# EE135L, Winter 2015, Section 01: lab3 (week of Feb. 23rd)

Due to the holiday and the midterm, lab #3 will meet during the week of Feb. 23rd.

How about the midterm?   Now that we are done with it, it is time for the next lab.   The lab manual is attached below.   We will most likely deviate from it again.   But, read it before the lab nontheless.   I will explain what is different at the beginning of the lab.   In one sentence, in lab #3 we will numerically - meaning, let computer - solve the Laplace's equations with the same boundary conditions (BC) we used in lab #2.   (Remember all the patterns we painted.   That was how we set up the BC for each problem.)   Specifically, we will use Matlab with PDE toolbox in this lab.

It wouldn't be fair to ask computer to do something we don't know how to ourselves.   So here are the pre-lab exercise for lab #3.

Pre-lab Exercises for Lab #3

Find the potential along the wire for 1 and inside the box for 2, by solving the Laplace's equation:

1. A conduction wire of length L, with one end held at a constant potential V0 and the other end grounded.

2. A cubical box, with sides of length L, made of a conducting material.   All the faces of the cube are grounded, except the top face which is held at a constant potential V0.

The first question is straight forward, but for the second one you need to use the separation of variales.   Forgot what it is?   It is a standard technique to solve a partial differential equations (PDE), and mentioned in any book about PDE.   Compared with the first problem, the second one will take ten times longer or more.   There are reasons I ask these two problems.   Once you know what to do, the first problem can be done in less than three minuate.   I just want you to see that in some cases the Laplace's equation can be quite simple.   But the second one will take some time and paper, even after you figure out what to do.   It is because of the dimension of the space in the problem is increased from 1 to 2.   Some of you might stil remember how complex the problem becomes when you transit from 1 dim. to multi-dimension in your vector calculus class.   I want to remind you to appreciate this increasing mathematical complexity, that comes with expanding dimensionality.