The original form of Maxwell's circuital law, which he derived as early as in his paper "On Faraday's Lines of Force"  based on an analogy to hydrodynamics, relates magnetic fields to electric currents that produce them. It determines the magnetic field associated with a given current, or the current associated with a given magnetic field. The original circuital law is only a correct law of physics in a magnetostatic situation, where the system is static except possibly for continuous steady currents within closed loops. For systems with electric fields that change over time, the original law as given in this section must be modified to include a term known as Maxwell's correction see below.
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Before proceeding to interpret this law, it is useful to see that it is dimensionally correct. See Section 7. That is, ACL provides a means calculate the magnetic field given the source current. ACL also has a similar limitation. Generally, symmetry is required to simplify the problem sufficiently so that the integral equation may be solved.
Fortunately, a number of important problems fall in this category. Examples include the problems addressed in Sections 7. For problems in which the necessary symmetry is not available, the differential form of ACL may be required Section 7. Finally, be aware that the form of ACL addressed here applies to magnetostatics only. In the presence of a time-varying electric field, the right side of ACL includes an additional term known as the displacement current Section 8.
Ellingson, Steven W. Report adoption of this book here. If you are a professor reviewing, adopting, or adapting this textbook please help us understand a little more about your use by filling out this form. Contributors and Attributions Ellingson, Steven W.
Ampère's circuital law