Ampère's circuital law

Template:Electromagnetism

In classical electromagnetism, Ampère’s circuital law, discovered by André-Marie Ampère, relates the integrated magnetic field around a closed loop to the electric current passing through the loop. It is the magnetic analogue of Gauss’s law, and one of the four Maxwell’s equations that form the basis of classical electromagnetism.

In its historically original form, Ampère’s Circuital law relates the magnetic field <math>\mathbf{B}</math> to its source, the current density <math>\mathbf{J}</math>. The equation is not in general correct (see “Maxwell’s correction” below), but is correct in the special case where the electric field is constant (unchanging) in time.

The law can be written in two forms, the “integral form” and the “differential form”. The forms are equivalent, and related by the Kelvin-Stokes theorem.

• Griffiths, David J. (1998). Introduction to Electrodynamics (3rd ed.). Prentice Hall. ISBN 013805326X.
• Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0716708108.

• a section on Ampere’s law from an online textbook
• MISN-0-138 Ampere’s Law (PDF file) by Kirby Morgan for Project PHYSNET.
• MISN-0-145 The Ampere-Maxwell Equation; Displacement Current (PDF file) by J.S. Kovacs for Project PHYSNET.
• The Ampère’s Law Song (PDF file) by Walter Fox Smith; Main page, with recordings of the song.
• Ampere’s Law on Project PHYSNET.

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