The flux associated with a magnetic field is defined in a manner similar to that used to define electric flux (see Eq. 24.3). Consider an element of area dA on an arbitrarily shaped surface, as shown in Figure 30.19. If the magnetic field at this element is B, the magnetic flux through the element is B.dA where dA is a vector that is perpendicular to the surface and has a magnitude equal to the area dA.
Hence, the total magnetic flux ΩB through the surface is
Consider the special case of a plane of area A in a uniform field B that makes an angle θ with dA. The magnetic flux through the plane in this case is
If the magnetic field is parallel to the plane, as in Figure 30.20a, then θ = 90° and the flux is zero. If the field is perpendicular to the plane, as in Figure 30.20b, then θ = 0 and the flux is BA (the aximum value).
The unit of flux is the T.m2, which is defined as a weber (Wb); 1 Wb = 1 T.m2.