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--- maxwell_equations [2024/06/07 14:58] – [Electromagnetic quantities] stan_zurek
+++ maxwell_equations [2024/06/07 15:00] (current) – [Maxwell's equations] stan_zurek
@@ Line 9: / Line 9: @@
 **Maxwell's equations** or **Maxwell-Heaviside equations** - a set of mathematical equations which describe the behaviour of electromagnetic field in space and time.[(Maxwell>[[https://doi.org/10.1098/rstl.1865.0008|James Clerk Maxwell, 1865 VIII. A dynamical theory of the electromagnetic field, Philosophical Transactions of the Royal Society of London, 155: 459–512. https://doi.org/10.1098/rstl.1865.0008]])][(Griffiths>[[http://books.google.com/books?isbn=0321856562|David J. Griffiths, Introduction to electrodynamics, 4th ed., Pearson, Boston, 2013, ISBN 0321856562]])][(Purcell>[[https://isbnsearch.org/isbn/9781107014022|E.M. Purcell, D.J. Morin, Electricity and magnetism, 3rd edition, Cambridge University Press, 2013, ISBN 9781107014022]])][(Fleisch_Maxwell>[[https://isbnsearch.org/isbn/9780521877619|Daniel Fleisch, A Student’s Guide to Maxwell’s Equations, Cambridge University Press, Cambridge, 2008, ISBN 9780521877619]])][(Feynman>[[https://www.feynmanlectures.caltech.edu/II_36.html|Richard Feynman, Robert Leighton, Matthew Sands, Ferromagnetism, The Feynman Lectures on Physics, Vol. II, Basic Books, ISBN: 9780465079988]])][(Band>[[https://isbnsearch.org/isbn/9780471899310|Yehuda B. Band, Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers, John Wiley & Sons, 2006, ISBN 9780471899310]])][(Fiorillo>[[https://isbnsearch.org/isbn/9780122572517|Fausto Fiorillo, Measurement and Characterization of Magnetic Materials, Academic Press, 2005, ISBN 9780122572517]])]
-In his original publication in 1865,[(Maxwell)] **James Clerk Maxwell** listed 20 equations, which were split for each orthogonal coordinates (hence the large number of equations). These equations were later rationalised by **Oliver Heaviside**, who expressed them in a [[vector]] form which is know today.[(Heaviside>[[https://macsphere.mcmaster.ca/bitstream/11375/14746/1/fulltext.pdf|Oliver Heaviside, Electromagnetic theory, Vol. I, 1893, Ernest Benn Limited]])] There are four basic electromagnetic equations, supplemented by additional [[constitutive relations]], as well as expressions of energy conservation, and force.
+In his original publication in 1865,[(Maxwell)] **James Clerk Maxwell** listed 20 equations, which were split for each orthogonal coordinates (hence the large number of equations). These equations were later rationalised by **Oliver Heaviside**, who expressed them in a [[vector]] form which is know today.[(Heaviside>[[https://macsphere.mcmaster.ca/bitstream/11375/14746/1/fulltext.pdf|Oliver Heaviside, Electromagnetic theory, Vol. I, 1893, Ernest Benn Limited]])] There are four basic electromagnetic equations, supplemented by additional [[constitutive relations]], as well as expressions of energy conservation, and [[electromagnetic force]].
-To fully quantify an electromagnetic vector field it is necessary to determine its [[divergence]] as well as [[curl]].[(Griffiths)] For other fields, such as [[thermal field|thermal]], it is also useful to calculate [[gradient]].
+To fully quantify an electromagnetic vector field it is necessary to determine its [[divergence]] as well as [[curl]].[(Griffiths)] For other fields, such as [[thermal field|thermal]], it is also useful to calculate [[gradient]], for example by employing [[vector calculus]].
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