Lecture
This lecture explores the concept of uniqueness in the context of Maxwell's equations, discussing the conditions under which the solutions to these equations are unique, focusing on the electromagnetic field in different media and with various sources. The instructor demonstrates the mathematical reasoning behind proving uniqueness, emphasizing the importance of boundary conditions and loss in the material. Through a step-by-step analysis, the lecture shows how to establish the uniqueness of the electromagnetic field solutions within a given volume, highlighting scenarios where uniqueness may not hold, such as in free space or materials without losses.