1. Does the function
![](Selv Assesment_clip_image002_0000.gif)
satisfy Laplace’s equation?
Yes, a direct calculation shows
![](Selv Assesment_clip_image002_0005.gif)
2.Find an expression for the potential in the region between two infinite parallel planes
on which the potentials are respectively given by
and 0.
In this case also we have solutions which are written as products of separate variables. The solution can be written as (since X and Y are hyperbolic functions, the function Z is a linear combination of sine and cosine),
The constants A and B can be determined by the boundary conditions. For z=0,
gives B=1. For
gives A=0. Thus
![](Selv Assesment_clip_image008.gif)
3. Find an expression for the potential in the region between two infinite parallel planes, the potential on which are given by the following :
![](Selv Assesment_clip_image002_0004.gif)
![](Selv Assesment_clip_image004_0000.gif)