Coulomb's law lab report example

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Florida International University

GENERAL PHYSICS

LABORATORY 2

MANUAL Edited Fall 2019

1

Florida International University

Department of Physics

Physics Laboratory Manual for Course

PHY 2049L

Contents

Course Syllabus 2

Grading Rubric 4

Estimation of Uncertainties 5

Vernier Caliper 9

Experiments

1. Electrostatics 10

2. Coulomb's Law 13

3. Electric Field and Potential 16

4. Capacitors 21

5. Ohm's Law and Resistance 27

6. Series and Parallel Circuits 33

7. Magnetic Force on Moving Charges 40

8. Magnetic Field of a Solenoid 44

9. Faraday's Law & Lenz's Law 49

10. Reflection & Refraction 53

11. Mirrors, Lenses, Telescope 57

12. Double-Slit Interference 62

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COURSE SYLLABUS

LAB COORDINATOR

Email: Please use Canvas Inbox

UPDATES

Updates to the lab schedule, make-up policy, etc. may be found on Canvas.

CLASS MEETINGS

• During Fall and Spring Semesters classes start the second week of the semester and end the week prior to the final exam week.

• Students that have missed their own section may attempt to make-up by attending another section during the time the same experiment is conducted (see PantherSoft for

available sections). Admission for make-up is granted by the Instructor on site, no

reservation, no guaranteed seating.

• Students must sign in each class meeting to verify attendance.

ACTIVE LEARNING

One of the important goals of this lab course is to strengthen your understanding of what you

have learned in the classroom. You will be working in groups and encouraged to help each other

by discussing among yourselves any difficulties or misconceptions that occur to you. Apart from

the instructor in charge, student Learning Assistants (LA) will be on hand to encourage

discussion, for example by posing a series of questions.

LAB REPORTS

You will be required to submit a lab report at the end of the class period. The format of the report

is dictated by the experiment. As you work your way through the experiment, following the

procedures in this manual, you will be asked to answer questions, fill in tables of data, sketch

graphs, do straightforward calculations, etc. You should fulfill each of these requirements as you

proceed with the experiment. Any preliminary questions could be answered before coming to the

lab, thereby saving time. This way, you will effectively finish the report as you finish the

experiment. Note that for experiments that require them, blank or partially filled in data tables

are provided on separate perforated pages in this manual at the end of the experiment. You may

carefully tear them out along the perforation and staple them to the rest of your report.

GRADES

• The weekly lab reports and your active participation will determine your grade in the

course. Each week you will receive 30% for active participation and up to 70% for your lab

report.

• A missed assignment or lab will receive a ZERO grade.

• Lab reports are to be handed in before you leave the lab.

• THERE IS NO FINAL EXAM

• The grading system is based on the following scale although your instructor may apply a

"curve" if it is deemed necessary. In addition, “+” and “-“may be assigned in each grade

range when appropriate.

o A: 90-100%

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o B: 75-90% o C: 60-75% o D: 45-60%

WHAT YOU NEED TO PROVIDE

Calculator with trig. and other math functions including mean and standard deviation.

AT THE END OF CLASS.

1. Disconnect all sensors that you have connected. 2. Report any broken or malfunctioning equipment. 3. Arrange equipment tidily on the bench.

DROPPING THE LECTURE BUT NOT THE LAB

If you find it necessary to drop the lecture course, PHY 2049 or PHY 2054, you do not also have

to drop this lab course, PHY 2049L. However, you will need to see a Physics Advisor and get a

waiver.

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GRADING RUBRIC

Expectations for a successfully completed experiment and lab report are indicated in the

following rubric. Note that not every scientific ability in the rubric may be tested in every

experiment. Therefore, the graders will determine the maximum number of points attainable for

an experiment (usually 18) and indicate your score as a fraction, e.g 16/18.

