There are two scientist to whom we owe a debt of gratitude in our study of electrical forces and fields. The first is Charles Augustin de Coulomb (Born: 14 June 1736 in Angouleme, France and died: 23 Aug 1806 in Paris, France), a military engineer and "Engineer to the King of France", who secluded himself in his country home at the beginning of the revolution. (At that time, France was not a healthy place for former members of the ruling class.) It is here that he did his work in electricity and magnetism. Physicists best know Coulomb for his law which states that the force between two point charges is proportional to each charge and inversely proportional to the square of the distance between them. Mathematicians may know him primarily from the fact that his work strongly enfluenced many of the theories of Poisson.
But Coulomb is better known outside the field of physics! He was a mechanical engineer (as were most military engineers in the 16th century) and did extensive work in the area of mechanical stress. He is best known (and perhaps best revered) as the grandfather of soil mechanics. He created the ground work for the study of soil movement.
Karl Friedrich Gauss (30 April 1777-23 Feb. 1855) was born and lived most of his life in a part of Prussia that is now Germany. He has left his mark in an astounding number of areas. It is hard to find an intermediate or upper level math text that is not filled with theorems and techniques that bear his name. His most recognized contribution to physics is his method of calculating the electric fields of geometrically symmetric charge distributions. This method connects the "flux" of electric field lines to the charge that creates the flux. In the PHY 212 course we have skipped Gauss's Law, but you can browse section 15.10 of the text for a flavor of how it works.
A short list of other accomplishments include Gauss's Hypergeometric equation, Gauss's error function, the Gauss-Jordan method of solving determinants, and so forth.
He led a tragic but interesting life. He had many friends and enemies alike.
There is a rather extensive
history of Gauss site with links to the many scientists and mathematicians with whom he worked. (This last link is from the The MacTutor History of Mathematics archive maintained by the University of St. Andrews in Scotland. It has biographies for most mathematicians.)
Gauss was also known for his philosophical inclinations. I'll leave you with a few quotes:
You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly
takes far more time than writing at length.
Quoted in G Simmons Calculus Gems (New York 1992).
God does arithmetic.
I have had my results for a long time: but I do not yet know how I am to arrive at them. (A. Arber, The Mind and the Eye, 1954.)
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Questions:
What important physical quantity, in addition to friction, did Coulomb introduce to the mechanics of soil movement?
Coulomb was appointed to the Academy of Science, but he left after two years. Why? (Check out the "dark side" link.)
What mathematical trick did Gauss perform when he was 7 that amazed his teachers?
What great axiom did Gauss's longtime friend, Farkas Bolyai, work on for many years? (Boylai's son finished the work for him.)
There are two scientist to whom we owe a debt of gratitude in our study of electrical forces and fields. The first is Charles Augustin de Coulomb (Born: 14 June 1736 in Angouleme, France and died: 23 Aug 1806 in Paris, France), a military engineer and "Engineer to the King of France", who secluded himself in his country home at the beginning of the revolution. (At that time, France was not a healthy place for former members of the ruling class.) It is here that he did his work in electricity and magnetism. Physicists best know Coulomb for his law which states that the force between two point charges is proportional to each charge and inversely proportional to the square of the distance between them. Mathematicians may know him primarily from the fact that his work strongly enfluenced many of the theories of Poisson. 
Karl Friedrich Gauss (30 April 1777-23 Feb. 1855) was born and lived most of his life in a part of Prussia that is now Germany. He has left his mark in an astounding number of areas. It is hard to find an intermediate or upper level math text that is not filled with theorems and techniques that bear his name. His most recognized contribution to physics is his method of calculating the electric fields of geometrically symmetric charge distributions. This method connects the "flux" of electric field lines to the charge that creates the flux. In the PHY 212 course we have skipped Gauss's Law, but you can browse section 15.10 of the text for a flavor of how it works.
A short list of other accomplishments include Gauss's Hypergeometric equation, Gauss's error function, the Gauss-Jordan method of solving determinants, and so forth.