magnetic_flux

# Magnetic flux

 Stan Zurek, Magnetic flux, Encyclopedia Magnetica https://E-Magnetica.pl/magnetic_flux

Magnetic flux, Φ - a physical quantity that expresses the amount of magnetic flux density B which penetrates the given cross-sectional area A of interest.1)2)3)4)

If there is some magnetic field in a given volume, there is always some magnetic flux Φ associated with it,2) provided that the area of interest is not defined as a closed three-dimensional surface. Φ is always a scalar value, even if B and A are treated as vectors in the calculations.

Magnetic flux Φ is the product of average normal component of magnetic flux density B and the surface area A 1)

The magnetic flux density B is the fundamental quantity which is used for defining the existence of magnetic field. And the magnetic flux Φ quantifies the amount of B that penetrates surface A. The names are related, because one quantity is calculated from the other.

Magnetic flux is measured in the SI unit of weber (Wb),5) (in the CGS system the unit was “maxwell”, Mx).

Relation of magnetic flux Φ and its unit weber (Wb) to other values
(1a)
(quantities)
$$Φ = \vec{B_{avg}}·\vec{a}·A ≡ V·t$$
(1b)
(units)
$\mathrm{ Wb ≡ T·m^2 ≡ V·s ≡ \frac{kg·m^2}{s^2·A} }$
where: $\vec{B_{avg}}$ - vector of magnetic flux density (T) averaged over area $A$, $\vec{a}$ - normal vector (unitless) to the surface $A$, $A$ - area (m2), $V$ - voltage (V), $t$ - time (s)

Changes in magnetic flux Φ induce voltage in the related electric circuit. Therefore, Φ is related to B and A, as well as to the induced voltage and time (through the Faraday's law of induction).

If the given coil has N number of turns, then the quantities such as induced voltage are scaled accordingly, as explained in the following sections.