# Poissons Equation

1. 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?

2. Homework Equations

3. The Attempt at a Solution

## Answers and Replies

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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
Homework Helper
Gold Member
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.

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.
But what is f actually doing to this cross section?

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.
And when f = 0 ? What does it mean in this case?

quasar987
Homework Helper
Gold Member
Well it means that this particular Maxwell's equation ($$\nabla^2\vec{E}=0$$) is describing the evolution of the electric field in a region where there are no electric charges and where the magnetic field is constant.

So say one is concerned with the heat distribution among a metal plate, what would f mean and what would f = 0 mean?

Maybe I should have written this in the undergraduate physics forum.

quasar987
Homework Helper
Gold Member
You can ask a mentor to move it.

HallsofIvy
That said, if you have $\nabla \phi= \kappa \partial \phi/\partial t+ f(x,y,t)$ specifically applied to heat distribution on a plate, then f(x,y,z) might represent an external heat source applied to every point of the plate.