WAC Essay#1 - PHY 244 Provide a brief description of Experiment #1 The Coulomb Balance. In your essay you can also discuss the broader implications of the analysis from this lab. - Your essay should be written in size 11 "Times New Roman" font, double-spaced with 1 inch left and right margins. - Place your name, the date, course name, professor, and TA in the top right corner of the essay. - Your essay must meet the 500-word minimum, headings not included. - Your essay will be checked for plagiarism. If this is detected the penalties specified in the Student Conduct Code will be applied. - Please submit an electronic copy of your essay on Blackboard by the specified deadline. Grading rubric for your essay: Possible Points Essay 1. Describe the goals of the experiment. 2. Concepts behind the experiment. 3. History & importance of the phenomena illustrated, or physical quantity measured. 4. Organization & Structure 5. Clarity of Expression 6. References - Minimum of three, MLA format. 7. Punctuality Essay Score 100 IF ESSAY IS NOT ACCEPTED: REVISE AND BE SURE TO INCLUDE THE ORIGINAL ESSAY AND SCORING RUBRIC WITH THE REVISION. REVISION DUE: In order to pass the WAC requirements, your essay score must be 70% or greater. 5 15 20 20 20 10 Your Score 10 PLEASE UTILIZE THE CSU WRITING CENTER. IT IS AVAILABLE TO ALL MEMBERS OF THE CSU COMMUNITY. FURTHER INFORMATION CAN BE FOUND ON THEIR WEBSITE: http://www.csuohio.edu/academic/writingcenter//n I. OBJECTIVES 1. To verify Coulomb's law by measuring the force between two charged spheres as a function of distance. 2. To investigate the effect of systematic errors on measurements. 3. To understand the limitations of modeling real charged systems as point charges II. EQUIPMENT EXPERIMENT 1 The Coulomb Balance - Coulomb Torsion Balance (Figure 1) (model PASCO ES - 9070). As part of the balance, a conductive sphere of radius 1.9 cm is mounted on a rod, counterbalanced, and suspended from a thin torsion wire. An identical sphere is mounted on a slide assembly allowing it to be placed at fixed distances from the equilibrium position of the suspended sphere. The electrostatic force between the spheres causes the torsion wire to twist. The experimenter then twists the torsion wire to bring the balance back to its equilibrium position. The angle through which the torsion wire must be twisted to reestablish equilibrium is directly proportional to the electrostatic force between the spheres. - High Voltage Power supply. This is used to charge the two spheres to the same potential, i.e. same charge since the spheres are identical. The Coulomb Balance |F| = k torsion knob index lines aligned degree scale charged spheres -torsion wire torsion wire retainer Figure 1. Side view of the Coulomb balance. slide assembly Historical Note The Coulomb law was published for the first time by Charles Augustine de Coulomb in 1785. It is also referred as the Coulomb's inverse square law indicating the particular distance dependence of the magnitude of the force F between two point-like charged particles: 9192 R2 (1) where k (~8.987x10⁹ Nm²/C²) is a constant, q, and q2 are the two charge values, and is the distance between the charges. A quick calculation with the charges q, and q2 set to 1 Coulomb would indicate that the force between them would be enormous. Despite this, we need a delicate balance to characterize the Coulomb's force because in reality only small charge differential can be sustained in the laboratory (much smaller than 1 C). The limit on the charge differentials possible is a direct consequence of the strength of this force that prevents the separation of the negative (electrons) and the positive (protons) charges. Page 4 ,copper rings lateral support bar Figure 2. Top view of the Coulomb balance. Page 3 A III. PROCEDURE In the event of high atmospheric humidity, the experiment might be particularly challenging due to the NOTE: possibility for the charges to leak of the spheres before an accurate measurement can be taken. The main goal of this lab is to verify the inverse square law dependence of the force on the separation between the charges. Since we are interested only in the qualitative behavior, we do not need to actually calculate the force. Thus we will not measure the charges placed on the spheres, but just make sure that they remain the same throughout the experiment by always using the same voltage source to charge the spheres. Also, we will consider that the value of the angle through which the torsion wire has to be twisted to reestablish equilibrium is in effect a measure of the strength of the electrostatic force between the spheres. 1. Preparing your experiment: Make sure that the spheres are fully discharged by touching them with a grounded probe. Move the sliding sphere as far as possible from the suspended sphere. Set the torsion dial to 0°. Zero the torsion balance appropriately by rotating the bottom torsion wire retainer until the pendulum assembly is at its zero displacement position as indicated by the index marks (see Figure 2). 2. With the spheres still at maximum separation, charge both spheres to the same potential ~ 6-7 kV, using the charging probe (one terminal of the power supply should be grounded.) Immediately after charging the spheres, turn the power supply off to avoid high voltage leakage effects. 3. Position the sliding sphere at a distance of 20 cm. The suspended sphere will deflect. Adjust the torsion knob as necessary to balance the forces and bring the pendulum back to zero position. Record the distance (R) and the angle 0 in Table 1 from page 4. 