Maxwell's equation and it's correction in Ampere's circuital law

In this presentation, you will get the detailed information about the problem with Ampere's circuital law and how Maxwell corrected Ampere's circuital law in the case of changing electric field or electric flux and also about Maxwell's equation of electrodynamics.

1. MAXWELL’S CORRECTION IN AMPERE’S CIRCUITAL LAW - Kamran Ansari CBS 5 th semester (Physics Stream)

2. Contents Electrodynamics before Maxwell Stoke’s theorem Problem with Ampere’s circuital law How Maxwell fixed Ampere’s circuital law Electrodynamics after Maxwell

3. Gauss’s law No monopole Faraday’s law Ampere’s circuital law Lorentz force   Electrodynamics before Maxwell In integral form

4. In differential form Gauss’s law No monopole Faraday’s law Ampere’s circuital law Lorentz force  

5. Stokes’ theorem The circulation of around the boundary C of an oriented surface S in the direction counterclockwise with respect to the surface’s unit normal vector equals to the integral of over S . . counterclock wise Curl integral circulation    

6. Problem with Ampere’s circuital law Mathematically, divergence of curl of any vector is always zero. Applying this rule to electric field . = = = 0 and if we apply thus rule to magnetic field than, . b ut in general, the divergence of is not zero. F or steady current, the divergence of is zero but for non steady current, . so that when we go beyond magnetostatics Ampere’s circuital law cannot be right.  

7. Ampere’s law in integral form, In the process of charging up a capacitor, Applying Ampere’s law in this amperian loop than in this case the simplest surface S in the plane of loop, so . Fine but if we draw instead the balloon shaped surface S’’ than value of must be same by Stokes’ theorem but no current passes through this surface so and 0. So that for non steady current “the current enclosed by the loop” is an ill defined notion. So there is need to correct Ampere’s law which must be correct also for non steady current.   Amperian loop Capacitor I I

8. How Maxwell fixed Ampere’s c ircuital l aw A pplying the continuity equation, = combine with in Ampere’s law than Ampere’s law with Maxwell’s correction + and in integral form, f or magnetostatics or when is constant, (Ampere’s Law)   ( By Gauss’s law )  

9. The extra term in Maxwell’s correction in Ampere’s law is called displacement current and its density is Now by Maxwell’s correction in Ampere’s law, calculating the value of divergence of curl of magnetic field will be zero, . + .  

10. and in the process of charging up a capacitor if we choose the flat surface S then =0 and = I , and in the balloon-shaped surface S’’ then = and so we get same answer in both surfaces   Amperian loop Capacitor

11. Maxwell’s term has a certain aesthetic appeal: Just as a changing magnetic field induces an electric field (Faraday’s law) So, A changing electric field induces a magnetic field.

12. Gauss’s law No monopole Faraday’s law Ampere’s circuital law Lorentz force     Electrodynamics before Maxwell Electrodynamics after Maxwell In integral form

13. In differential form Gauss’s law No monopole Faraday’s law Ampere’s circuital law Lorentz force    

14. THANK YOU