Maxwell's third equation proof / Maxwell's 3rd equation

 Maxwell's third equation

From faraday's lenz law of electromagnetic induction

we know that induced emf

Again 

Emf = the work done by the applied electric field or external electric field to move a unit electric charge through a closed circuit,

        F = qE

        F = E       (q = 1)

     Using stoke's theorem of vector integration in LHS of equation 2

  

Note- from equation three we can say that a time varying  magnetic field can produce time varying electric field.