How to use spreadsheet to solve laplace equation?

Question

I need help on this:
The Laplace equation for electrostatics is 2V=0. This is easily solved for simple cases such as the parallel plate capacitor. For more involved situations, numerical methods are usually required. To give you some insight into numerical solutions, lets use a spreadsheet (such as Excel) to solve the Laplace equation in cartesian coordinates.

For the voltage, Vi at the point xi, a simple approximation for the derivative is

and the second derivative is obtained from the first as

(i) Take the case of a parallel plate capacitor with 5V across it. Set up a spreadsheet to solve for the voltage from the grounded plate to the 5V plate. Plot V versus x to ensure the solution is correct.

(ii) Extending this to 2 dimensions (x,y) and setting Δx=Δy=h then

Using the spreadsheet, compute the voltage inside a long conducting box (in the z direction) with square cross section (in the x-y plane) that has one side at 5V and the rest at zero volts.

Answer 1

Sorry, do not understand 2V=0. It would have been helpful had you defined the factors. What's the box? Is that the integrating sign in a Laplacian?

Further, sounds to me like you've already done numerical analysis using Excel. What more do you need to know?

I use to do a lot of work with Laplace (and his cousin Fourier), but have no clue what you are asking.