A huge, imaginary loop of wire can be used to illustrate the principle of inductance.
Suppose you have a wire 1 million miles long (about 1.6 million kilometers). Imagine that you make this wire into a huge loop, and connect its ends to the terminals of a battery (above figure). An electrical current will flow through the loop of wire, but this is only part of the picture.
If the wire was short, the current would begin to flow immediately, and it would attain a level limited by the resistance in the wire and in the battery. But because the wire is extremely long, it takes a while for the electrons from the negative terminal to work their way around the loop to the positive terminal. It will take a little time for the current to build up to its maximum level.
The magnetic field produced by the loop will be small during the first few moments when current flows in only part of the loop. The magnetic field will build up as the electrons get around the loop. Once a steady current is flowing around the entire loop, the magnetic field will have reached its maximum quantity and will level off (see following figure). A certain amount of energy is stored in this magnetic field. The amount of stored energy depends on the inductance of the loop, which is a function of its overall size. Inductance, as a property or as a mathematical variable, is symbolized by an italicized, uppercase letter L. The loop constitutes an inductor, the symbol for which is an uppercase, non italicized letter L.
Relative magnetic flux in and around a huge loop of wire connected to a current source, as a function of time