Maxwell's Equations: Derivation and Implications

This lecture covers the derivation of the 4th Maxwell's equation, which relates the magnetic field to the current distribution. It explains the need for this equation to describe time-varying fields and introduces the concept of displacement current. The instructor demonstrates how the 4th Maxwell's equation is derived using Stokes' theorem and discusses its implications, such as the creation of magnetic fields by variable electric fields. The lecture also highlights the limitations of Ampère's circuital law and the significance of introducing the displacement current to ensure charge conservation. The Maxwell's equations are summarized, emphasizing their role in determining electric and magnetic forces based on charge and current distributions.