Grade Scientific

ability

Missing

(0 pt)

Inadequate

(1 pt)

Needs

improvement

(2 pt)

Adequate

(3 pt)

Attempt to

answer

Preliminary

Questions

No attempt to

answer

Preliminary

Questions

Answers to

Preliminary

Questions

attempted

Able to draw

graphs/diagrams

No graphs or

drawings

provided

Graphs/drawings

poorly drawn with

missing axis labels

or important

information is

wrong or missing

Graphs/drawings

have no wrong

information but a

small amount of

information is

missing

Graphs/drawings

contain no

omissions and are

clearly presented

Able to present

data and tables

No data or

tables

provided

Not all the relevant

data and tables are

provided

Data and tables are

provided but some

information such as

units is missing

Complete set of

data and tables

with all necessary

information

provided

Able to analyze

data

No data

analysis or

analysis

contains

numerous

errors

Data analysis

contains a number

of errors indicating

substantial lack of

understanding

Data analysis is

mostly correct but

some lack of

understanding is

present

Data analysis is

complete with no

errors

Able to answer

Analysis

questions

No Analysis

questions

answered

Less than half the

questions

unanswered or

answered

incorrectly

Less than a quarter

of the questions

unanswered or

answered

incorrectly

All questions

answered

correctly

Able to conduct

experiment as

evidenced by the

quality of results

Little or no

experimental

ability as

evidenced by

poor quality of

results

Results indicate a

marginal level of

experimental ability

Results indicate a

reasonable level of

experimental

ability with room

for improvement

Results indicate a

proficient level of

experimental

ability

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ESTIMATION OF UNCERTAINTIES

The purpose of this section is to provide you with the rules for determining the uncertainties in

your experimental results. All measurements have some uncertainty in the results due to the fact

you can never do a perfect experiment. We begin with the rules for estimating uncertainties in

individual measurements, and then show how these uncertainties are to be combined to produce

the uncertainty in the final result.

The “absolute uncertainty” in a measured quantity is expressed in the same units as the quantity

itself. For example, length of table = 1.65 ± 0.05 m or, symbolically, L ± L. This means we are

reasonably confident that the length of the table is between 1.60 and 1.70 m, and 1.65 m is our

best estimate. If L is based on a single measurement, it is often a good rule of thumb to make L

equal to half the smallest division on the measuring scale. In the case of a meter rule, this would

be 0.5 mm. Other considerations, such as a rounded edge to the table, may make us wish to

increase L. For example, in the diagram, the end of the table might be estimated to be to be at

35.3 ± 0.1 cm or even 35.3 ± 0.2 cm.

If the same measurement is repeated several times, the average (mean) value is taken as the most

probable value and the “standard deviation” is used as the absolute uncertainty. Therefore, if the

length of the table is measured 3 times giving values of 1.65, 1.60 and 1.85m, the average value

is

The deviations of the 3 values from the average are -0.05, -0.10 and +0.15m, and the standard

deviation

So now we express the length of the table as 1.7 ± 0.1 m.

Note: Your calculator should be capable of providing the mean and standard deviation

automatically. Excel can also be used to calculate these quantities.

165 160 185

3 170

   

+ + = m

= sum of squares of deviations

number of measurements

= + +

= 0 05 010 015

3 01

2 2 2. . . . m

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Generally, it is only necessary to quote an uncertainty to one, or at most two, significant

figures, and the accompanying measurement is rounded off (not truncated) in the same decimal

position.

“Fractional uncertainty” or “percentage uncertainty” is the absolute uncertainty, expressed as a

fraction or percentage of the associated measurement. In the above example, the fractional

uncertainty, L/L is 0.1/1.7 = 0.06, and the percentage uncertainty is 0.06 x 100 = 6%.

Rules for obtaining the uncertainty in a calculated result.

We now need to consider how uncertainties in measured quantities are to be combined to

produce the uncertainty in the final result. There are 2 basic rules:

A) When quantities are added or subtracted, the absolute uncertainty in the result is equal to

the square root of the sum of the squares of the absolute uncertainties in the quantities.

B) When quantities are multiplied or divided, the fractional uncertainty in the result is equal

to the square root of the sum of the squares of the fractional uncertainties in the

quantities.

