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9.3 Inductance
Earlier we have introduced very useful and important devices in electric circuits, which were called “capacitors”. A capacitor consists of two conducting plates separated by an insulating medium. When we charge these plates, we generate a magnetic field originating from the positive plate and entering into the negative plate. Then, we said one can use these fields, these small electric field packages, in electric circuits to store energy.
By the same token, later on we have introduced solenoids and toroids. In these devices we have seen that once we let the current flow through these devices, we generate magnetic fields, which fills the region inside of these devices. Therefore, similar to the case of capacitors, one can use these devices to store the energy now into the magnetic field lines. We call these devices, commonly, inductors.
Therefore, if we recall, again, capacitors, we use this symbol in order to represent a capacitor. We defined capacitance, C, as the ratio of the magnitude of the charge stored in the capacitor to the potential difference between the plates of the capacitor.
Now, we’re going to introduce this symbol to represent the inductors. This can be either a solenoid, or a toroid, a simple coil. The physical quantity associated with the inductors is called “inductance”, and we will denote that by capital L. It is defined as number of flux linkages, NΦB divided by i. That is inductance defined. Here, N represents the number of turns of the inductor. ΦB is the magnetic flux through the cross-sectional area of the inductor. And i, of course, represents the current flowing through the inductor.
If you look at the units of inductance in a SI unit system, by using its definition, since it is number of turns times magnetic flux divided by current and an SI unit system, and of course, it’s just number of turns, ΦB is Weber, and its explicit form is tesla meters squared (magnetic field times area) and the unit of current in SI unit system is in amperes. Therefore tesla meters squared per amp is the unit of inductance, and we have a special name for this ratio. It is called “Henry”.