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 handoutSome 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 ourLab 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 1Electric 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 3Force 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 experimentsWill n

ot do!

Lab 4RC 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 5RC Circuits driven by a sine wave voltage generator, part I

• Remember “AC” circuits

• Remember about phases in AC circuits

Lab 6RC 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, 1997Use 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 ErrorsUsually distributed according to a Gaussian Distribution

2 2( ) / 21

2xe

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?

1 2 3

2

( , , ,...)

( )iy x

i i

y f x x x

y

x

Error Propogation: ExampleLength 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?

2 2

2 2

( ) ( )

((1 )(0.01 )) ((2 )(0.005 ))

A A W

A L W

AW

LA

LW

W L

m m m m

Error Propagation: ExampleYou 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?

1 2

1 2

1 2 3

2 2 23

1 2 3

1

2 2 23

14.93

( ) ( ) ( )

1

3

( ) ( ) ( )3 3 3

10.03

3

x x xT

x x xT

x x xT

T T T

x x x

T

x

Error Propagation: Try itCalculate 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: Chi2You’ve made a measurement and want to compare it to theory. How do you do this?

Degrees of freedom: number of data points – number of parameters in the theory that are determined using the data

22

2

( )

data

data theory

error

If the data is in good agreement with the theory, what should the value of chi^2 be?

How far is the data from the theory in natural units (size of the error)?

Reduced chi2: chi2/ndof

Review: Chi2Estimating the chi2 for this data to the theory curve by eye (no fitting parameters). Put the result in your spreadsheet.

Review: Chi2Using 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: ReviewHave 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.

z=y-(mx+b) “perfect fit” z would be zero. Theory is that z is zero. Have 2 fitting parameters. m and b. Measurements are x and y

2 2

2 2

2 22

2 2 2

( ) ( )

( ) ( )

( 0) ( )

( ) ( )

z y x

y x

data dataz y x

z z

y x

m

z y mx b

m

Practice linear fittingMake 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 28+-2

6+-0.1 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!