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Nusc
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Homework Statement
So poissons equation takes the for uxx + uyy = f(x,y)
Laplace is where f(x,y). What does the f(x,y) physically represent?
buzzmath said:Laplace equation is when f(x,y)=0. f(x,y) can represent many things physically. the solution of this problem can represent many things for example u could be a steady state temperature of the cross section of a rod with an electrical current.
quasar987 said:What you wrote does not make sense to me, but the question got throught nonetheless.
In Maxwell's theory of electromagnetism, the electromagnetic field is governed by a set of 4 equations and one of them is Poisson's equation where u is the electric field in space-time (x,y,z,t) and f(x,y,z,t) is an expression taking into account the density of charge and the rate of change of the magnetic field at the point (x,y,z,t) in space-time.
The Poisson's equation is a partial differential equation that describes how a potential field is influenced by a given source distribution.
Poisson's equation has a wide range of applications in physics, engineering, and mathematics. It is commonly used in electrostatics, fluid dynamics, heat transfer, and quantum mechanics.
Poisson's equation is typically solved using numerical methods, such as finite difference, finite element, or boundary element methods. Analytical solutions are also possible for simple configurations.
f(x,y) is the source term in Poisson's equation, representing the distribution of sources or sinks in the potential field. It can be a function of position, time, or other variables depending on the specific problem.
Exploring f(x,y) can provide insights into the behavior of the potential field and its relationship with the source distribution. It can also help in identifying patterns or trends in the solution and determining the boundary conditions for a given problem.