# EE135L, Winter 2015, Section 01: lab1 (week of Jan. 19th)

The lab 1 will be on the week of Jan. 19th.

Unfortunately (or fortunately depending on the perspective ^^), we don't have school next Monday (the MLK day).   Therefore, two Monday sections will be held on Monday a week after (Jan. 26th).

Tueday and Thursday section will meet next week on 20th and 22nd as planned.

Complete the pre-lab exercise before the lab.   I will collect it as you come into the lab.

There are some confusion regarding the first problem on the pre-lab exercises.   Here are some hints.

First, clarify the symbols for the coordinates in each coordinate system.   There are many different convention around.   For the spherical coordinate system in the pre-lab exercises, they use r for the radial, φ for the azimuthal, and θ for the polar coordinates.

Secondly, unlike in the Cartesian coordinate system where the standard unit vectors are i, j, and k regardless of your position, in the spherical, as well as in the cylindrical coordinate system, the standard unit vectors (ar, aθ, aφ for the spherical coordinate system in the pre-lab exercises) are position dependent.   In other words, the standard unit vectors (ar, aθ, aφ for our problem) will be differenet depending on where you are.   That is why they provide the Cartesian coordinate for the points.   Imagine putting the tail end of the given vector on the given point.

Lastly, you have been asked to find the direction of vectors in spherical coordinates, not to convert the vector from the Cartesian system into the spherical system.   As for #2, if you simply convert the vector (x,y,z) = (1,0,0), it would be (r,θ,φ) = (1,π/2,0).   But the given answer is aθ, i.e. the (1,0,0) vector is pointing into the direction of the unit vector of θ component at the point (0,0,1).   Figure out the unit vectors in the spherical coordinate system at each point, and start from there.

To answer the pre-lab exercises, you need to find the standard unit vectors in the spherical coordinate system at the given point first.   Then express the given vector as a linear combination of the standard unit vectors you just found.   Once you have the expression, you will see what direction in the spherical coordinates is the given vector is in easily.

Read the lab work sheet before the lab, so you can finish the lab in time.

From the lab 1 worksheet, # 1.3 is optional (extra credit if done right!), and for #2 and #3, make sure to include the plots of electric feild and the equi-potential of two equal charges at a large distance apart and close together, in addition to those plats of the charge distributions in the manual (9Q at (-1,0) and +/-Q at (1,0)).

The lab report is due in two weeks.   Attach the signed off lab work sheet (or the copy of it) to the lab report, and submit it in person in next lab meeting, or via e-mal to tkim6@ucsc.edu.

For the lab 1 report, you can put "what the lab is about" into the introduction, "what is used" in the materials and methods, and "what you observed and learned" in the result and analysis.   For example, one of the things we looked at in lab 1 is eletric field line.   So after introducing the concept of electric field in the introduction, you can put the web-site of the appalet we used and how you used it in the materials and methods, and finally put a particular things you observed and learned with the data you have in the results and analysis, including the plots you produced.   I am looking forward to seeing what you can do...