What are Maxwell’s Equations?

Maxwell’s Equations

Maxwell’s Equations are a set of four equations. These equations successfully explain the entire world of electromagnetic. The whole of classical electromagnetic phenomena can be explained by Maxwell equations. As light can be described as electromagnetic radiation thus Maxwell equations are very useful to explain many characteristics of light including polarization. Here I am just stating these equations without derivation. Since my goal is simply to familiarize you with this concept. 

Maxwell’s four equations are given by

∇·E = ρ/ε0                                                                                         (1)
∇·B = 0 (2)
∇×E = −∂B/∂t (3)
∇×H = J + ∂D/∂t (4)

∇·E = ρ/ε₀                                                                                          (1)

∇·B = 0                                                                                   (2)

∇×E = −∂B/∂t                                                                                    (3)

∇×H = J + ∂D/∂t                                                                                 (4)

As you can see these equations explain the unique co-occurrence of the electric field and the magnetic field. Maxwell is the first scientist who discovered that the speed of electromagnetic waves is equal to the speed of light and he also concluded that light is an electromagnetic wave itself.

Physical significance of Maxwell’s 1st equation

∇·E = ρ/ε₀

According to Gauss’s law of electrostatics, total electric flux through any closed surface is equal to 1//ε₀ times the total charge enclosed by that closed surface. It is a steady state equation as it is independent of time.

Physical significance of Maxwell’s 2nd equation

∇·B = 0

It represents Gauss law of magnetostatic as ∇·B = 0 resulting in isolated magnetic poles or magnetic monopoles cannot exist as they appear only in pairs and there is no source or sink for magnetic lines of forces. It is also independent of time i.e. steady state equation.

Physical significance of Maxwell’s 3rd equation

∇×E = −∂B/∂t           

It shows that according to Faraday’s law of electromagnetic induction, time varying magnetic flux produced electric field. This is a time dependent equation.

Physical significance of Maxwell’s 4th equation

∇×H = J + ∂D/∂t      

Maxwell’s fourth equation represents the modified differential form of Ampere’s circuital. This is a time dependent equation. This explains that magnetic fields are produced due to the combined effect of conduction current density and displacement current density.

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