Magnetic Flux

Consider an open surface . Then the differential magnetic flux is defined by:

where is the angle between and .

So the total flux through a surface will be:

Equation

(see integral)

Warning

Not to be confused with Maxwell's second equation, which is for a closed surface, not open.

Intuition

This means the B-field is actually magnetic flux density (see Interpretation of Integrals)

Flux Linkage

What if we have more than one loop? What if our conducing wire has a thickness to it? We define a term flux called flux linkage . There is no specific definition of flux linkage.

The induced voltage across the conducting circuit is given as:

Equation

(see derivative)

Consider a circuit which has loops in a region with changing magnetic flux.

Case I: the loops go in the same direction. Then the induced voltages add up, and the linkage is defined as:

Case II: the loops go in opposite direction. Then the induced voltages cancel out. E.g if there are 3 clockwise loops and 5 counter-clockwise loops, then it's the same as having 2 counter-clockwise loops. The linkage is (sorta) defined as: