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| maxwell_equations [2025/12/06 12:51] – [Maxwell's equations] stan_zurek | maxwell_equations [2025/12/06 12:53] (current) – [Maxwell's equations] stan_zurek |
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| 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 known 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]]. | 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 known 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]]. |
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| To fully quantify an electromagnetic vector field $F$ it is necessary to determine its [[divergence]] ($∇⋅F$) as well as [[curl]] ($∇×F$).[(Griffiths)] For other fields, such as [[thermal field|thermal]], it is also useful to calculate [[gradient]], for example by employing [[vector calculus]]. | To fully quantify an electromagnetic vector field $F$ it is necessary to determine its [[divergence]] ($∇⋅F$) as well as [[curl]] ($∇×F$).[(Griffiths)] For other fields, such as [[thermal field|thermal]], it is also useful to calculate [[gradient]] ($∇F$), for example by employing [[vector calculus]]. |
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