Maxwell's four equations in em theory

engineering physics

1. Name : Shubhajit Chatterjee. Student Code : BWU/BEC/19/028. Course Name :Electromagnetism and Field Theory. Course code : BSC(ECE)301 . Program : Bachelor of Technology in Electronics & Communication Engineering. Semester : 3 rd Semester. Topic: Maxwell’s Four Equations In EM Theory

2. MAXWELL’S EQUATIONS In 1865, James Clerk Maxwell (1831-1879) published  A Dynamical Theory of the Electrodynamic Field , which featured the original set of what is now referred to as Maxwell's equations. Through these equations, Maxwell described scientifically the propagation of light and electromagnetic waves travelling through space at the speed of light. These equations are: 1) Gauss’s law in electrostatics. 2) Gauss’s law in magnetostatics . 3) Faraday’s law of electromagnetic induction 4) Ampere’s law with Maxwell’s correction. 1

3. Maxwell’s Equation In Differential Form  Maxwell’s 1 st Equation :   Maxwell’s 2 nd Equation :      Maxwell’s 3 rd Equation :     Maxwell’s 4 th Equation :   =     2 The 1 st equation represents Gauss’ law in electrostatics. The 2 nd equation is represents Gauss’ law in magnetostatics . The 3 rd equation is represents Faraday’s law of electromagnetic induction . The 4 th equation is represents modified ampere’s(Ampere’s law with Maxwell’s correction) .

4. Maxwell’s Equation In Integral Form 3

5. Physical Significance of Maxwell’s equations  Maxwell’s 1 st Equation:  Maxwell’s 2 nd Equation: 4 Steady state equation. Total electric flux through any close surface is time the total charge include with in the surface. Electric field lines start from positive charges and end at negative charge.  

6.  Maxwell’s 3 rd Equation:  Maxwell’s 4 th Equation: 5

7. Maxwell’s Equation for free space ,       =     In free space ,the following physical conditions are satisfied Under these condition, Maxwell’s equations take the following form: 6 (2) (1) (3) (4)

8. 7 Maxwell’s Equation in static field           For static field conditions are Under these condition, Maxwell’s equations take the following form: (1) (4) (3) (2)

9. 8