28.4: Magnetic Flux
The magnetic flux measures the number of magnetic field lines passing through a given surface area. The SI unit for magnetic flux is the weber (Wb). Magnetic flux is a scalar quantity. It depends on three factors: the strength of the magnetic field B, the area through which the field lines pass, and the relative orientation of the field with the surface area.
Suppose a surface is divided into elements of area dA. For each element, the component of the magnetic field that is normal to the surface at the position of that element is determined. This component generally varies from point to point on the surface. The magnetic flux through this element is defined as the dot product of the magnetic field vector and the area element vector. The total magnetic flux through any surface, open or closed, is the sum of the flux contributions from all the individual elements.
If the magnetic field is perpendicular to the surface and is uniform throughout it, then the magnetic flux has the maximum value of BA. When the field is parallel to the surface, the magnetic flux has a minimum value of zero.
According to Gauss's law, the total electric flux that passes through a closed surface is proportional to the total electric charge inside the surface. The total electric flux is zero when an electric dipole is enclosed by a closed surface since there is no overall charge. By analogy, the total magnetic flux through a closed surface would be proportional to the total magnetic charge enclosed if there were a single magnetic charge or magnetic monopole. However, despite extensive searches, no magnetic monopole has ever been seen. Hence, the total magnetic flux across a closed surface is always zero.
Since magnetic field lines always form closed loops or originate in the north and south poles of the same magnet, the total number of field lines entering a closed surface is always equal to the total number of field lines exiting the surface. Hence, the net flux through the surface is zero. This observation is called Gauss's law of magnetism.