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Reshma
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Can someone explain me the Dirac Delta function for the function:
[tex]\vec A = \frac{\hat r}{r^2}[/tex]
[tex]\vec A = \frac{\hat r}{r^2}[/tex]
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Reshma said:Can someone explain me the Dirac Delta function for the function:
[tex]\vec A = \frac{\hat r}{r^2}[/tex]
Reshma said:Thanks for the link, Vivek. But it did not completely solve my problem. The proofs given in most texts are too mathematical. I need a more physical interpretation of the problem.
himanshu121 said:I believe You want to interpret its curl or div in terms of Dirac Delta Function
[tex]\vec{\nabla} X \vec A [/tex]
maverick280857 said:Yes they are mathematical because of the very definition of DDF. Strictly, it is not a function but it is considered a function. If you want good physical interpretations of its applications, get a copy of Classical Electrodynamics by Griffiths and read the first chapter (I think its called mathematical preliminaries but I'm not very sure).
Hope that helps...
cheers
vivek
dextercioby said:You want the proof that the [itex] \nabla \cdot \frac{\vec{r}}{r^{3}} [/itex] is proportional (it's a "-1" the coefficient of proportionaliry,IIRC) to delta-Dirac...?
That's a pretty delicate matter.It's not really for physicists...Any book on PDE-s should have it,when discussing Laplace & Poisson equations.
Daniel.
The Dirac Delta Function, denoted by δ(x), is a mathematical function that is used to describe the distribution of a point mass or impulse at a specific point in space. It is characterized by being zero everywhere except at the point where it is defined, where it has an infinite value, and its integral over the entire real line is equal to one.
In physics, the Dirac Delta Function is often used to model point particles, such as electrons, which have no size and are concentrated at a single point in space. It is also used to describe the probability distribution of a particle's position or momentum in quantum mechanics. The Dirac Delta Function also plays a role in electromagnetism, where it is used to represent electric and magnetic point charges.
The vector potential, &vec;A, is a mathematical quantity used to describe the magnetic field in electromagnetism. It is related to the magnetic field, &vec;B, through the equation &vec;B = ∇ × &vec;A. The Dirac Delta Function can be used to express the vector potential, where &vec;A = ∫ &vec;B × δ(x) dx, allowing for a more convenient representation of the magnetic field in certain situations.
No, the Dirac Delta Function is undefined at points other than zero. It is a mathematical idealization that has a finite value only at the point where it is defined, and is zero everywhere else. However, it can be scaled and shifted to represent point masses at other locations.
Some important properties of the Dirac Delta Function include: