Transcript Welcome to PHYS 276!!

Welcome to PHYS 276!!
Instructor: Professor Sarah Eno
• at MD since 1993
• Research Specialty: Experimental Particle Physics
• http://www2.physics.umd.edu/~eno/Default.htm
The LHC
turns on in
2007; I am the
co-head of the
CMS new
particles
search group;
I travel to
CERN a lot.
http://www.fnal.gov
http://cmsdoc.cern.ch/
TA
TA Introduction: Dan Schwartz
Introductions
Name, class, major?
Goals for this Course
• Learn experimental techniques and equipment for studying electricity and
magnetism
• Reinforce understanding of E&M and electronics gained last semester in
lecture course through hands-on experience
• Learn importance of proper recording keeping and scientific writing for
experimental science: learn how to write a lab report
• Further develop skills in error analysis, beyond that gained in 174, 275
Class web page: http://www2.physics.umd.edu/~eno/teaching/276/f07/f07.htm
Schedule
See handout
Some oddness comes from my travel requirements
Syllabus
Our contract: let’s go through it.
Blackboard
Will use to turn in our in-class spreadsheets and our
Lab reports. Will try it out at the end of this class, after
we do a little refresher exercise
Goals
•Learn experimental techniques and equipment for studying
electricity and magnetism
• Reinforce understanding of E&M and electronics gained
from lecture course through hands-on experience
Lab 1
Electric Circuit Basics
• Remember what current, voltage, resistance are.
• Remember the basic symbols used for common circuit elements
• Measure the internal resistance of a battery
• learn how to take into account imperfections in meters when doing data
analysis
• practice doing linear fits
• learn about diodes and LEDs
Lab 2
Magnetic Fields due to Currents
• Remember the Biot and Savart law and Ampere’s Law
• learn how to use a Hall probe to measure magnetic fields
• remember the field due to a current loop, a coil, and a toroid
Lab 3
Force on charged particle due to electromagnetic fields
• Remember the Lorentz Force
• use an electron gun
• learn how to take into account the earth’s magnetic field when doing
magnetic experiments
Lab 4
RC and RL circuits driven by a step-function voltage source
• remember what capacitance and inductance are
• remember what the time constant is for circuits containing RC and RL
elements
• use WAVESTAR to transfer data from an oscilloscope to a computer
Lab 5
RC Circuits driven by a sine wave voltage generator, part I
• Remember “AC” circuits
• Remember about phases in AC circuits
Lab 6
RC Circuits driven by a sine wave voltage generator, part II
• Observe resonance in an LRC circuit
• LRC circuits driven by a square wave voltage generator
Lab 7
Diode and Rectifier Circuits
• more on diodes
• building a crude AC to DC converter
Goals
• learn importance of proper recording keeping and scientific writing for
experimental science: learn how to write a lab report
A Dzero Note
http://www2.physics.umd.edu/~eno/teaching/276/f07/lectures/example_modern_lab_report.pdf
Lab Reports
See pg 3 of lab manual and “rubric” on class web page
Figures from lab manual available on class web page.
Goals
•further develop skills in error analysis, beyond that gained in 174, 275
Introduction to Error Analysis, J. Taylor, Unversity Science Books, 1997
Use it!
Estimating Errors: Review
•Systematic errors : sources of error that have the same size
effect on every measurement that is made (or a correlated effect)
• a ruler that was not manufactured correctly
• a consistently delayed reaction when using a stop watch
• your inability to perfectly estimate the size of a stray
magnetic field from your computer that leaks into your
experimental area
• Random errors : sources of error whose effect varies with each
measurement
• precision of your measuring device
• when using a stop watch, a reaction time that sometimes
anticipates the event, some times is in retard of the event.
Systematic Errors
Usually estimated using information from the manufacturer of the measuring
device or by making measurements of a calibrated standard.
“Mistakes” are not systematic errors. They are mistakes. Do not use data
that has known mistakes, if the data can not be reliably corrected for the
mistake. If you have made a mistake, you need to correct the data or retake
the data. For example, failing to take into account the resistance of your
ammeter when testing ohm’s law is a mistake, not a systematic error.
Uncertainties on its resistance, because your ability to measure its value is
limited, do lead to a systematic error.
Systematic errors instead come from your limits on your ability to asses the
accuracy of the device, even when it is being used correctly.
Random Errors
Usually distributed according to a Gaussian Distribution
1
 ( x   ) 2 / 2 2
e
 2
68% of data within 1 “sigma”
95% within 2 “sigma” ()
What were some random errors from 174?
How did we estimate them?
Error Propagation: Review
You have taken a measurement, which has an error (uncertainty), and
want to use it in a calculation. What is the uncertainty on the result of the
calculation due to the uncertainty on the measurement?
y  f ( x1 , x2 , x3 ,...)
y
2
 y   (  xi )
xi
i
Error Propogation: Example
Length of a table is 2 m +- 0.01 m
Width is 1 m +- 0.005 m
What is the area? What is the error on the area?
A L W
A
W
L
A
L
W
 A  (W  A )2  ( L  W ) 2
 ((1m)(0.01m)) 2  ((2m)(0.005m)) 2
Error Propagation: Example
You take 3 independent measurements of the period of a pendulum. You
get 15+-0.1s, 14.8+-0.1s, and 14.9+-0.1s. What is the average of these 3
measurements?
T 
T
x1  x2  x3
 14.9
3
 T
 T
 T
2
2
 (
 x1 )  (
 x2 )  (
 x 3 )2
x1
x2
x3
 T
1

