
AndréMarie Ampère was a French physicist who laid the foundations for the science of electrodynamics through his demonstration that electric currents produce magnetic fields, and through his subsequent investigation into the relationship between these two phenomena. 


AndréMarie Ampere, the son of a Lyon city official, was
born in PolemieuxauMontd'Or, near Lyon. AndréMarie Ampère's father,
JeanJacques Ampère, was a prosperous man who owned a home in Lyon and a
country house in Poleymieux, which is only 10 km from Lyon. Up till
AndréMarie was seven years old the family spent most of the year in Lyon
except the summer months which were spent at Poleymieux. However, in 1782,
the home at Poleymieux became their main residence since AndréMarie's
father wished to spend more time on his son's education. Only a short time
in winter was spent at Lyon where AndréMarie's father saw to his business
interests. Ampère was born in this house in the village of Poleymieux, near Lyons, France, and lived there through the 1790's. It is now a national museum. 
Despite not attending school, AndréMarie was to be given an excellent education. He describes this education in autobiographical writings (rather strangely referring to himself in the third person):
"His father, who had never ceased to cultivate Latin and French literature, as well as several branches of science, raised him himself in the country near the city where he was born. He never required him to study anything, but he knew how to inspire in him a desire to know. Before being able to read, the young Ampère's greatest pleasure was to listen to passages from Buffon's natural history."
Ampère read articles from L'Encyclopédie many of which, Arago remarked many years later, he could recite in full in later life. Arago also claims that Ampère read the Encyclopédie starting at volume 1 and reading the articles in alphabetical order. Whether Ampère's later desire for classification in all subjects arose from this education, or whether he enjoyed Buffon and the Encyclopédie because of a natural liking for classifying, is hard to say.
It has been claimed that Ampère had mastered all known mathematics by the age of twelve years but this seems somewhat of an exaggeration since, by Ampère's own account, he did not start to read elementary mathematics books until he was 13 years old. However Ampère was always one to feel very confident in his own abilities and he certainly began to develop his own mathematical ideas very quickly and he began to write a treatise on conic sections. Ampère had no contacts with anyone with any depth of mathematical knowledge so it is not surprising that he felt that his ideas were original.
While still only 13 years old Ampère submitted his first paper to the Académie de Lyon. This work attempted to solve the problem of constructing a line of the same length as an arc of a circle. His method involves the use of infinitesimals but since Ampère had not studied the calculus the paper was not found worthy of publication. Shortly after writing the article Ampère began to read d'Alembert's article on the differential calculus in the Encyclopédieand realised that he must learn more mathematics.
After taking a few lessons in the differential and integral calculus from a monk in Lyon, Ampère began to study works by Euler and Bernoulli. He then acquired a copy of the 1788 edition of Lagrange's Mécanique analytique and began serious study of the work. Ampère writes (again writing about himself in the third person):
"... the reading of [Mécanique analytique] had animated him with a new ardour. He repeated all the calculations in it ..."
However his life was soon to be shattered. The French Revolution began with the storming of the Bastille on 14 July 1789 but the effect on the Poleymieux region was not very great at first. Ampère's father kept out of trouble until late in 1791 when he accepted the position of Justice of the Peace in Lyon. This post made it virtually impossible for him to avoid trouble but the first tragedy to hit the family was in 1792 when AndréMarie's sister died. The city of Lyon refused to carry out instructions from Paris and the city was besieged for two months. On the fall of the city Ampère's father was arrested for issuing an arrest warrant for the Jacobin Chevalier who had then been put to death. Ampère's father went to the guillotine with remarkable composure writing to Ampère's mother from his cell:
"I desire my death to be the seal of a general reconciliation between all our brothers; I pardon those who rejoice in it, those who provoked it, and those who ordered it...."
The effect on Ampère of his father's death was devastating. He gave up his studies of Mécanique analytique and did not return to the study of mathematics for 18 months. He only returned to something like his old self when he met a girl, Julie, who he fell deeply in love with. Julie seemed less attracted to Ampère:
"He has no manners; he is awkward, shy and presents himself
poorly."
Lycee LaLande at BourgenBresse 
Despite this coolness they were engaged to be married in 1797 and Ampère decided he better show that he could earn a living so began tutoring mathematics in Lyon. He married Julie in 1799 and their son JeanJacques was born in 1800. Ampère continued tutoring mathematics until 1802 when he was appointed professor of physics and chemistry at Bourg Ecole Centrale (Lycee LaLande at BourgenBresse). This was a difficult time for Ampère since Julie became ill before he made the move to Bourg leaving her at Poleymieux. 

While Ampère was in Bourg he spent much time teaching physics and chemistry but his research was in mathematics. This research resulted in him composing a treatise on probability, The Mathematical Theory of Games, which he submitted to the Paris Academy in 1803. Laplace noticed an error, explaining the error to Ampère in a letter, which Ampère was able to correct and the treatise was reprinted. In fact the treatise was modified a number of times and Ampère was reluctant to call it completed for fear that further changes might be required. This work was followed by one on the calculus of variations in 1803. 
After a year in Bourg, Ampère moved closer to Poleymieux being appointed to a mathematics position at the Lycée in Lyon on Delambre's recommendation. His time spent in Lyon had been made difficult due to the continuing decline in his wife's health. Mathematically he continued to produce good work, this time an interesting treatise on analytic geometry. Like a number of other mathematicians, Ampère seemed able to concentrate on his theorems despite the personal tragedy around him and, sadly, this would be required of him throughout his unhappy life. After his wife died in July 1803, Ampère was left with feelings of guilt for he had lived apart from his wife during much of their short marriage. He decided to leave Lyon for Paris. Hofman writes in [4] regarding his feelings following his wife's death:
"His subsequent depression contributed to his decision to take the earliest opportunity to leave Lyon for new surroundings in Paris. Later he would regret this decision. The Lyon friends who attempted to fill the emotional void left by Julie's death were missed painfully. Although Ampère gradually adjusted to the priority disputes and infighting of the Parisian scientific community, he always longed for a return to the intellectual life he experienced in Lyon."
AndréMarie Ampere, oil painting by an unknown artist (The
Mansell Collection)

By this time Ampère had a fair reputation as both a teacher of mathematics and as a research mathematician and on the strength of this reputation he was appointed répétiteur (basically a tutor) in analysis at the Ecole Polytechnique in 1804. Without a formal education and formal qualifications his appointment is surprising but shows that his potential was recognised at this stage. His life, already containing many tragedies, did not improve and he embarked on a disastrous marriage. Lagrange and Delambre attended his wedding to Jenny on 1 August 1806 but, before the birth of their daughter on 6 July 1807, the couple were living apart and were not on speaking terms. They were legally separated in 1808 and Ampère was given custody of their daughter Albine. 
Appointed professor of mathematics at the Ecole
Polytechnique in 1809 he held posts there until 1828. Ampère and Cauchy
shared the teaching of analysis and mechanics and there was a great contrast
between the two with Cauchy's rigorous analysis teaching leading to great
mathematical progress but found extremely difficult by students who greatly
preferred Ampère's more conventional approach to analysis and mechanics. Ampère
was appointed to a chair at Université de France in 1826 which he held until his
death.

In Paris Ampère worked on a wide variety of topics. Although a mathematics professor, his interests included, in addition to mathematics, metaphysics, physics and chemistry. In mathematics he worked on partial differential equations, producing a classification which he presented to the Institut in 1814. This seems to have been a crucial step in his election to the Institut National des Sciences in November 1814 when he defeated Cauchy, receiving 28 of the 56 votes cast. 
Ampère was also making significant contributions to chemistry. In 1811 he suggested that an anhydrous acid prepared two years earlier was a compound of hydrogen with an unknown element, analogous to chlorine, for which he suggested the name fluorine. After concentrating on mathematics as he sought admission to the Institut, Ampère returned to chemistry after his election in 1814 and produced a classification of elements in 1816.
Ampère also worked on the theory of light, publishing on refraction of light in 1815. By 1816 he was a strong advocate of a wave theory of light, agreeing with Fresnel and opposed to Biot and Laplace who advocated a corpuscular theory. Fresnel became a good friend of Ampère's and lodged at Ampère's home from 1822 until his death in 1827.
In the early 1820's, Ampère attempted to give a combined theory of electricity and magnetism after hearing about experimental results by the Danish physicist Hans Christian Ørsted. Ampère formulated a circuit force law and treated magnetism by postulating small closed circuits inside the magnetised substance.
Ampère was not a methodical experimenter; he was subject to
brilliant flashes of inspiration, which he would then pursue to their
conclusion. It is worth commenting on how quickly Ampère produced this theory,
the inspiration striking him immediately he heard of Ørsted's experimental
results.
Ampere and Arago investigate magnetism 
Danish physicist Hans Christian Ørsted's discovered in 1820 that a magnetic needle is deflected when the current in a nearby wire varies  a phenomenon establishing a relationship between electricity and magnetism. Ørsted's work was reported the Academy in Paris on 4 September 1820 by Arago and a week later Arago repeated Ørsted's experiment at an Academy meeting. Ampère demonstrated various magnetic / electrical effects to the Academy over the next weeks and he had discovered electrodynamical forces between linear wires before the end of September. He spoke on his law of addition of electrodynamical forces at the Academy on 6 November 1820 and on the symmetry principle in the following month. Ampère wrote up the work he had described to the Academy with remarkable speed and it was published in the Annales de Chimie et de Physique. 
He formulated a law of electromagnetism (commonly called Ampère's law) that describes mathematically the magnetic force between two electric currents. He also performed many experiments, the results of which served to develop a mathematical theory that not only explained electromagnetic phenomena already reported but predicted new ones as well. Among his laws of electrodynamics are: 1) parallel conductors currying currents in the same direction are attacted to each other and 2) parallel conductors carrying currents in the opposite directions are repelled from each other. He also suggest that electromagnetism could be used in telegraphy.
Ampère was assisted over the next few years in his work by Felix Savary whose help in getting Ampère to write up his results was invaluable [4]:
"... beginning with the memoir he completed early in 1823, Savary now made much more creative contributions. But more than his creativity, it was Savary's discipline and ability to concentrate at length on specific problems that proved especially valuable to Ampère. There is room to speculate that, without Savary's aid. Ampère might never have found time to complete the detailed calculations required to apply his force law to magnetic phenomena."
However Ampère was not the only one to react quickly to Arago's
report of Danish physicist Hans Christian Ørsted's discovery in 1820. Biot, with
his assistant Savart, also quickly conducted experiments and reported to the
Academy in October 1820. This led to the BiotSavart Law. Another who worked on
magnetism at this time was Poisson who insisted on treating magnetism without
any reference to electricity. Poisson had already written two important memoirs
on electricity and he published two on magnetism in 1826.

The first person to develop measuring techniques for electricity, Ampère built an instrument utilizing a freemoving needle to measure the flow of electricity. Its later refinement was known as the galvanometer. He used a highly sensitive galvanometer to make his measurements. A galvanometer is a device used to detect and measure the flow of electricity. A simple galvanometer is a compass with a wire wrapped around it. Connect either end of the wire to whatever you want to test (such as a battery) if the needle is deflected then a current has been created. The stronger the current the greate the needle will be deflated. Ampere invented the astatic needle, which made possible the modern astatic galvanometer. 
Ampère's most important publication on electricity and magnetism was also published in 1826. It is called Memoir on the Mathematical Theory of Electrodynamic Phenomena, Uniquely Deduced from Experience and contained a mathematical derivation of the electrodynamic force law and describes four experiments. Maxwell, writing about this Memoir in 1879, says:
"We can scarcely believe that Ampère really discovered the law of action by means of the experiments which he describes. We are led to suspect, what, indeed, he tells us himself, that he discovered the law by some process which he has not shown us, and that when he had afterwards built up a perfect demonstration he removed all traces of the scaffolding by which he had raised it."
Ampère's theory became fundamental for 19th century
developments in electricity and magnetism. Faraday
discovered electromagnetic induction in 1831 and, after initially believing that
he had himself discovered the effect in 1822, Ampère agreed that full credit for
the discovery should go to Faraday. Weber also developed Ampère's ideas as did
Thomson and Maxwell.

