# The Mystery of Inductance of Lead Wire

We sometimes see "inductance of lead wire" in Electrical Engineering technical books. For example, the following expression is found in a book titled "Analytical Noise Mechanism" by CQ Publishing Co. at its 120th page.

```L = 2*l*(log(4*l/d)-3/4)   (nH/m)  (1)

where, L = inductance of lead wire (nH/m)
d = diameter of lead wire  (cm)
l = length of lead wire  (cm)
```
Before adapting the formula for circuit calculation, please see it carefully. There is something very inexplicable with it. First of all, it says that, because inductance of lead wire per unit length is L/l:
```(1)  its inductance per unit length gets infinitely bigger as lead wire gets
longer and longer.
```
This does not make sense from the standpoint of physical science. It also says,
```(2)  when the length of lead is a half of its radius, the inductance
becomes zero!
```
That sounds more strange, because, if that's the case, it will be possible to do wiring without inductance by connecting a small piece of cable of 1/2 the radius length in series. In addition, it says,
```(3)   When the length of lead is less than the half of its radius,
inductance becomes negative figures.  As the length of lead gets to zero
closer and closer, the inductance approaches to negative infinite!!
```
If so, it enables to make a circuit of negative inductance. But, inductance is inertia against current and is circuit element which functions to prevent current alteration. Therefore, inductance in negative figures would help current alteration, which would enable the current to increase dramatically only by adding a little amount of current. That would lead to an amazing theory that a small piece of copper wire picked up from a garbage dump would solve the problem of the global energy crises. This, of course, is against one of the basic rules of physical science, the rule of Energy Preservation, and impossible to happen.

There is no explanation in the book about the basis of this formula, though I assume it is referred to the calculation by "Geometric Mean Distance"(G.M.D.) basing upon the Newmann's formula. For example, see in the 392th page of the classical famous book "Electromagnetics Phenomenon Theory" (Maruzen Publishing) by Setsuzo Takeuchi, where you will find the following formula:

```L = (u0*l)/(2*PI)*(log(2*l/a)-3/4)   (H/m)  (2)
where, L = inductance of columnar conductor   (H/m)
a = radius of column   (m)
l = length of column   (m)
u0 = permeability (H/m)
PI = 3.14159265358979..
```
Since lead is a columnar conductor, the formulae (1) and (2) completely correspond each other in consideration of u0 being vacuous permeability (4* PI*1e-7 H/m).

In other words, the inductance of lead looks as if it has affirmative theoretical background, while believing in it may mean denial of the base of modern physical science. How can we understand this "inductance of lead?"