Maxwells equations &their integral and differential forms

Prepared by

MUHAMMAD HASSAN MALIKReg#4362&MUHAMMAD HUSNAINReg#4363

Table of contentsHistory and importanceConceptual descriptionLawsIntegral form of Maxwell's equationsDifferential form of Maxwell's equationsSummaryReferences

James Clerk Maxwell (1831 - 1879)

History & ImportanceJames Clerk Maxwell(13 June 1831 5 November 1879) was aScottish theoretical physicist and mathematician. His most prominent achievement was formulating classicalelectromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and even optics into a consistent theory.Maxwell's equationsdemonstrated that electricity, magnetism and even light are all manifestations of the same phenomenon, namely theelectromagnetic field. Subsequently, all other classic laws or equations of these disciplines were simplified cases of Maxwell's equations. Maxwell's achievements concerning electromagnetism have been called the "second great unification in physics",after the first one byIsaac Newton.

Conceptual description Maxwell formulated four equations. That together form a complete description of the production and interrelation ofelectric andmagnetic fields. Maxwell based his description ofelectromagnetic fields on these four statements

The statements of these four equations are :

Electric field diverges fromelectric charge.

There are no isolated magnetic poles.

Electric fields are produced by changing magnetic fields.

Circulating magnetic fields are produced by changing electric fields and by electric currents.

Laws Maxwells equations relate with four basic physical laws

Maxwells 1st law from Gauss's law of electrostatics.Maxwells 2nd law from Gauss's law of magnetism. Maxwells 3rd law from Faradays law of induction.Maxwells 4th law from Amperes circuital law.

Maxwells 1st law from Guasss law of electrostatics.

This lawdescribes the relationship between anelectric fieldand the generatingelectric charges. The electric field points away from positive charges and towards negative charges. In the field line description, electric field lines begin only at positive electric charges and end only at negative electric charges. Counting the number of field lines in aclosed surface yields the total charge enclosed by that surface. More technically, it relates theelectric fluxthrough any hypotheticalclosed"Gaussian surface" to the electric charge within the surface.

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Maxwells 2nd law from Guasss law of magnetism.

The magnetic field is generated by a configuration called adipole and not due to material. Magnetic dipoles are best represented as loops of current but resembles a positive and negative magnetic charges bound together and having no net magnetic charge.

Contt.In terms of field lines, this equation states that magnetic field lines neither begin nor end but make loops or extend to infinity and back.

In other words, any magnetic field line that enters a given volume must somewhere exit that volume.

Equivalent technical statements are that the totalmagnetic fluxthrough any Gaussian surface is zero.

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Maxwells 3rd law from Faradays law of inductionThis lawdescribes how a time varyingmagnetic fieldcreates ("induces") anelectric field.This aspect of electromagnetic inductionis the operating principle behind manyelectric generators: For example a rotatingbar magnetcreates a changing magnetic field, which in turn generates an electric field in a nearby wire. (Note: there are two closely related equations which are called Faraday's law. The form used in Maxwell's equations is always valid but more restrictive than that originally formulated byMichael Faraday.)

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Maxwells 4th law from Amperes circuital law.

This law states that magnetic fields can be generated in two ways: By electrical current(this was the original "Ampere's law") and by changing electric fields (this was "Maxwell's correction").Maxwell's correction to Ampere's law is particularly important: It means that a changing magnetic field creates an electric field,anda changing electric field creates a magnetic field.Therefore, these equations allow self-sustaining "electromagnetic waves" to travel through empty space .

Contt.The speed calculated for electromagnetic waves, which could be predicted from experiments on charges and currents,exactly matches thespeed of light; lightisone form of electromagnetic radiation (as areX-rays,radio waves, and others). Maxwell understood the connection between electromagnetic waves and light in 1861, thereby unifying the previously-separate fields ofelectromagnetismandoptics

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Maxwells equations in integral form 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

Maxwells equations in differential form Differential form in the absence of magnetic or polarizable media:

I.Gausss law for electricity

II.Gausss law for magnetism

III.Faraday's law of induction

IV.Ampere's law

SummaryIn short Maxwell introduced the concept of magnetic and electric fields.He did this by deriving his ideas from the basic electric and magnetic laws given by other scientists like Gauss , Faraday & Ampere.He formulated four equation using the previous knowledge from the laws of the above mentioned scientists.And derived these equations in integral as well as in their differential from.Maxwell also help in determining the speed of electromagnetic waves And considered light also as electromagnetic waves This idea helped a lot in expanding the field of optics He also worked with the theory of relativity.

Referencess http://en.wikipedia.org/wiki/Maxwell's_equationshttp://en.wikipedia.org/wiki/James_Clerk_Maxwellhttp://www.answers.com/topic/maxwell-s-equationshttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq.htmlhttp://en.wikipedia.org/wiki/File:VFPt_dipole_magnetic2.svg (picture)http://www.radioelectronicschool.net/files/downloads/faradyanim.gif(picture)http://www.mikesmagnetsplus.com/sol.gif (picture)

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