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If the magnetic field is constant, the magnetic flux passing through a surface of vector area S is = = , where B is the magnitude of the magnetic field (the magnetic flux density) having the unit of Wb/m 2 , S is the area of the surface, and θ is the angle between the magnetic field lines and the normal (perpendicular) to S.
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.
Thus, for a typical inductance (a coil of conducting wire), the flux linkage is equivalent to magnetic flux, which is the total magnetic field passing through the surface (i.e., normal to that surface) formed by a closed conducting loop coil and is determined by the number of turns in the coil and the magnetic field, i.e.,
B 0 is the flux density very close to each pole, in T, A is the area of each pole, in m 2, L is the length of each magnet, in m, R is the radius of each magnet, in m, and; x is the separation between the two magnets, in m = relates the flux density at the pole to the magnetization of the magnet.
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 n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
For a magnetic component the area S used to calculate the magnetic flux Φ is usually chosen to be the cross-sectional area of the component. The SI unit of magnetic flux is the weber (in derived units: volt-seconds), and the unit of magnetic flux density (or "magnetic induction", B) is the weber per square meter, or tesla.
Instead the parameter that is listed is residual flux density (or remanence), denoted B r. The formula needed in this case to calculate m in (units of A⋅m 2) is: =, where: B r is the residual flux density, expressed in teslas. V is the volume of the magnet (in m 3).
The above equations are the microscopic version of Maxwell's equations, expressing the electric and the magnetic fields in terms of the (possibly atomic-level) charges and currents present. This is sometimes called the "general" form, but the macroscopic version below is equally general, the difference being one of bookkeeping.