the wire as having a varying charge (one that varies as a function of position along the length of the wire, ), we can write: = Each infinitesimal unit of charge, , is equal to ...
Linear charge density (λ) is the quantity of charge per unit length, measured in coulombs per meter (C⋅m −1), at any point on a line charge distribution. Charge density can be either positive or negative, since electric charge can be either positive or negative.
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.
Lambda indicates an eigenvalue in the mathematics of linear algebra. In the physics of particles, lambda indicates the thermal de Broglie wavelength; In the physics of electric fields, lambda sometimes indicates the linear charge density of a uniform line of electric charge (measured in coulombs per meter).
The equations introduce the electric field, E, a vector field, and the magnetic field, B, a pseudovector field, each generally having a time and location dependence. The sources are the total electric charge density (total charge per unit volume), ρ, and; the total electric current density (total current per unit area), J.
where ρ is the charge density, which can (and often does) depend on time and position, ε 0 is the electric constant, μ 0 is the magnetic constant, and J is the current per unit area, also a function of time and position. The equations take this form with the International System of Quantities.
R is a region containing all the points at which the charge density is nonzero; r ' is a point inside R; and; ρ(r ') is the charge density at the point r '. The equations given above for the electric potential (and all the equations used here) are in the forms required by SI units.
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.