PHYSICS EXPERIMENTS 133 Cuent Balance-1 Cuent Balance Wam Up 1. Foce between cuent-caying wies Wie 1 has a length L (whee L is "long") and caies a cuent I 0. What is the magnitude of the magnetic field a distance R fom the wie? Give you answe in tems of the vaiables given and constants. B wie 1 (d = R) = Daw the diection of the magnetic field due to the wie at the dot ( ) fo each of the two views below. Anothe identical wie with cuent I 0 is placed a distance R above wie 1. On the pictue below, indicate the diection of the magnetic field at the position of wie 2. Wite down the magnitude of the magnetic field expeienced by wie 2 in tems of the vaiables given and constants? B exp eienced by wie 2 = On each of the above pictues, indicate the diection of the foce exeted on wie 2. S: 10/20/08 2:08 PM 9_CuentBalance.doc
11-2 PHYSICS EXPERIMENTS 132 Calculate the magnitude of the foce exeted on wie 2. Give you answe in tems of the vaiables given and constants. Show you wok. F on wie 2 = 2. A diffeent aangement Two identical wies (wie 1 and wie 2), each having a length L and mass m w ae connected by spings. Wie 1 is attached to a table so that wie 2 sits off the table as shown below. Situation 1: Equilibium (no cuent) When thee is no cuent in the wies and the top wie is in equilibium, wie 2 is a distance R above wie 1 as shown. Detemine the foce the sping exets on wie 2 in tems of known vaiables and constants. Justify you wok. F sping on wie 2 (y = R) =
PHYSICS EXPERIMENTS 133 Cuent Balance-3 Situation 2: Mass added (no cuent) A small block (mass M) is placed on top of wie 2 compessing the sping so that the distance between the wies is now b. Detemine the foce the sping exets on wie 2 in tems of known vaiables and constants. Justify you wok. F sping on wie 2 (y = b) = Situation 3: Mass added (cuent) The small block (mass M) is left on top of wie 2, but now the cuent is tuned on in each of the wies so that wie 2 moves back to its oiginal equilibium position at y = R.
11-4 PHYSICS EXPERIMENTS 132 What is the total foce on wie 2? What is the foce the sping exets on wie 2 in tems of given vaiables and constants? Explain this. F sping on wie 2 (y = R) = Detemine the cuent I 0 though the wies in tems of known vaiables and constants. Justify you wok. I 0 (y = R) = STOP! Check this esult with you instucto befoe poceeding. 3. An "expeiment" A student takes the pevious aangement and measues that at equilibium R = 4 mm and the length of the wies is 25 cm. The student places 3 mg on wie 2 and tuns up the cuent to bing wie 2 back to its equilibium position at R = 4 mm. The student adds anothe 3 mg to wie 2 and tuns the cuent up moe to bing wie 2 back to its equilibium position at R = 4 mm. The student epeats this a numbe of times and gathes the following data. Added mass (mg) Total mass added (mg) Distance between wies (mm) 0 0 4 3 3 4 3 6 4 3 9 4 3 12 4 3 15 4 I (A) Complete the table by calculating the cuent in the wie fo each total mass. Caeful with units! Stop! Check the enties in you table with you instucto.
PHYSICS EXPERIMENTS 133 Cuent Balance-5 Cuent Balance GOAL. To measue the magnetic foce between two wies. To expeimentally detemine the pemeability constant, µ 0. To detemine the mass of an unknown. EQUIPMENT. Cuent balance with lase Factional gam mass set micomete calipe vaiable tansfome step-down tansfome with ated output of 20 ampees at 6 volts AC voltmete WARNING: Lase light can damage the etina. Keep the lase level at all times to avoid shining the light into an eye eithe diectly o fom a eflecting suface. Note: The appaatus is vey sensitive and is easily damaged, handle with cae. In this lab we will use a cuent balance to detemine the pemeability constant. To do this we ae going to use a pocedue simila to that analyzed in the Wam-up activity. The cuent balance consists of a long fixed conducting ba and a paallel movable ba a few millimetes above it. The movable ba is pat of a igid fame balanced on knife edges (the counte-balance acts like the sping in the wam-up); see Figue 1. The same cuent passes though the fixed and movable bas in opposite diections causing a epulsive magnetic foce. We will measue the equilibium position. Then we will add mass which will move the wie away fom equilibium. Then we will incease the cuent until the wie moves back to its equilibium position. Q1. With a caefully dawn diagam show why two paallel wies with cuents in opposite diections expeience a epulsive foce. (Use answe sheet at the end.) You found in the Wam-up that the cuent in the wie, I, was elated to the mass added to the wie, M, the length of the wie, L, the distance between the wies in equilibium, R, and the pemeability constant, µ 0, (1) I = 2"RMg µ 0 L. The added mass is easy to measue. The distance between the wies is a little moe difficult because the distances ae so small and we cannot just gab this sensitive appaatus and use a ule. The movement of the uppe ba is magnified by the use of a moving mio that eflects a lase beam onto a piece of pape on the wall; see Figue 2.
