- #1
shanesworld
- 28
- 0
This is not my theory, or even new, rather pertaining to established physical knowledge, but I simply find it fascinating. It pertains to several areas of physics, and/or variational mathematics, so I've posted it here in the General Physics area. My reasons for posting is because it is one of my favorite interpretations Vector Potential (I find it interesting and gratifying) So here we go, it's time to share.
Vector potential, which is often perceived as a somewhat abstract idea to the layman, and even those knowledgeable about physics, has a very simplifying interpretation, something that makes it appear quite intuitive. The path of deriving this from items such as Maxwell's equations isn't necessarily that simple...the result, however is awfully pleasing.
Quite simply, the vector potential ,(\vec{A} in TeX), is constantly proportional to the momentum contained within the fields of a system. Explicitly, for example in classical electrodynamics, vector potential=c/charge*(field momentum).
The notion of field momentum sometimes confuses people, however it is relatively (no pun intended)approachable from the stance of conservation of momentum. For example one may consider a system in which energy and momentum are each conserved. A field acting on a charge may cause the charge to gain kinetic momentum, however that momentum did not just spontaneously come into existence...No... No... Rather it came from somewhere, namely the field itself.
So next time you are looking at something like max well's equations and you see something like the magnetic field = the curl of the vector potential, it might be interesting to realize in amazement that this also means the magnetic field is proportional to the curl of "the momentum contained in the electromagnetic fields". Personally, my brain likes that interpretation because the concept of momentum is more graspable to me in some ways than "Vector potential", but that is besides the point.
Vector potential, which is often perceived as a somewhat abstract idea to the layman, and even those knowledgeable about physics, has a very simplifying interpretation, something that makes it appear quite intuitive. The path of deriving this from items such as Maxwell's equations isn't necessarily that simple...the result, however is awfully pleasing.
Quite simply, the vector potential ,(\vec{A} in TeX), is constantly proportional to the momentum contained within the fields of a system. Explicitly, for example in classical electrodynamics, vector potential=c/charge*(field momentum).
The notion of field momentum sometimes confuses people, however it is relatively (no pun intended)approachable from the stance of conservation of momentum. For example one may consider a system in which energy and momentum are each conserved. A field acting on a charge may cause the charge to gain kinetic momentum, however that momentum did not just spontaneously come into existence...No... No... Rather it came from somewhere, namely the field itself.
So next time you are looking at something like max well's equations and you see something like the magnetic field = the curl of the vector potential, it might be interesting to realize in amazement that this also means the magnetic field is proportional to the curl of "the momentum contained in the electromagnetic fields". Personally, my brain likes that interpretation because the concept of momentum is more graspable to me in some ways than "Vector potential", but that is besides the point.
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