Maxwell's Equations

Maxwell's equations represent one of the most elegant and concise ways to state the fundamentals of electricity and magnetism. From them one can develop most of the working relationships in the field. Because of their concise statement, they embody a high level of mathematical sophistication and are therefore not generally introduced in an introductory treatment of the subject, except perhaps as summary relationships.

These basic equations of electricity and magnetism can be used as a starting point for advanced courses, but are usually first encountered as unifying equations after the study of electrical and magnetic phenomena.

Maxwell's Equations

Integral form in the absence of magnetic or polarizable media:

I. Gauss' law for electricity

II. Gauss' law for magnetism

III. Faraday's law of induction

IV. Ampere's law

Maxwell's Equations

Differential form in the absence of magnetic or polarizable media:

I. Gauss' law for electricity

II. Gauss' law for magnetism

III. Faraday's law of induction

IV. Ampere's law

Note:

here represent the vector operations divergence and curl, respectively.

Maxwell's Equations

Differential form with magnetic and/or polarizable media:

I. Gauss' law for electricity

II. Gauss' law for magnetism

III. Faraday's law of induction

IV. Ampere's law

Note:

here represent the vector operations divergence and curl, respectively.