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  2. Ampère's force law - Wikipedia

    en.wikipedia.org/wiki/Ampère's_force_law

    The best-known and simplest example of Ampère's force law, which underlaid (before 20 May 2019 [1]) the definition of the ampere, the SI unit of electric current, states that the magnetic force per unit length between two straight parallel conductors is =,

  3. Mathematical descriptions of the electromagnetic field

    en.wikipedia.org/wiki/Mathematical_descriptions...

    There are various mathematical descriptions of the electromagnetic field that are used in the study of electromagnetism, one of the four fundamental interactions of nature. In this article, several approaches are discussed, although the equations are in terms of electric and magnetic fields, potentials, and charges with currents, generally ...

  4. Ampere - Wikipedia

    en.wikipedia.org/wiki/Ampere

    As of the 2019 revision of the SI, the ampere is defined by fixing the elementary charge e to be exactly 1.602 176 634 × 10 −19 C, [6] [9] which means an ampere is an electric current equivalent to 10 19 elementary charges moving every 1.602 176 634 seconds or 6.241 509 074 × 10 18 elementary charges moving in a second.

  5. André-Marie Ampère - Wikipedia

    en.wikipedia.org/wiki/André-Marie_Ampère

    Ampère began developing a mathematical and physical theory to understand the relationship between electricity and magnetism. Furthering Ørsted's experimental work, Ampère showed that two parallel wires carrying electric currents attract or repel each other, depending on whether the currents flow in the same or opposite directions ...

  6. Maxwell's equations - Wikipedia

    en.wikipedia.org/wiki/Maxwell's_equations

    The publication of the equations marked the unification of a theory for previously separately described phenomena: magnetism, electricity, light, and associated radiation. Since the mid-20th century, it has been understood that Maxwell's equations do not give an exact description of electromagnetic phenomena, but are instead a classical limit ...

  7. Monge–Ampère equation - Wikipedia

    en.wikipedia.org/wiki/Monge–Ampère_equation

    In mathematics, a (real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function u of two variables x,y is of Monge–Ampère type if it is linear in the determinant of the Hessian matrix of u and in the second-order partial derivatives of u.

  8. List of incomplete proofs - Wikipedia

    en.wikipedia.org/wiki/List_of_incomplete_proofs

    For example, a Fourier series of sine and cosine functions, all continuous, may converge pointwise to a discontinuous function such as a step function. Carmichael's totient function conjecture was stated as a theorem by Robert Daniel Carmichael in 1907, but in 1922 he pointed out that his proof was incomplete. As of 2016 the problem is still open.

  9. Ampère's circuital law - Wikipedia

    en.wikipedia.org/wiki/Ampère's_circuital_law

    In the 1850s Scottish mathematical physicist James Clerk Maxwell generalized these results and others into a single mathematical law. The original form of Maxwell's circuital law, which he derived as early as 1855 in his paper "On Faraday's Lines of Force" [ 9 ] based on an analogy to hydrodynamics, relates magnetic fields to electric currents ...