inductance

Let's walk through these equations again, but with a time-varying twist. A solenoid with a changing current running through it will generate a changing magnetic field. which may not look like much, until you realize that the terms in the first fraction are largely determined by the geometry of the solenoid. Had we chosen a different configuration of wires, the same basic thing would have happened. Inductance is best defined by its role in the equation derived from Faraday's law of induction. (This is how we will derive the inductance equations for a few easy circuit elements later in this section.) Some people don't like this and prefer definitions written in the subject-verb-object form of a simple sentence. The unit of inductance is the henry, named after Joseph Henry US") (1797–1878), the American scientist who discovered electromagnetic induction independently of and at about the same time as Michael Faraday England") (1791–1867) did in England. Faraday published his findings first and so gets most of the credit. Henry also discovered self inductance and mutual inductance (which will be described later in this section) and invented the electromechanical relay (which was the basis for the telegraph). A circuit with a self inductance of one henry will experience a back emf of one volt when the current changes at a rate of one ampère per second. Inductance is a function of geometry. Let's derive some inductances for a few circuit elements with simple geometries. (There aren't many.) Start with the definition of magnetic flux for a region of uniform strength. We can't assume a uniform field strength in this case. Start with an equation for magnetic flux that can handle this. One that integrates an infinite number of infinitesimally small areas where the field is effectively constant. The difference in two logs is the log of their ratios. (That's not quite the right way to say it.) I haven't figured out how to explain this one yet. Here's the answer. The function cosh−1 is the inverse hyperbolic cosine, by the way. Fun stuff.