Magnetic Flux

Picture a wire loop held in a steady magnetic field like a net dipped in a flowing river. When the net's face is square to the flow, it catches the most water. Tilt it, and less water passes through even though the river hasn't changed at all. Magnetic flux works the same way: it counts how much field threads through the loop's area, and that depends on the loop's orientation relative to the field, not just on how strong the field is.

The formula is flux equals B times A times sin of the angle measured from the plane of the loop, where B is the field strength and A is the loop's area. Flux is biggest when the loop's face is perpendicular to the field, so the field lines pierce straight through, and it drops to zero when the loop is edge-on to the field, because then the field lines glide along the surface without crossing it. Many textbooks define the angle from the loop's normal instead, using cosine. Both describe the same physical picture. The key is to know which angle you're given: the angle from the plane, or the angle from the normal, since they are complements of each other.

Flux itself is just a snapshot, a number describing the field threading the loop right now. It says nothing about motion. That distinction matters because the next idea, Faraday's law, cares only about how flux changes over time. A loop sitting still in a constant field can have huge, unchanging flux and produce no current at all, while a loop with modest flux that is rapidly changing, by rotating, moving, or sitting in a varying field, can generate a strong induced emf.