x1
3
T  (

x
1
3
) (
2
1
  0.03
3
x
2
3
)2  (
 x3
3
)2
Error Propagation: Try it
Calculate this in EXCEL. You will submit your work at the end of class. We’ll
move on when all of you are done.
You drop a ball (initially at rest) and it falls 3 m +- 0.01 m in 0.785+-0.002 s.
What is g?
Review: Chi2
You’ve made a measurement and want to compare it to theory. How do you
do this?
(data  theory )
 
2
error
data
2
2
How far is the data from the theory in natural units (size of the error)?
If the data is in good agreement with the theory, what should the value of
chi^2 be?
Degrees of freedom: number of data points – number of
parameters in the theory that are determined using the data
Reduced chi2: chi2/ndof
Review: Chi2
Estimating the chi2 for this data to the theory curve by eye (no fitting
parameters). Put the result in your spreadsheet.
Review: Chi2
Using this table, find
the probability that
the graph on the
previous slide would
have a chi^2 that big
or bigger from
random errors
alone. Put the result
in your spreadsheet.
Fitting: Review
Have some data points. What straight line curve best “fits” the
data? -> what values of m and b minimize the chi^2 between the
line and the data.
“perfect fit” z would be zero. Theory is that z is
z=y-(mx+b)
zero. Have 2 fitting parameters. m and b.
Measurements are x and y
z
z
2
 z  (  y )  (  x )2
y
x
 ( y ) 2  ( m x ) 2
2  
data
( z  0) 2
 2z
( y  mx  b) 2

2
2
(

)

(
m

)
data
y
x
Practice linear fitting
Make a plot of this data including error bars.
Time (s)
Position (cm)
1+-0.1
2+-2
2+-0.1
11+-2
3+-0.1
13+-2
4+-0.1
20+-2
5+-0.1
6+-0.1
28+-2
31+-2
Practice: Linear Fit
Use fred’s template to fit this data. Calculate the chi^2 and calculate
the probability to get a chi2 this big or bigger due to random errors.
Can go when get right answer.
(for discussion on an alternative way to understand this fitting
procedure, and how to get the errors on the slope, intercept, see
Taylor, chapter 8)
Next week
No lab next week
Week of Sept 24: Bring your lab manual and notebook and be ready to work!