In 1831, Michael Faraday discovered that turning on or off the current in one coil induces a transient electric current in another coil. Faraday thought that the induction was caused by a changing magnetic flux. So what is magnetic flux?

Imagine a coil with cross sectional area *A* directly facing a uniform magnetic field *B*. Does it look like some kind of magnetic flow is captured by the coil? That thingy captured by the coil is called the magnetic flux *f*. Quantitatively, it has the formula

The SI unit for *f *is the weber (symbol Wb). 1 Wb is 1 T m^{2}.

Notice that . That’s actually where the name magnetic flux density came from.

If the coil is rotated 90° so its plane is parallel to *B*, then the area *A* will not be facing the magnetic field at all. So the magnetic flux (of the coil) is now zero.

If the axis of the coil is oriented at an angle *a* to *B* (so the plane of the coil makes an angle *b* with *B*), then the coil is partially facing the magnetic field. We can think of the coil as directly facing (the component of *B* perpendicular to its area *A*), but completely dodging (the component of *B* parallel to *A*). So the magnetic flux (of the coil) can be expressed as

Now, if the coil has *N* turns (instead of a single turn), then each turn will be capturing the same magnetic flux . Logically, the total flux “captured” will be . We have a term specially to denote the total flux captured by a coil of many turns. It is called the magnetic flux linkage *F*.

The SI unit for *F *is the weber-turn (symbol Wb-turn).

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**Concept Test**