Examples

1. In calculating a quantity x using the formula x = a + b - c, measurements give

a = 2.1 ± 0.2 kg

b = 1.6 ± 0.1 kg

c = 0.8 ± 0.1 kg

Therefore, x = 2.9 kg

The result is therefore x = 2.9 ± 0.2 kg

2. In calculating a quantity x using the formula x = ab/c, measurements give

a = 0.75 ± 0.01 kg

b = 0.81 ± 0.01 m

c = 0.08 ± 0.02 m

Therefore x = 7.59375 kg (by calculator).

Fractional uncertainty in x,



x

x =

0.01

0.75



 



 

2

+ 0.01

0.81



 



 

2

+ 0.02

0.08



 



 

2

= 0.25

Absolute uncertainty in x, x = 0.25  7.59375

= 2 kg (to one significant figure)

The result is therefore x = 8 ± 2 kg

Note: the value of x has to be rounded in accordance with the value of x. If x had been

calculated to be 0.003 kg, the result would have been x = 7.594 ± 0.003 kg.

3. The following example involves both rule A and rule B.

In calculating a quantity x using the formula x = (a + b)/c, measurements give

Absoluteerror in x x kg, . . . . = + + =0 2 01 01 0 22 2 2

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a = 0.42 ± 0.01 kg

b = 1.63 ± 0.02 kg

c = 0.0043 ± 0.0004 m3

Therefore x = 476.7 kg/m3

Absolute uncertainty in kg 02.002.001.0 22 =+=+ ba

Fractional uncertainty in a + b = 0.02 / 2.05 = 0.01

Fractional uncertainty in c = 0.0004 / 0.0043 = 0.093

Fractional uncertainty in 094.001.0093.0 22 =+=x

Absolute uncertainty in x, x = 0.094 476.7 = 40 kg/m3 (to one significant figure)

The result is therefore x = 480 ± 40 kg/m3

Note that almost all of the uncertainty here is due to the uncertainty in c. One should therefore

concentrate on improving the accuracy with which c is measured in attempting to decrease the

uncertainty.

Uncertainty in the slope of a graph

Often, one of the quantities used in calculating a final result will be the slope of a graph.

Therefore, we need a rule for determining the uncertainty in the slope. Graphing software such as

Excel can do this for you. Another way to do this is “by hand” as follows: In drawing the best

straight line (see figure on following page),

1. The deviations of the data points from the line should be kept to a minimum. 2. The points should be as evenly distributed as possible on either side of the line. 3. To determine the absolute uncertainty in the slope:

a. Draw a rectangle with the sides parallel to and perpendicular to the best straight line that just encloses all of the points.

b. The slopes of the diagonals of the rectangle are measured to give a maximum slope and a minimum slope.

c. The absolute uncertainty in the slope is given by:



max slope - min slope

2 n , where n

is the number of data points.

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What has been described above is known as “standard uncertainty theory”. In this system, a

calculated result, accompanied by its uncertainty (the standard deviation s), has the following

properties: There is a 70% probability that the “true value” lies within the ± s of the calculated

value, a 95% probability that it lies within the ± 2s, a 99.7% probability that it lies within ± 3s,

etc. We may therefore state that the “true value” essentially always lies within plus or minus 3

standard deviations from the calculated value. Bear this in mind when comparing your result

with the expected result (when this is known).

Some final words of warning

It is often thought that the uncertainty in a result can be calculated as just the percentage

difference between the result obtained and the expected (textbook) value. This is incorrect. What

is important is whether the expected value lies within the range defined by your result and

uncertainty.

Uncertainties are also sometimes referred to as “errors.” While this language is common practice

among experienced scientists, it conveys the idea that errors were made. However, a good

scientist is going to correct the known errors before completing an experiment and reporting

results. Erroneous results due to poor execution of an experiment are different than uncertain

results due to limits of experimental techniques.

