# Electric field of periodic charge density.

## Homework Statement

Find electrostatic field and potential created by a two-dimensional charge density:
$$\rho \sin (kx) \cos (ky) \delta (z)$$
at the distance d from the the plane z=0 where the charge is placed (taking into account that it is embedded in a three dimensional space).
In your calculations you are required to use Fourier analysis.

## The Attempt at a Solution

My initial thought was to use the differential form of Gauss's law:
$$\nabla \cdot E = \frac{\rho}{\epsilon_0}$$

However I am unsure of where Fourier analysis comes into play, any pointers as to where to go from here would be great. My instinct tells me that the delta function should be what gets the Fourier treatment, however it isn't periodic.