Doubt related to notation used in writing Maxwell's equations

AI Thread Summary
The notation ##S=\partial V## and ##C=\partial S## refers to the boundary operator in the context of Maxwell's equations. Here, ##\partial V## represents the surface that forms the boundary of a volume ##V##, while ##\partial S## denotes the closed loop that is the boundary of a surface ##S##. This clarification helps distinguish between the use of ##C## for line integrals over curves and ##S## for surface integrals. Understanding these definitions is crucial for correctly applying integrals in electromagnetic theory. The discussion emphasizes the importance of precise notation in mathematical physics.
Hamiltonian
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Homework Statement
not exactly a home work problem, just a small confusion as to what ##\partial S## and ##\partial V## mean in the equations given bellow.
Relevant Equations
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What does ##S=\partial V## and ##C=\partial S## signify, usually I have only seen books writing ##C## when evaluating a line integral over a curve ##C## and ##S## when evaluating a surface integral over a surface ##S##. Could someone clarify what ##\partial S## and ##\partial V## mean?
 
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##\partial## here is the boundary operator. In other words, ##\partial V## is the surface that is the boundary of the volume ##V## and ##\partial S## is the closed loop that is the boundary of the surface ##S##.
 
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