Understanding Maxwell's Equations in Electromagnetism
Explore the derivation and significance of Maxwell's equations in electromagnetism. Dr. R. R. Mistry, an experienced assistant professor, explains the four fundamental equations in differential form as established by Maxwell. Gain insights into Gauss's law, magnetostatics, Faraday's law, and more through a comprehensive analysis of electromagnetic induction. Unravel the empirical basis and modifications in Ampere's law, shedding light on the differential forms and practical applications. Dive into the rigorous derivations of each equation, including Gauss's law for electrostatic fields and the depiction of magnetic lines of force. Utilize Gauss's divergence theorem to delve deeper into the relationship between surface and volume integrals, enhancing your understanding of foundational concepts in electromagnetism.
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Presentation Transcript
Dr. R. R. Mistry M.Sc. (Physics), SET, Ph.D. Assistant Professor
Maxwells Equations and Their Empirical Basis:- There are four fundamental equations of electromagnetism known Equations which may be written in differential form as as Maxwell s
Equation (1) represents the differential form of Gauss s law in electrostatics which is derives from Coulomb s law. Equation (2) represents magnetostatics which is represent that isolated magnetic poles do not exist in our physical world. Equation (3) represents differential form of Faraday s law of electromagnetic induction. Equation (4) represents Maxwell s modification of Ampere s law to include timevarying fields. Gauss s law in
Derivation of Maxwells Equations:- 1)Derivation of Maxwell s first Equation Gauss s law for electrostatic field is known as Maxwell s first equation. Gauss s law states that the electric flux over a closed surface is equal to 1/ 0times the total charge enclosed within the surface.
2) Derivation of Maxwells second Equation The number of magnetic lines of force entering any arbitrary closed surface is exactly the same as leaving it. It means that the flux of magnetic induction B across any closed surface is always zero.
Using Gausss divergence theorem to change surface integral into volume integral, weget As the surface bounding the volume is arbitrary, therefore the integral of this equation mustvanish.
3) Derivation of Maxwells Third Equation, According to Faraday s law of electromagnetic induction it is known that e.m.f. induced in a closed loop is equal to negative rate of changeof magnetic flux i.e.
Consider a capacitor consisting of two parallel plates P1and P2as shown in figure. The closed path C encloses two surfaces S1 and S2; S1intersects a current I and S2 passes between thecapacitorplates. Ampere s law forpath C and surface S1is
The current density is zero for every point on S2. Equations (3) and (4) contradict each other. Equation (3) does not involve the capacitor for equation (4) we modify to include thecapacitor. Since divergence of curl is zero, we have from equation (2)
There is electric charge accumulated on P1 enclosed by surfaces S1and S2 We haveequation of continuityas
