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Welcome to PHYS 276!!
Instructor: Johnpierre Paglione, Assistant Prof.
• Started Jan 2008
• Area of Research: Condensed Matter Physics
Exotic Metals, Magnets and Superconductors
Professor Johnpierre Paglione
high magnetic
field
experiments
exploration of new
phases of matter
ultra-low temperature
thermoelectric transport
measurements
new materials
exploration
see http://www.vector.umd.edu
My Office:
1367 – CNAM 2nd floor
Teaching Assistant:
Introduction: Nightvid Cole
Introductions
Name, class, major?
PHYS 276: E & M experiments
PHYS 276: E & M experiments
• 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
web page: http://www.physics.umd.edu/courses/Phys276/
PHYS 276: Syllabus
Our contract: let’s go through it.
ELMS/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
Lab Reports
See pgs. 2-3 of lab manual and “rubric” on class web page
lab reports for 4 labs:
#1 - Ohm’s Law
#2 - Magnetic Fields
#4 - RC/LR Circuits
#6 - LRC Circuits (6a and 6b – combined report)
please hand in hard copy AND upload doc/pdf/tex to ELMS
Note: figures from lab manual available on 276 web page.
REPORTS DUE: 1 week after lab @12PM
(first one to my office)
Schedule
XLS spreadsheet due after EACH LAB
Schedule
FORMAL REPORT DUE
Lab 0 (today!)
Error Analysis and Oscilloscope Refresher
• Remember error calculation…
• practice doing linear fits
• practice measuring signals with the scope
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
FORMAL REPORT
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
FORMAL REPORT
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 LR circuits driven by a DC/step 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 an AC source
• Remember “AC” circuits
• Remember about phases in AC circuits
FORMAL REPORT
Lab 6
LRC Circuits driven by a sine wave voltage generator (2 parts)
• Observe resonance
• LRC circuits driven by a square wave voltage generator
FORMAL REPORT
Lab 7
Diode and Rectifier Circuits
• more on diodes
• building a crude AC to DC converter
Lab 8
Transistor circuits (new lab)
• basic stuff – IV characteristics, amplification
• building a simple oscillator
• help us debug!
Goals
further develop skills in error analysis, beyond that gained in 174, 275
• propagation of error
• chi-squared
Introduction to Error Analysis, J. Taylor, Unversity Science Books, 1997
Use it!
Review: Estimating Errors
1. 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
2. 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 assess 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 you estimate them?
Review: Error Propagation
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
y ( xi ) 2
i xi
Error Propagation: 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 Lx W
A
W
L
A
L
W
A (W x L ) 2 ( L x W ) 2
A
((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 +/- 0.1 s, 14.8 +/- 0.1 s, and 14.9 +/- 0.1 s. What is the average of
these 3 measurements?
x1 x2 x3
T 14.9
3
T T T
T ( x1 ) (
2
x2 ) (
2
x 3 )2
x1 x2 x3
T 1
x1 3
x x x3
T ( 1
) (
2 2
)2 ( )2
3 3 3
1
0.03 …which is smaller than 0.1s –
3 make sense?
EXERCISE: Error Propagation
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?
I Strongly suggest you put each number in a separate cell, the formula
for each partial derivative in a cell, and then multiply, square and add
them up. It makes it easier to spot errors!
Review: Chi^2
You’ve made a measurement and want to compare it to theory. How do you
do this?
( data theory ) 2
2
2
data error
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?
N= Degrees of freedom: number of data points – number of
parameters in the theory that are determined using the data
“Reduced chi^2” = chi^2/N
Review: Chi^2
Estimating the chi^2 for this data to the theory curve by eye (no fitting
parameters). 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
z ( y ) ( x )2
2
y x
( y )2 (m x )2
( z 0)2 ( y mx b) 2
2
data 2z data ( y )2 (m x )2
Practice linear fitting
Use XLS template to plot and fit given data: “linear_fitter_276.xls” in
folder “shortcut to p276” on your desktop.
Calculate the chi^2 and calculate the probability to get a chi2 this big or
bigger due to random errors.
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