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# Maxwell’s Equations for Electromagnetic Fields

DOI link for Maxwell’s Equations for Electromagnetic Fields

Maxwell’s Equations for Electromagnetic Fields book

# Maxwell’s Equations for Electromagnetic Fields

DOI link for Maxwell’s Equations for Electromagnetic Fields

Maxwell’s Equations for Electromagnetic Fields book

## ABSTRACT

Maxwell’s equations describe the basic laws of the electromagnetic field. Over the 40 years preceding Maxwell’s enunciation of his equations (1865), the four fundamental laws describing the electromagnetic field had been discovered. They are known as Ampère’s Law, Faraday’s Law, Coulomb’s Law, and the magnetic continuity law. These four laws were cast by Maxwell, and further refined by his successors, into four differential equations:

∇ × = ∂ ∂

H j D

+ t

∇ × − ∂ ∂

E B

= t

∇ ⋅ =D ρ, (27.3)

∇ ⋅ =B 0. (27.4)

These are Maxwell’s famous equations for fields and sources in macroscopic media: E and H are the instantaneous electric and magnetic fields, D and B are the displacement vector and the magnetic induction vector, and j and ρ are the current and the charge density, respectively. We note that Equation 27.1 without the term ∂D/∂t is Ampère’s Law; the second term in Equation 27.1 was added by Maxwell and is called the displacement current. A very thorough and elegant discussion of Maxwell’s equations is given in the text Classical Electrodynamics by J. D. Jackson, and the reader will find the required background to Maxwell’s equations there [1].