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 = ∫{ B⋅ds } 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.