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Physical interpretation

Formulation by Maxwell in terms of Fields

Beginning in the 1850s, Maxwell started work on the qualitative ideas about lines of force ofFaraday and produced a completely different account of electrodynamics, based on the concept

of continuous fields. He showed that the inverse-square force laws of Michell and Coulomb can

equally well be expressed in terms of fields. In integral form, the flux of the electric field overany closed surface equals the charge enclosed within that surface. In differential form the same

field law can be expressed by stating that the divergence of the field at any point equals the

charge density at that point. Hence at any point free of charge, the divergence of the field is zero.(Incidentally, the fact that magnetic charges, i.e. mono-poles are absent, leads to the conclusion

that the divergence of the magnetic field vanishes everywhere). Maxwell also expressed the

dynamical relations of Ampere and Faraday in terms of fields associated with moving magnets

and electric charges. The equations he derived were later converted to a set of four partial

differential equations called as Maxwells equations. All the information encoded in these fourequations had been derived directly from experimental observations and the laws of Michell,

Coulomb, Ampere, Faraday etc. Maxwell had only corrected the Amperes law by adding the

displacement current term. The rest of the equations were discovered by his predecessors. Still,all four of them are referred to as Maxwells equations. The reason is that Maxwell was the first

one to realize that these four equations were all there is to Electromagnetic fields (i.e., the theory

was complete). Maxwells equations, along with the Lorentz force equation, defineElectrodynamics completely.

Maxwell attempted to present formulation of electrodynamics in such a way that it did not relyon the concept of action at a distance. Similar to M. Faraday he regarded that the fields of force

have consecutive parts and that the force is communicated from one part to adjacent parts overtime. In other words, his main emphasis was on the idea of local action and not on the materialmechanism for this action. He was of the opinion that a material mechanism would certainly

satisfy local action, but that local action need not imply a material mechanism.

Einstein said: "Since Maxwell's time, physical reality has been thought of as represented by

continuous fields, and not capable of any mechanical interpretation. This change in the

conception of reality is the most profound and the most fruitful that physics has experiencedsince the time of Newton"

Analogy and Differences in Electric and Magnetic Fields

The additional term (Displacement current) Maxwell added to the right hand side of the equation

for Ampere's law is analogous to that on the right hand side of Faraday's law. In Faraday's lawthat term is the derivative of the magnetic flux, while Maxwell's new term in Ampere's law

equation has the derivative of the electric flux. Physically this term means that a changing

electric field can create a magnetic field. Thus Maxwells equations (Amperes law andFaradays law) contain some analogus quantities in electric and magnetic fields.

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There are in fact two origins for the magnetic field:

(1) the current densityj, as Ampre had already established, and (2) due to called as the

Displacement current.

Though Maxwell added the electric current term in Ampere's law but he did not add a magneticcurrent term in Faraday's law. Here the analogy does not exist. All magnetic fields are created by

some type of changing electric field because free magnetic monopoles do not exist and without

magnetic monopoles there can be no magnetic current. Thus one of the important consequence of

Faradays law- that All magnetic poles occur in pairs (i.e. dipoles)- was emphasized by Maxwellalso.

The Concept of Electromagnetic Fields

The electromagnetic wave equation which evolved from Maxwells equations predicted that theelectromagnetic radiation could propagate indefinitely through space, far away from their origin.

Speed of Light

Maxwell discovered that electromagnetic waves propagate at the speed of light. The speed in

vacuum is independent both of the motion of the light source and of the inertial frame ofreference of the observer. Thus he discovered a fundamental constant of nature: the speed of

light.

Similarity in the Field Equations of Electromagnetism and Relativity

Maxwell augmented the Amperes law equation by the term or called as thedisplacement current. It is interesting to note that the process by which Maxwell found the finalform of electromagnetic field equations is very much similar to the process by which Einstein

arrived at the final field equations of general relativity. In both cases, the extra term was added in

order to give a divergenceless field.