The total amount of magnetic induction passing through a surface, s. It is represented by the symbol Phi, and measured in units of Webers. Typically calculated as:

Phi = { Bds } over s.

That's:

Phi = Integral{ B dot ds} over s.

Here Phi is a scalar quantity, like any flux, because it measures the sum of the magnetic flux density field passing normal to the surface of s at any given point (and here s is a normal vector to surface s at any given point), summed over the whole surface of s.

Magnetic flux is a useful concept because it is preserved throughout a branch of a magnetic circuit in much the same way as current is preserved in an electric circuit. See Ohm's Law for Magnetics. One may change the area of the material in a magnetic circuit, but the magnetic flux flowing through the section must remain the same.

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