Siméon Denis Poisson
Created by Benjamin Bierbaum
Siméon Poisson was a French mathematician best known for his work on definite integrals and electromagnetic theory.
Personal Life
Early Life
Poisson was born in Pithiviers, Loiret, France on June 21, 1781. The son of a soldier, he showed great promise in mathematics and science and started at Paris' École Polytechnique as first in his class. His focus was on mathematics, and at 18 was published in the esteemed journal Recueil des savants étrangers for his writings on finite difference equations.
Poisson is most remembered for his work involving the application of mathematics to electricity, magnetism, mechanics, and other areas of physics. He is known for Poisson's equation, which is a partial differential equation that is useful in electrostatics, mechanical engineering and theoretical physics. For example, it can be used to describe the potential energy field caused by a given charge.
Family Life
Poisson married Nancy de Bardi in 1817. Together they had four children.
Death and Legacy
Poisson's health was weak throughout his lifetime - he had several older siblings that died during childhood, and he was entrusted to a nurse during his early life. His health declined rapidly in 1840, and although extremely impaired, he continued to attend meetings of the French Academy of Sciences.
Poisson died on April 25, 1840. Attendees of his funeral included numerous French scientists, as well as the youngest son of King Louis Philippe I, who studied under Poisson.
Poisson was President of the French Academy of Sciences at the time of his death, and was also a member of the Royal Society of London. His name is inscribed on the Eiffel Tower in Paris alongside 71 other prominent French scientists, mathematicians, and engineers.
Scientific Contributions
A Mathematical Model
Solving the Poisson equation lets one find the electric potential φ for a charge distribution [math]\displaystyle{ \rho_f }[/math]. Poisson's equation is:
- [math]\displaystyle{ \Delta\varphi=f }[/math]
and can also be written as:
- [math]\displaystyle{ \nabla^2 \varphi = f. }[/math]
Electrostatics
Assuming that the magnetic field is not changing with time, Poisson's equation for electrostatics is:
- [math]\displaystyle{ {\nabla}^2 \varphi = -\frac{\rho_f}{\varepsilon}. }[/math]
Solving for the potential using Poisson's equation necessitates knowledge of the charge density distribution. If the charge density comes out to be zero, then you get Laplace's equation, another differential equation named after Pierre-Simon Laplace.
The potential at a distance r from a point charge Q is:
- [math]\displaystyle{ \varphi(r) = \dfrac {Q}{4 \pi \varepsilon r}. }[/math]
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