Home » Articole » Articles » Science » Physics » Electromagnetism » Henri Poincaré: Potential of an electric mass distributed on the surface of a sphere (2)

# Henri Poincaré: Potential of an electric mass distributed on the surface of a sphere (2)

1. Suppose that we propose to find a function F which satisfies Laplace’s equation inside the sphere S and which, at the different points M of the surface of this sphere, take given values .

The value of this function V at a point P inside the sphere will be the integral

∫(R2 – OP2)/4πr V°/MP3

extended to all the elements of the sphere.

1. Let w and W be the smallest and the largest value that can take; they will also be, as we know, the smallest and the largest value that V can take.

If w is positive, so will be and V.

Besides, as MP is always included between R – OP and R + OP; we will have

V < (R + OP)/(R – OP)2∫V°dω/4πR

V > (R – OP)/(R + OP)2∫V°dω/4πR

Source: Henri Poincaré, Sur les Equations aux Dérivées Partielles de la Physique Mathématique, American Journal of Mathematics, Mar., 1890, Vol. 12, No. 3 (Mar., 1890), pp. 211-294. Translation by Nicolae Sfetcu. © 2023 Nicolae Sfetcu

##### Solaris, directed by Andrei Tarkovsky – Psychological and philosophical aspects

About the main psychological and philosophical aspects detached from the film Solaris directed by Andrei Tarkovski, as well as the cinema techniques used by the director to convey his messages to the spectator. In the “Introduction” I briefly present the … Read More

not rated \$0.00