PHYSICS EXPEIMENTS 133 Current Balance-1 Current Balance Warm Up 1. Force between current-carrying wires First, let us assume only one wire exists,. Wire 1 has a length (where is "long") and carries a current I 0. What is the magnitude of the magnetic field at a point a distance from the wire? Give your answer in terms of the variables given and constants. B r from wire1at the point Draw the magnetic field vector due to at the dot ( ) for each of the two views below. I0 Now, another identical wire with current I 0 is placed a distance above. On the picture below, draw the magnetic field vector at the position of wire 2. I 0 wire 2 wire 2 I 0 Write down the magnitude of the magnetic field experienced by wire 2 in terms of the variables given and constants? B r experienced by wire 2 from wire1 On each of the above pictures, indicate the direction of the force exerted on wire 2.
11-2 PHYSICS EXPEIMENTS 132 Calculate the magnitude of the force exerted on wire 2. Give you answer in terms of the variables given and constants. Show your work. F r on wire 2 from wire1 2. A different arrangement Two identical wires ( and wire 2), each having a length and mass m w are connected by springs. Wire 1 is attached to a table so that wire 2 sits off the table as shown below. wire 2 wire 2 Situation 1: Equilibrium (no current) When there is no current in the wires and the top wire is in equilibrium, wire 2 is a distance above as shown. Determine the force the spring exerts on wire 2 in terms of known variables and constants. Justify your work. F r of spring on wire 2
PHYSICS EXPEIMENTS 133 Current Balance-3 Situation 2: Mass added (no current) A small block (mass M) is placed on top of wire 2 compressing the spring so that the distance between the wires is now b. M b wire 2 wire 2 b M Determine the force the spring exerts on wire 2 in terms of known variables and constants. Justify your work. F r of spring on wire 2 Situation 3: Mass added (current) The small block (mass M) is left on top of wire 2, but now the current is turned on in each of the wires so that wire 2 moves back to its original equilibrium position at y. M I 0 M wire 2 wire 2 I 0
11-4 PHYSICS EXPEIMENTS 132 What is the total force on wire 2? What is the force the spring exerts on wire 2 in terms of given variables and constants? Explain this. F r of spring on wire 2 Determine the current I 0 through the wires in terms of known variables and constants. Justify your work. I o STOP! Check this result with your instructor before proceeding. 3. An "experiment" A student takes the previous arrangement and measures that at equilibrium 4 mm and the length of the wires is 25 cm. The student places 3 mg on wire 2 and turns up the current to bring wire 2 back to its equilibrium position at 4 mm. The student adds another 3 mg to wire 2 and turns the current up more to bring wire 2 back to its equilibrium position at 4 mm. The student repeats this a number of times and gathers the following data. Total mass added (mg) Distance between wires (mm) 0 4 I (A) 3 4 6 4 9 4 12 4 15 4 Complete the table by calculating the current in the wire for each total mass. