Like many electrical researchers and theoreticians of his time, André-Marie Ampère endured a measure of tragedy and misfortune, in part because of the excesses of the French Revolution. But personal setbacks did not impede the great energy that he brought to his work.
In early life, young André-Marie’s benevolent father was a formative, defining influence. An enthusiastic adherent of the philosophy of Jean-Jacques Rousseau (who argued that the stage of human development associated with what he called “savages” was better than that of decadent civilization), the elder Ampère devised an at-home study program that emphasized a nature-based education as opposed to formal schooling. This worked well for the inquisitive youth, but then a traumatic event occurred that cast a dark and lasting shadow across Ampère’s entire life.
Following the rise of the doctrinaire and brutal Jacobin faction within the French Revolution, Ampère’s father, who had been a justice of the peace under an earlier regime, succumbed to the guillotine. Following a period of intense sorrow, Ampère married the girl of his dreams and immersed himself in mathematical and astronomical research. His interests were wide-ranging. He wrote about probability theory and engaged in teaching and research, but another crushing event was the death of his young wife. Despite intense sorrow, he pursued his life work, writing, teaching and experimentation.
Today his name is a household word. Homeowners speak knowledgeably about 15-A as opposed to 20-A circuits and discuss the benefits of a 200-A service. The SI unit of current, the ampere, is named after him.
Learning of Hans Christian Ørsted’s discovery that a magnetic needle is deflected by current in a nearby conductor, Ampère further demonstrated that two current-carrying wires either attract or repel one another depending on the direction of the current flow. A logical step that followed was his formulation of what came to be known as Ampère’s law. It states that the mutual attraction or repulsion of two parallel wires is proportional to the amount of current and lengths of those conductors.
When expressed as an equation, Ampere’s law is often given in its integral form. There are two equations of note. The first is in terms of total current, which includes both free and bound current. Free current is that flowing through the wire, i.e. current carriers (electrons and electron holes). Bound current refers to the idea of electrons bound to atoms but which can be polarized by a magnetic field. The total current expression for Ampere’s law says that the line integral of the magnetic B-field (in tesla, T) around closed curve C is proportional to the total current Ienc passing through a surface S (enclosed by C), where J is the total current density (in ampere per square meter, A/m2).
The second integral form of Ampere’s law is expressed in terms of free current. It says the line integral of the magnetic H-field (in amperes per meter, A/m) around closed curve C equals the free current If,enc through a surface S, where Jf is the free current density only. Here the double integral denotes a 2D surface integral over S enclosed by a curve C. Note also the • is the vector dot product, dℓ is a differential of the curve C (i.e. a vector with magnitude equal to the length of the infinitesimal line element, and a direction given by the tangent to the curve C); dS is the vector area of an infinitesimal element of surface S (that is, a vector with magnitude equal to the area of the infinitesimal surface element, and direction normal to surface S. The direction of the normal must correspond with the orientation of C by the right hand rule).
At this point, Ampère turned his attention to the phenomenon of magnetism. He conceived an “electrodynamic molecule” that would be the fundamental carrier of magnetic as well as electrical energy. Today we call this particle the electron. It is a true elementary particle inasmuch as to the best of our knowledge it cannot be further subdivided.
Kjell Prytz says
Hi!
Thanks for info.
Could you give the reference where Ampere derives or presents this integral law.
Greetings
Kjell