Maxwell's equation

It covers all the Maxwell's Equation for Point form(differential form) and integral form. It also covers Gauss Law for Electric Field, Gauss law for magnetic field, Faraday's Law and Ampere Maxwell law. It also covers the reason why Gauss Laws are also known as Maxwell's Equation.

1. Maxwell’s Equation In Integral and Differential Form A Presentation By: Abhijeet Gupta-14011011101 Prerak Trivedi-140110111045 Kunal Sheth-140110111054

2. CONTENTS Introduction Gauss Law for Electric Fields Gauss Law for Magnetic Fields Faraday’s Law The Ampere-Maxwell Law

3. The equations describing the relations between cha nging electric and magnetic fields are known as Maxwell’s equations. Maxwell’s equation are extensions of the known work of Gauss, Faraday and Ampere. There are two forms of each Maxwell equation namely Integral form and Differential form(point form). Maxwell’s equation in the Integral form governs the interdependence of certain field and source quantities(charge and current) associated with regions in space, surfaces and volumes. The Differential form of Maxwell’s equations relate characteristics of the field vectors at a given point to one another and to the source densities at that point. The Maxwell’s equations provides the mathematical background for the study of electromagnetic waves, transmission lines and antenna.

4. Gauss law for Electric Field The total electric flux crossing the closed surface is equal to the total charge enclosed by that surface. The electric flux through the closed surface is:- The charge can be expressed in terms of where D is the Flux Density Then the Gauss’s law for electric field is expressed as:-

5. The previous relation is called as Integral form of Maxwell’s equation derived from Gauss’s law for the electric field. To relate D with del operator to convert surface integral into volume integral using Divergence theorem as:- Comparing two integrals, we can say that,

6. Gauss’s law for Magnetic F ields The total magnetic flux crossing the closed surface is equal to zero. The reason for this is that the magnetic flux lines are always closed in nature . Due to which a closed surface in the presence of these lines will have same number of incoming and outgoing flux lines. The incoming flux, is considered as “ + “ and the outgoing flux, is considered as “ – “.

7. Faraday’s Law Michael Faraday discovered experimentally that a current was induced in a conducting loop when a magnetic flux linking the loop is changed. The current which is induced indicates the existence of a voltage or an relationship between the induced emf and the rate of change of flux linkage is known as Faraday’s law. In a closed path the electric potential is developed due to time varying magnetic field in the vicinity of closed path. The “ –VE “ sign in the equation indicates a LENZ LAW, which states that the current induced in a loop in such a direction as to oppose the cause producing it.

8. Ampere’s-Maxwell Law Ampere's circuit law states that the line integral of the tangential component of H around a closed path is the same as the net current I enc enclosed by the path . So, in other words, the circulation of Magnetic Field H equals I enc Ampere's law is similar to Gauss's law and it is easily applied to determine H when the current distribution is symmetrical. The above equation always holds whether the current distribution is symmetrical or not but we can only use the equation to determine H when symmetrical current distribution exists. Ampere's law is a special case of Biot -Savart's law

9. By applying Stoke's theorem to the left-hand side of above equation, we obtain But, Comparing surface integrals, we get that

10. Application of Ampere-Maxwell’s L aw  Thank You 