4. Repeat steps 2 and 3 two more times recording the data in the table. NOTE: Sometimes during the experiments you might accidentally touch the spheres or breathe near them adding moisture to the air and thus promoting charge leaking. In these situations the results for the deflection of the suspended sphere will be inconsistent. If such a situation occurs you should discard that particular measurement and repeat it. Typically, with the PASCO balance, measurements taken within the same conditions (same charge and same distance between the spheres) should be around ±1° from each other. 5. Repeat steps 2-4 for separations 14, 10, 9, 8, 7, 6, and 5 cm. IV. DATA ANALYSIS Even without knowing the details of the Coulomb's law, based on the data obtained we can infer that there is a relationship between the force between the spheres (measured by the angle ) and the distance R between them. One general type of relationship that we can consider between the numerical values of 0 and R is: 0= b.Rn (2) where b is onstant (related with the magnitude of the charges of the spheres) and n is an exponent that we would like to determine as it represents the essence of the Coulomb law. If we take the log of both sides of the relationship (2) between the numerical values of and R and using the properties of the log function we obtain: loge = logb + nlogR The Coulomb Balance (3) Page 4 Question 1: If we graph t Slope 1 aken. hallenging due to the tually separation S fu Bal. Question 1: If we graph the loge vs. logR how can we determine the exponent n from the data? Slope of togo vs log R is the Q vs 1. For each distance R calculate the mean of the three angles recorded. 2. Plot the logarithm of the mean angles calculated as a function of the distance R. 3. From the log Oavg vs. logR determine the slope n and the intercept logb. 4. Since n is determined as a slope, use the formula (5) from the "Brief Notes on Measurement and Errors" to calculate its uncertainty. Note that in this particular case in the formula: y, are the values for log Oavg; X, are the values for logR; A = n i.e. the slope; B = logb i.e. the intercept; and N is the number of distances used. -1.64±3.$9357. Question 2: What is the value of n determined? 32 A pot avea Value of n = YOY Question 3: Is this value consistent with the accepted value n = -2 from the Coulomb law? You should justify your answer in terms of the criteria x ±1.96s (see "Brief Notes on Measurement and Errors" page 1-4 for details) Yes it is very is the " nell The Coulomb Balance sitt JOS HITOV SW amo is the Question 4: Chances are that the value obtained is not exactly 2. Provide some ideas of why this is case. (Hints: Look at your graph. Is it really linear? Are we justified to use a linear fitting?) that could close to to-2 corrected [-164]. It is because could occur. errory systematic. One of the major flaws in the above analysis was considering the spheres as point objects. The main assumption is that the distance between the charges involved is equal with the distance between the centers of the spheres. However, as the charges are distributed on the surface of the spheres this is not true. While charge distribution on macroscopic objects is something that you will investigate later in the course, your data can be corrected for this effect by dividing the angles by a correction factor: a³ of various errors Weather, Human error. random C=1-4 where a = 1.9 cm is the radius of the spheres and R is the distance between their centers. 5. Calculate corrected values for your angle using the above correction factor: Javg R3 = wid NS. (5) Page 5 - PRE-LAB Report - Due prior to lab (If you need more pages to answer the questions below, staple them together.) Full Name: Full Title of Experiment: The coulumb 1 Khizar Ismail - Effect of - of 1) 2pts What are the objectives of the lab? -Verify coulumb's Law by measuring spheres! Lab Section: Make sure with the spheres still to the same potential we 2 systematic errors on Understand the limitations. Of modeling reat charg c 2) 4pts Briefly describe the procedure of the laboratory and the equipment/software that will be used. discharge the spheres Positioning the Sliding sphere -suspended sphere will deflect -Repeat steps. The Coulomb Balance Balance force, blu and record dada. measurements log@= log b + nlog R. | Qcorrected = Qaug C. a) man seperation charge both spheres using the chargingen proble arstance of пост. 6-7 kv 3) 4pts Briefly describe the theory, including all relevant equations and calculations. PH00=n4 bekq19/2 R² K₂ 8. 987x 10⁹ Nm²/C² 2 charged → Coulumb law was published by charles Augustine. Q= b.R" C= 1-4 93 R³ systems. Page 2 I. OBJECTIVES The distance. 1. To verify Coulomb 2. To investic 3. To II. E n goal of this lab is to very uic IIVEIoE squale law upcaucuce UI LIE JUIVE UMI uv Depaiauvi charges. Since we are interested only in the qualitative behavior, we do not need to actually force. Thus we will not measure the charges placed on the the same throughout the re been ans that missing avg [1 19.7 34.0 63.7 76.0 95.7 107.7 36.0 !! or An .049 in log(R) (x) 1.30 1.15 1.00 0.95 0.90 0.85 0.78 (y-Ax-B)^2 5.27E-06 3.72E-04 1.64E-04 2.09E-04 9.17E-04 1.90E-04 5.02E-04 Khizar Ismail (y-Ax-B)^2 5.85E-05 4.66E-04 1.60E-05 3.32E-05 5.69E-04 1.84E-04 3.54E-05 log(0avg) (y) 1.29 1.53 1.80 1.88 1.98 2.03 2.13 x^2 1.693 1.314 1.000 0.911 0.816 0.714 0.606 log(R) (x) log(corrected) (y) 1.30 1.30 1.15 1.54 1.00 1.82 0.95 1.90 0.90 2.00 0.85 2.07 0.78 2.19 x^2 1.693 1.314 1.000 0.911 0.816 0.714 0.606 2867688 log theta avg (y) log theta corrected 2.50 2.00 1.50 1.00 0.50 0.00 2.50 2.00 1.50 1.00 0.50 0.00 0.00 0.00 0.20 0.20 log theta(y) vs log R(x) 0.40 0.60 0.40 log R (x) log theta(y) vs log R(x) 0.80 0.60 log R(x) 0.80 y=-1.6446x +3.4357 1.00 1.20 y=-1.7421x 3.5541 1.00 1.20 1.40 140

Fig: 1