How to use Laplace's eqn to do this?

[neelakash]

Homework Statement

We are to calculate gravitational field and potential at a point near an infinitely extended thin sheet of mass by using Laplace's equation...

Homework Equations

The Attempt at a Solution

I have already calculated this directly,using fundamental formula.
Now I wonder how to use laplace's equation to solve this.Should we make an attempt like method of images?How else an be done?

 

[Dox]

For gravitation, the potential must satisfy the equation
\begin{equation}
\nabla^2 \phi = \frac{4\pi G}{c^2} \rho,
\end{equation}
where $\rho$ is the mass density, so outside the plate, the potential satisfy the Laplace equation.

But.., I don't know the well-posed boundary conditions you must apply in order to solve your problem. I'm sorry, is as far as I can help you. Keep trying.

Good luck.

 

[aiy1tm]

Hi --

hope this isn't too late.

But yes, this problem becomes most simple when you note the analogy to gauss's law the Gravitational laplace equation has. Except charge density has been replaced by mass density.