Il campo elettrico fuori dal conduttore percorso da corrente

The electric field outside a conductor in which was flowing a current was observed experimentally by  Oleg J. Jefimenko. "He had an ingenious idea of utilizing grass seeds as test particles near current carrying wires. They are electrically neutral in normal state so that they do not induce any charges in the conductor. On the other hand, they are easily polarized in the presence of an electric field, aligning themselves with it. The lines of electric field are then observed in analogy with iron fillings generating the lines of magnetic field." [Assis, A. K. T., Rodrigues, W. A., & Mania, A. J. (1999). The electric field outside a stationary resistive wire carrying a constant current. Foundations of Physics, 29(5), 729-753.]. Jefimenko presented his results in Plate 6 of  his Electricity and Magnetism, Meredith Publishing. 1966. 

Earnshaw's Theorem

Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. This was first proven by British mathematician Samuel Earnshaw in 1842. It is usually referenced to magnetic fields, but was first applied to electrostatic fields. Earnshaw's theorem applies to classical inverse-square law forces (electric and gravitational).
It means that it is linked to the Gauss Law. And here a proof.

Bernoulli Numbers: from Ada Lovelace to the Debye Functions

Bernoulli Numbers: from Ada Lovelace to the Debye Functions: Jacob Bernoulli owes his fame for the numerous contributions to calculus and for his discoveries in the field of probability. Here we will discuss one of his contributions to the theory of numbers, the Bernoulli numbers. They were proposed as a case study by Ada Lovelace in her analysis of Menabrea's report on Babbage Analytical Engine. It is probable that it was this Lovelace's work, that inspired Hans Thirring in using the Bernoulli numbers in the calculus of the Debye functions.