## Refuting the laws of physics (II)Man creates laws of physics to describe reality. But then he gets so much attached to them that he often forgets that theory ought to obey the facts and not viceversa. Continuing my struggle against this "scientific" idolatry initiated with my article on hydrogen atom in normal state, I would like to consider with your help, dear reader, the legitimacy of the claim that
## Electrostatic field does not penetrate into a conductor.Well, you may ask now, what about Ohm's law? In the presence of tension, electric field is unavoidable. Of course, it is not my intention to catch you on such obvious things. I am thinking of an electrostatic field, i.e. a field which exists in the state of static equilibrium when there is no current flowing. No current indeed? For you to judge.
a) in an activated field b) in the state of equilibrium The motion will persist as long as there is any field in the conductor. When the field disappears completely, a static situation is attained - the state of equilibrium.
## And yet it does penetrateTo see this, let's take a closer look at the conductor. The situation presented in Fig. 1, with free charges of either sign, is quite rare (e.g. the plasma formed by an ionized gas). Most frequently, charges are all of the same sign (in metals - negative electrons), while compensating charges of opposite sign (in metals - positive ions) remain fixed in the conductor, forming a periodic space lattice (crystals) or a chaotic system (amorphic bodies). If an electric field is applied so as to push the free charges into the conductor, the surface layer of the charge which compensates the field within it is due to a fixed charge, uncovered by the retractation of free carriers. The surface density of the charge is determined by the electric field surrounding the conductor and can be computed by Gauss' theorem. To attain that surface density, free charges must be moved back to a depth sufficient to uncover the required number of fixed ions of opposite sign. A charged layer of thickness
is thus formed (where
a)The field with movable ( - ) and fixed ( + ) particles. b)Field intensity dependent on the distance from conductor surface. c)Electric charge density dependent on situation. We have thus proved that the field penetrates into the conductor. Let's estimate the thickness of the layer under the assumption that the electric field intensity at the metal surface is
(typical for electrostatic experiments) and copper is the conductor - volume density of the charge is then given by
Then the thickness will be equal to
Now you may exclaim: This is absurd! Why should I ever bother about a layer devoid of carriers, the thickness of which is moreover neglectably small with respect to atom dimensions? This is all true, but take a look at semiconductors. For them, the concentration of free carriers being less by several orders of magnitude than in metals, the penetration depth of the field may be significant. What is more, this fact makes possible volume density measurement of the fixed charge and it even led to the emergence of a new experimental technique known as capacitive spectroscopy. This technique is used to investigate the evolution of admixtures in semiconductors in charge state. Why capacitive? Because the layer devoid of free carriers forms a condenser of a sort. By measuring its capacity we can determine the thickness of the layer and hence also the density of the charge. How? Let's leave it for some other time. All this may be true, you may object, but this is not a conductor. A layer without carriers does not conduct electricity, so no wonder the field gets inside. We have refuted nothing so far! Well, if this is not sufficient evidence for you, I am not giving up yet. We shall now see that
## The field penetrates into a conductor tooTo this aim let's have a look at the other end of the conductor considered.No problems to be encountered there, you may say, free charge can reach the surface and form a layer compensating the electric field. Using this argument, we forget a frequent phenomenon which smooths all irregularities: diffusion. It is well known that when the concentration of movable particles is irregular, they are displaced so as to diminish the degree of irregularity. This process is described by the diffusion equation, which in the one-dimensional case has the following form:
where Diffusion leads to the erosion of the immense (theoretically infinite) volume density of the charge concentrated on the surface, needed to prevent the field from penetrating into the conductor. In turn, the erosion of the charge on the surface allows the field to enter into the conductor to some depth. The field, by pulling the carriers towards the surface, stops the diffusion process, thus establishing equilibrium (Fig.3).
Fig. 3. Fading of the electric field in a conductor when the field is directed inwards (notation as in Fig.2) If the qualitative argument does not satisfy you, you may ask
## How deep does the field penetrate into the conductor?To find the equation showing how the field depends on its positionx in the semiconductor, we must require that the
electric current emanating from the field be compensated by the
diffusion current. The sources of these two currents are related
to charge distribution, so we may hope the above condition will
make possible the computation of the distribution.
The value of the diffusion current must be equal to minus the density of the electric current caused by the field, divided by the charge of a single carrier.
But
Volume density of the free charge being
related to carrier concentration Since we arrive at
On the other hand,
where $\sigma$ is the specific conductivity of the material. Substituting (2) and (3) into (1) we now have i.e. Observe that the dimension of the constant is the inverted square of some distance. Call this distance x_0. Then,
obviously,
Thus the electric field must fade away according to the equation It can be easily verified that this equation is satisfied by an exponentially fading field:
where Substituting values known for copper: and assuming that epsilon is equal to 1, we get
Now you will accuse me of pulling your leg by suggesting that
field penetration with depth comparable to the dimension of an
atom can be treated seriously. Well, my answer is that you are
absolutely right. However, in semiconductors, for which specific
conductivity is by far smaller, whereas diffusion is by far
greater than in metals, the distance It's time to ask again: what has been refuted above? A law of physics or a commonplace belief? It's for you to judge, dear reader. |