'Bulletin Board' - Answers to Students' Questions
If a student poses a question that I think will be of interest to others in the class, I will place a copy of the question and answer on this page.
POSTED: Tuesday, September 28
Question: Scope Error Analysis
While doing the report for P2 Lab #3,
I have come across some trouble dealing with the error analysis for the scope
experiment. In the lab book, it says to "estimate the precision with
which you can measure times / voltages". By saying estimate, this
says to me that no formal error analysis is needs...it's just a best
guess. However, both the skeleton lab report and my TA lead me to believe
that I do need to do error analysis. Do I just need to explain why the
precision is what it is (i.e. explain that different TIME/DIV and VOLT/DIV give
different precision's), or do I need to do actual error equations. If I
do need equations...I'm not even sure what they'd be....maybe you could shed
some light on this confusing issue for me.
ANSWER:
The formal error
analysis that I'm looking for is rather trivial, basically asking for the error
when you multiply two numbers, only one of which has any significant
uncertainty. If you will learn to think in terms of the derivative
method of error analysis rather than the computational method you can readily
write a general purpose formula for the percentage error in a full-scale
reading on the scope independent of the settings used for a particular
measurement. You should then give specific error estimates for a
particular reading, in this case using the calibration signal.
Any error analysis
of this type involves 'estimates' of how well you can use the scope. I wouldn't
call this 'just a best guess' but a reasoned estimate that you could
justify as to why it can't be a lot bigger or a lot smaller than your
estimate. You do need to explain the source of uncertainty in your
numbers for time and voltage but I hope this source is obvious (assume the
scope TIME/DIV and VOLT/DIV controls are well-calibrated).
POSTED: Wednesday, September 15
Question: Drawing Electric Field Lines
I seem to be having trouble drawing the electric
field lines on my drawings from Lab #2. I know how they should look
(perpendicular to the equipotentials), but I'm not sure how to take the results
of my calculated electric fields from the x-axis and use those numbers to draw
the lines. Could you briefly explain to procedure for drawing the lines
-- the lab manual seemed vague on the exact method.
ANSWER:
First, you should
NOT be using your x-axis calculations for this purpose. Those are used
for calculating the magnitude of the electric field vectors along the x-axis
(only), which is a different thing from electric field lines
(everywhere).
Conceptually, field
lines are created by joining up field vectors but this must be done in a way
that preserves information about the strength of the field. In practice
this means starting at each charge (dipole electrode in our case) and drawing a
set of short, equally spaced lines emanating from that charge. The number
of lines should be proportional to the strength of the charge since the density
of the field lines must be proportional to thhe strength of the field.
Our two electrodes are of equal strength and so should have the same number of
field lines. A reasonable number might be 8 (spaced 45 degrees apart) or
12 (spaced 30 degrees apart). Then just focus on each line and continue
drawing it as it moves away from the charge, keeping the line perpendicular to
the equipotential surfaces. Because of the symmetry of this problem, many
of the lines that start on one electrode should terminate on the equivalent
line at the other electrode. A few lines may just travel to the edge of
our universe (the water tray). Normally when you finish drawing these
lines, you put an arrow on each one to indicated that the field actually points
from positive to negative charges. We don't have charges or even simple
DC potentials, so there is no real fixed direction in our case.
Your textbook should provide further information on drawing field lines. You might also look up dipole fields to find a picture of how the lines should appear.
POSTED: Wednesday, September 15
Question: I have a question about my p2 lab report. It's the
second one, and I am not understanding what we have to do with the origin
graphs. Could you please
help? What data are we supposed to
plot?
ANSWER:
The only required use of Origin was a test of whether the dipole setup
gives numbers for a pair of spherical point charges or rather a pair of
parallel line charges. You were asked to determine this by taking
quantitative readings of the potential along the x-axis and then trying to fit
these numbers to theoretical formulae that describe point and line charges. When you do this fit, the
right answer should jump out at you.
You should have done this DURING the lab period, unless you ran out of time, so
that the TA's can help spot problems and explain what this is all about. Don't
be shy about asking for help during lab
POSTED: Tuesday, August 31
Question: I had one other question about the lab
manual portion of the lab due this week. During the lab, I wrote all of my
data, and some of my analysis, in the lab notes section of my notebook (because
I didn't want to start the data & analysis sections because I wasn't sure
much room I needed to leave...). Should I just copy that information to the
data and analysis sections of my lab notebook?
Answer:
The lab notebook should not have 'sections' in the same sense that a report has clearly marked sections. Material in the notebook should be entered sequentially in real time as you do a task with no concern for whether it is 'Analysis' or 'Data' or whatever. Of course, an entry in your notebook should start with a quick note about what you're doing, like, 'I'm going to analyze the parallel resistor data with Origin.' or "Setting up the LED experiment." The Lab Manual breaks things down into these categories only as a way to organize the thoughts explained in the manual. This was not meant to indicate that your notebook should emulate that format. Think of a notebook as your laboratory 'diary' and leave your notes as they are.
POSTED: Monday, August 30
Question: I had E & M Lab #1 last Wednesday, and
I was wondering what, if any, error analysis we need to do for the report. I
assume we should just take the uncertainties that we wrote in our lab book
while taking measurement and factor them into any equations we used (very few).
Also, should we include the analysis in both the lab book and the report? Just
trying to get used to the new system....
Answer:
I do regard error analysis as a critical part of experimental research but do not plan to require it to appear in your reports in as much detail as in PHYS 121 . In general I will try to point out in the manual and in the draft report those numbers for which the error analysis is particularly important. The graders will search for these.
Any number that you measure or calculate, such as the total resistance of the wire, will require an error estimate. The basis for this estimate should be explained in the report. This might be as simple as saying it came from the least squares fitting routine or might involve carrying estimated errors through an equation, using one of the two approved methods. In the latter case, put this work in an appendix. I'd also suggest just writing it out by hand rather than taking the time to type it into a computer. Don't forget to describe the major sources of error; for example, is it the meter stick or the DMM?
Your notebook should contain all of the gory details of your work, except for those things done directly on the computer. In this case, the notebook should just refer to the computer file and state what you did and found. So you should be writing out your error analysis in your notebook (and not on scratch paper) as you think about it and do it. You should then transcribe to your report the important parts, those that you think a reader needs to see to understand what you have done or those that are required according to the manual or draft report.
POSTED: Monday, August 30
Question: The draft report instructs me to make a figure 2 that sounds like the setup already described in Figure 1.
Answer: I made a mistake in the original drafts. Figure 2 should refer to the second experiment with the resistance board, with data taken every 10 cm and not every 20 cm as in the first experiment. I corrected the drafts Monday, August 30 at about 11:00 AM so you may not notice this error.
POSTED: Monday, August 30
Question: I am confused about the various question marks you have in the draft report.
Answer: The question marks may refer to items that you should fill in with numbers or text or they may just mark a comment addressed to you. If you download the HTML or txt versions, things are even more confusing. In the doc version, I put in a few places something like ?+? where the plus is actually a plus or minus symbol, which isn't converted into HTML or txt, so it comes out as ??. This is an example of why I recommend that you use the doc version if you can.
Another confusing item is the heading labeled INTRODUCTION (?THEORY AND BACKGROUND). The ? here marks a comment. In the Lab Manual appendix on reports, you are told that these early sections might be labeled as THEORY and BACKGROUND. However, in writing the draft report, I felt that INTRODUCTION was more appropriate. The ? just marks a comment to you that you have some options in how to organize and title your sections. I also wanted to avoid confusing you with conflicting instructions on how to name this part. (I failed.)