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.

Symbols Used
E = Electric fieldρ = charge densityi = electric current
B = Magnetic fieldε0 = permittivityJ = current density
D = Electric displacementμ0 = permeabilityc = speed of light
H = Magnetic field strengthM = MagnetizationP = Polarization
Integral formDifferential form
Index

Maxwell's equations concepts
 
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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
Differential formDiscussion
Index

Maxwell's equations concepts
 
HyperPhysics***** Electricity and Magnetism R Nave
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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.
Integral formDiscussion
Differential form with magnetic and polarizable media
Index

Maxwell's equations concepts
 
HyperPhysics***** Electricity and Magnetism R Nave
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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.
Integral formDiscussion
Index

Maxwell's equations concepts
 
HyperPhysics***** Electricity and Magnetism R Nave
Go Back