Magnetic flux is the measure of the magnetic field that passes through an area of space or an object. Its mathematical definition is: Φ = ∫ B · dA.
Suppose you have a copper ring on the plane x, y as indicated in the figure above. Imagine that a constant magnetic field passes through it, given by the vector B = By + Bz. The magnetic flux must be:
Φ = ByTa + BzTa