Fig. 1 Graph of extension vs. mass

Mass (kg)

2 3 4 5 6 7

Exten sion(

mm)

4

6

8

10

12

14 Best line

Min. slope Max. slo

pe

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VERNIER CALIPER

A Vernier scale allows us to measure lengths to a

higher degree of precision than can be obtained with,

say, a millimeter scale. In Fig. 1, a moveable Vernier

scale V is placed next to a millimeter scale M (e.g. on a

meter rule). V is 9mm long and has 10 divisions, each

of length 0.9 mm, so each division on V is shorter than

each division on M by 0.1 mm Fig. 1

Suppose we wish to measure the position on a

meter rule of the right-hand end of an object. V is

positioned as shown in Fig. 2. Clearly the required

reading is somewhere between 24 and 25 mm. To

obtain the fractional part, we note which graduation

on V lines up (or comes closest to lining up) with a

graduation on M. In Fig. 2 it is the 7th, labeled B,

which lines up with C, and the required reading is

therefore 24.7 mm. The reasoning is as follows: Fig. 2

The graduation on V to the left of B is 0.1 mm to the right of the closest graduation on M. The

graduation on V two to the left of B is 0.2 mm to the right of the closest graduation on M, etc.

Therefore the graduation labeled A will be 0.7 mm to the right of the graduation D on scale M.

A tool to measure linear dimensions is the Vernier caliper shown in Fig. 3. It consists of a scale

M graduated in millimeters and attached to a fixed jaw A, and a Vernier scale V on a moveable

jaw B.

Fig.3

Fig. 3

Note that part of the scale M can be seen through an opening in the moveable jaw. When the

jaws are closed, the zero graduations on M and V coincide. The object, C, to be measured is

placed snugly between the jaws by sliding B. The length can then be read from scales M and V.

In Fig. 3, the reading is 2.57 cm. (By counting backwards from the 3 cm graduation, you can see

that the leftmost graduation on V is between 2.5 and 2.6 cm.)

20 mm 30 mm

V

M

A B

CD

Object

1cm0cm 5cm M

A B

C

3

V

cm

B

30 mm 40 mm

V

M

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Lab 1. Electrostatics

Electric charge, like mass, is a fundamental property of the particles that make up matter. However, unlike mass, charge comes in two forms that we label positive (e.g. the charge of a proton) and negative (e.g. the charge of an electron). Normal matter is made up of "neutral" atoms having equal numbers of protons and electrons but, for example, can become negatively charged by gaining electrons, or positively charged by losing electrons. Charged objects of the same sign repel each other whereas those of opposite sign attract each other. In the first part of this experiment, an "electroscope" will be used to demonstrate the existence of the two types of charge and a few of their basic properties. In the second part, the attractive and repulsive forces that charges can exert on each other will be investigated. In the third part, a "Faraday pail" and charge sensor will be used to determine the sign of the charge resulting from rubbing objects together. OBJECTIVES

Demonstrate that a material can acquire a net charge by rubbing it with a dissimilar material.

Demonstrate that either of the two types of charge may be acquired, depending on the material, and demonstrate the forces that charges exert on each other.

Demonstrate that charge can be either transferred to an object or "induced" on an object.

Determine the signs of the charges acquired by rubbing two dissimilar materials together.

MATERIALS

various rods and rubbing cloths Faraday pail and charge sensor electroscope charge separators swivel Labquest Mini

connecting wires computer

PRELIMINARY QUESTIONS

1. If something is "charged," what does that mean?

2. If something is "neutral," what does that mean"

3. What happens if you have two positively charged objects near each other?

4. What happens if you have a positively charged object near a negatively charged one?

PROCEDURE

Part I Demonstrations with the electroscope

The electroscope, shown in Fig. 1, consists of a metal conducting rod with a

metal ball at the upper end and a pair of light, hinged, conducting leaves at

the lower end. The rod is insulated from the electroscope’s metal case by

an insulating stopper. If both leaves acquire either a net positive charge or

a net negative charge, they will separate due to the repulsive forces that the

leaves exert on each other. Fig. 1 shows the situation when the ball, rod,

and leaves have acquired positive charge. Figure 1