In 1826 Ampère began to teach at the Collège de France. Here he was in a position to teach courses of his own design, rather than at the Ecole Polytechnique were the topics were set down. Ampère therefore taught electrodynamics at the Collège de France and this course was taken by Liouville in 182627. This was the second time Ampère had taught Liouville since Liouville had taken Ampère's courses at the Ecole Polytechnique in the previous session. Liouville made an important contribution to Ampère's electrodynamics course by editing a set of notes taken from Ampère's lectures. 
Portrait of Ampère by Leonard de Selva 
Given the tragedy in Ampère's life it might have been hoped that his children would bring him some happiness. His son certainly achieved fame as a historian and philologist who studied the cultural origins of western European languages. He was appointed to a chair of history of foreign literature at the Sorbonne in 1830. However his relationship with his father was difficult. Hofmann in [4] writes: "Both men were temperamental and subject to long periods of brooding followed by explosive outbursts of anger. Ampère's home simply was not expansive to house both of them for any extended period of time." Ampère had an even more difficult time with his daughter. She married one of Napoleon's lieutenants in 1827 but he was an alcoholic and the marriage soon was in trouble. Ampère's daughter fled to her father's house in 1830 and, some days later, Ampère allowed her husband to live with him also. This proved a difficult situation, led to police intervention and much unhappiness for Ampère. 

AndréMarie Ampère died on June 10, 1836, in Marseille, France, in his fiftysecond year and was buried on Cimetiere de Montmartre, Paris. 


Sculptor: Fernand David (1872  1927) 
Sculptor: Charles Textor (18351905); Engraver: Henri Dochy Engraving from a statue: 41 cm x 30.5 cm Printed in Le Monde Illustre, Oct. 13, 1888 
Ampere's law:
The line integral of the magnetic flux around a closed curve is proportional to the algebraic sum of electric currents flowing through that closed curve.
The basic premise of ampere's law can be explained by the following simple integral:
This integral can be interpreted to mean the magnetic induction around a closed path is proportional to the net current passing through the area enclosed by the path. In the above integral B is the magnetic flux, I is the net current and m is the permeability. This law can be altered into different forms, depending upon the application in which it is to be used.
In general Ampere's law is similar to Gauss's Law of electric fields, except for the fact that it deals with magnetic fields, and uses a line integral instead of the surface integral used in Gauss's Law.
In the case of the outside of a long, straight wire, one gets the following derivation:
Ampere's law can also be used to find the magnetic fields of solenoids and torroids. A solenoid is a long hollow tube with many loops of wire wrapped around it. When current is run through the wires, a magnetic field is created inside the tube that is basically a straight line. It operates by the equation:
The practical uses of solenoids are very common, they operate the power door locks in your car and they also are an integral part of many doorbells, not to mention their role in starting your car.
In spite of its wondrous capabilities, Ampere's Law is limited and needs to be modified before it can be used in certain situations that involve currents distributed more generally than those generated by continuous conducting wires.
The necessary modification was proposed by Maxwell himself and looked something like this:
A permanent memorial to Ampere is the use of his name for the unit of electric current.
The ampere is the unit for measuring electric current. As more accurate procedures have been devised, the definition of the quantity has been changed. The most modern definition is based on the ability of a specified current to deposit a precise amount of a substance on an electrode during electrolysis. Formerly, the definition involved the force that was produced between parallel wires carrying a current; still earlier, the ampere was defined as a flow of one coulomb per second, where the coulomb (a quantity of electrical charge) was taken as the basic unit.
Ampere, basic unit of electric current, symbol A or amp, named
for the 19^{th}century French physicist André
Marie Ampère. The ampere was first defined as a flow of 1 coulomb of electricity
per second, and later in terms of
the current required to produce a certain amount of force between two wires:
The ampere is that constant current which, if maintained in two straight
parallel conductors of infinite length, of negligible circular cross section,
and placed 1 meter apart in vacuum, would produce between these conductors a
force equal to 2x10^{7} newton per meter of
length.
Ampere table, 1890 (from the collection "Sparkmuseum") 
This instrument was named for AndréMarie Ampère. This is an early model of the same apparatus constructed by Ampere for his famous experiments on the relationship between magnetic fields and electric current. 





