WINSEM2024-25_BPHY101L_TH_VL2024250505527_2025-01-20_Reference-Material-I.pptx

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1. Maxwell’s Equations Ezhil Vizhi R Professor VIT

2. James Clerk Maxwell was a Scottish mathematician and theoretical physicist. His most significant achievement was the development of the classical electromagnetic theory. His set of equations demonstrated that electricity, magnetism and even light are all manifestations of the same phenomenon. These equations are called the “Maxwell's equations” . James Clerk Maxwell (1831–1879) Ezhil Vizhi R Professor VIT

3. Maxwell's work in electromagnetism has been called the "second great unification in physics" , after the first one carried out by Isaac Newton. Maxwell demonstrated that electric and magnetic fields travel through free space in the form of waves at the speed of light. They apply to all charge and current densities, whether static or dynamics (time-dependent). Moreover, divergences and curls have clear physical interpretations, telling us how the fields spread out and circulate at each point. Ezhil Vizhi R Professor VIT

4. Maxwell’s modified Ampere’s law Differential form of Maxwell equations Relative permittivity of medium Permittivity of free space       Relative permeability of medium Permeability of free space     Ezhil Vizhi R Professor VIT

5. The physical significance of Maxwell’s equations is easily understood by converting from differential form into integral form. Two important theorems help us to convert differential form into integral form are Electric charge density Electric current density Electric flux density/displacement field Magnetic flux density Electric field strength/intensity Magnetic field strength/intensity   Ezhil Vizhi R Professor VIT

6. Useful Mathematical Theorems Gauss’ Divergence Theorem Stokes’ Curl Theorem Ezhil Vizhi R Professor VIT

7. Integral form of Maxwell equations Ezhil Vizhi R Professor VIT

8.   Taking volume integral on both sides   From Gauss divergence theorem, LHS of above equation changes from volume integral into surface integral,   Maxwell equation - 1 : Gauss’s law of electrostatics Ezhil Vizhi R Professor VIT

9.       Electric flux It states that “the total electric flux  passing through a closed surface is equal to  times the net charge with in the volume enclosed by the surface” .   Ezhil Vizhi R Professor VIT

10.   Taking volume integral on both sides   From Gauss divergence theorem, LHS of above equation changes from volume integral into surface integral,   Maxwell equation - 2 : Gauss’s law of magneto-statics   Magnetic flux It states that “the total magnetic flux  emerging through a closed surface is zero” .   Ezhil Vizhi R Professor VIT

11. Maxwell equation - 3 : Faraday’s law of induction   Taking surface integral on both sides   From Stoke’s curl theorem, LHS of above equation changes from surface integral into line integral,   It states that “the magnitude of induced emf is equal to the rate of change of magnetic flux linked with any surface closed by the circuit” . Ezhil Vizhi R Professor VIT

12. Maxwell equation - 4 : Maxwell’s modified Ampere’s law   Taking surface integral on both sides   From Stoke’s curl theorem, LHS of above equation changes from surface integral into line integral,   Ezhil Vizhi R Professor VIT

13. It states that ”the magnitude of induced mmf around any closed path or circuit is equal to the sum of conductions current and displacement current (or times rate of change of electric flux) through any surface bounded by the path” .     Ezhil Vizhi R Professor VIT

14. Gauss’s law of electro-statics The total electric flux passing through a closed surface is equal to  times the net charge with in the volume enclosed by the surface Gauss’s law of magneto-statics The total magnetic flux emerging through a closed surface is zero. Faraday’s law of induction The induced emf is equal to the rate of change of magnetic flux linked with any surface closed by the circuit. Maxwell modified Ampere’s law The induced mmf any closed path is equal to sum of conductions current and displacement current through any surface bounded by the path” . Gauss’s law of electro-statics Gauss’s law of magneto-statics The total magnetic flux emerging through a closed surface is zero. Faraday’s law of induction The induced emf is equal to the rate of change of magnetic flux linked with any surface closed by the circuit. Maxwell modified Ampere’s law The induced mmf any closed path is equal to sum of conductions current and displacement current through any surface bounded by the path” .         Physical significance of Maxwell equations Ezhil Vizhi R Professor VIT