Inductance

Disambiguation: Not to be confused with Mathematical Induction

These notes focus on the physics behind inductance. For use of a inductor, see inductor.

Inductance

Recall the equation of an induced EMF:

But will be proportional to the current since it is creating the field. This proportionality constant is called the inductance :

Since , we have:

and the negative in front comes from Lenz's Law.

We can calculate inductance as:

Self and Mutual Inductance

Consider two loops carrying current and . Then we will have:

(see magnetic flux, integral)

If there is more than 1 loop, we will have flux linkage:

However, the flux linkage is going to affect the current of that same circuit. Thus, we the self-inductance of a circuit is given as:

the same would apply for loop 2.

There is also mutual inductance. The current will also create enclosed flux on loop 2 and affect the current in that loop. Thus we would have:

that is, the affect of the B-field from loop 1 on loop 2.

If there is more than 1 loop, we will have flux linkage:

Thus, the mutual effect of current on loop 2 is given as:

the same would apply for the current on loop .

Magnetic Energy

Recall from earlier that if we have a coil/circuit with self-inductance , with time varying current , then the instantaneous induced EMF would be:

The power absorbed is going to be . We also know that power is work over time, so:

if we want to find the magnitude of the total work in changing a current from to :

So we have:

recall .