First, the Lorentz force. The force that prevents a charged particle from moving along straight paths in a magnetic field. The force that curls the trajectories of charged particles in a cloud chamber and allows the researcher to determine the speed and charge of the particles.
Where do these twists and curls come from? Look at the figure: the Lorentz force is always directed so that its vector forms a right angle with the directions of the particle's velocity and the magnetic field. Therefore, it is able to play the role of a centripetal force necessary for movement in a circle. This is how particles move.
In a cloud chamber filled with rarefied gas, particles are free to walk along bizarre trajectories. What about in a solid? Can, for example, the Lorentz force spin a free electron in a metal if the metal is placed in a strong magnetic field? It would seem that thermal motion will knock the electron off the circular path. However, this obstacle can be circumvented by cooling the metal: the cold will suppress the thermal motion.
And then a curious phenomenon will be revealed: the metal ceases to be a current conductor! Conductivity across a magnetic field is extremely low because, by circling into place, the electrons are unable to carry charge. The metal conducts current well only along the field: electrons can move along spiral trajectories wound on magnetic lines of force. But it turns out there are exceptions to this rule.
Exceptions to the rule
Real crystals, as a rule, consist of randomly mixed crystallites - pieces with a strictly consistent structure. The term "polycrystal", generally accepted for real crystals, well reflects this structural feature. In a polycrystal, there are crystallites in which the current can also flow across the field. This possibility is connected with the successful orientation of the crystallographic planes: the electrons move in jumps, being reflected from them. The fraction of such crystallites will be denoted by c, and their characteristic size by a.
Now everything is ready to explain the curious paradox discovered by Yu. A. Dreizin and A. M. Dykhne (Institute of Atomic Energy, Moscow).
That's what it is. Two gold plates are taken (the structure of gold is polycrystalline) and included in the chain. Then the plates are folded. The conductivity of the circuit increases sharply.
Why does the conductivity of the circuit increase?
It is not difficult to imagine how a current can flow through a polycrystal: for this it is necessary that under or above a crystallite with conductivity across the field there is another one of the same kind, slightly shifted along the direction of the current; above or below it - another one and so on. And the picture will become quite clear if you look at it from above: in terms of projection, such crystallites should overlap each other. And this will happen when the thickness of the sample exceeds a certain limit, approximately equal to a/c.
In the experiment described, the thickness of each plate did not reach this value and the conductivity across the field was low; the total thickness of the plates exceeded the indicated limit, and that conductivity appeared, which is schematically described by the figure in the second column.
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