Cuent Balance 6 PHYSICS EXPERIMENTS 133 The distance between wies when in equilibium is R, as measued fom cente to cente. Using simila tiangles we can find the sepaation, s, of the bas of the cuent balance: (2) s A = D/2 B AD o s = 2B, whee A is the distance fom the moving ba to the knife edges, B is the distance fom the mio to the wall, and D is the diffeence between the equilibium and touching positions of the lase beam on the wall. You also need d, the diamete of the bas (equies using a micomete to measue). Adding d to the value of s calculated fom Eqn. (2) gives R, the equilibium cente-to-cente distance between the bas: (3) R = d + AD/2B. I. Measuing the equilibium distance between the bas Initial adjustment of the appaatus Measue the diamete of the cuent-caying wie. Adjust the leveling scews so that the whole balance ests fimly on the table. Adjust the countepoise (countebalancing mass) behind the mio until the fame oscillates feely and comes to est with the uppe ba about 1 millimete above and paallel to the fixed ba. Adjust the countepoise below the mio until the peiod of oscillation is 1 to 2 seconds. It should come to est in about 10 seconds when the poles of the damping magnets ae about 2 mm apat. Place enough mass on the scale pan so that the bas ae in contact (the amount of mass is not impotant). Caefully align the two bas one above the othe; thumbscews on each post pemit eithe end of the lowe ba to be aised o loweed. Simila thumbscews on the ea of each block pemit eithe end of the uppe ba to be moved fowad o backwad. If the bas ae not staight, call this to the attention of you instucto. Detemining R, the equilibium cente-to-cente distance You cuent balance is now in adjustment, with the two bas in contact. They ae held togethe due to the mass placed on ealie. Adjust the lase so that its eflection off the mio is visible on a wall about 2 o 3 metes fom the mio. Tape some pape on the wall at that location and mak the position of the lase spot with bas in contact. Now emove the mass fom the weight pan and wait fo the oscillations to stop. Mak this "equilibium" position on the wall (engage the beam lift gently and elease it to make sue that the new est point is epoducible). The diffeence in spot positions between "bas in contact" and "bas without added mass in equilibium" is the distance D shown in Figue 1. Using equation (3) detemine R (the cente-to-cente distance), this only needs to be done once povided you don't jostle you appaatus. Put the elevant values fo the physical quantities in Table 1.
PHYSICS EXPERIMENTS 133 Cuent Balance 7 II. Measuing the cuent 1. Connect the cicuit as shown in Figue 3 fo AC opeation. The cuent is measued using a shunt (a known esistance) and a voltmete V (be sue it is in AC mode). The shunt is made so that 1.0 A coesponds 1.0 mv. The cuent though the bas will be measued with the shunt/voltmete. 2. Stat with the bas in the equilibium position you found above (about 1 mm apat with no cuent and no added mass). 3. Add 20 mg to the weight pan. (If necessay, each time a mass is added o emoved use the ba lift mechanism because of the likelihood of jaing the ba and shifting the knife edges on thei beaing posts. Opeate the lift mechanism vey caefully while aising and loweing the ba.) 4. Afte adding the 20 mg mass, incease the cuent by closing the switch until the spot on the wall indicates that the beam has etuned to its equilibium position. 5. Detemine the cuent using the shunt/voltmete. Be sue you ae in AC mode! Do not keep the switch closed. 6. Recod this combination of added mass and cuent. (Caeful with units!) 7. Repeat, using successive 20 mg incements in mass, but do not exceed the maximum cuent allowed by the appaatus, oughly 10 A. Usually this means M total < 150 mg. If you did not get at least 10 points befoe eaching the limit of 10 A, go back and fill in using othe masses. 8. Remove the added mass, but do not jostle o modify the appaatus. 9. We now have expeimental data elating cuent and added mass. 10. Look at Equation 1 and notice that, if it coectly descibes ou expeiment, a plot of I 2 vs. M should be a staight line. Make this plot using you data and find the best-fit line. III. Finding the pemeability constant. 11. Look at Equation 1 and, assuming a plot of I 2 vs. M, find a symbolic expession fo the slope? Q2. What is the expession fo the slope when you plot I 2 vs. M? 12. Fom you best-fit line though the data detemine the expeimental slope. 13. Now calculate the pemeability constant, µ 0. 14. Pint out you gaph. Q3. What is you expeimentally detemined value fo the pemeability constant? What is the pecent diffeence between you value and the accepted value? IV. Detemining the mass of an unknown. 15. Obtain an unknown mass fom you instucto and ecod its identifying label. 16. Place the unknown on the cuent balance and adjust the cuent until the balance is in equilibium. 17. Recod this cuent. 18. Using you plot of I 2 vs. M and I you just measued, detemine the mass of the unknown. Q4. Recod the label and you detemination of the unknown mass.
Cuent Balance 8 PHYSICS EXPERIMENTS 133 NAME: REPORT. COURSE/SECTION: d A D B R Table 1. Relevant physical quantities. ANSWERS TO QUESTIONS (Q1-4).