The property of inductance

Suppose you have a wire a million miles long. What will happen if you make this wire into a huge loop, and connect its ends to the terminals of a battery (Fig. 1)? You can surmise that a 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 will take a while for the electrons from the negative terminal to work their way around the loop to the positive terminal.
The effect of the current moves along the wire at a little less than the speed of light. In this case, it’s about 180,000 miles per second, perhaps 97 percent of the speed of light in free space. It will take a little time for the current to build up to its maximum level. The first electrons won’t start to enter the positive terminal until more than five seconds have passed.
The magnetic field produced by the loop will be small at first, because current is

Figure 1: A huge loop of wire illustrates the principle of inductance. See text.

flowing in only part of the loop. The flux will increase over a period of a few seconds, as the electrons get around the loop. Figure 2 is an approximate graph of the overall magnetic field versus time. After about 5.5 seconds, current is flowing around the whole loop, and the magnetic field has reached its maximum.

Figure 2: Relative magnetic flux in the huge wire loop, as a function of time in seconds.

A certain amount of energy is stored in this magnetic field. The ability of the loop to store energy in this way is the property of inductance. It is abbreviated by the letter L.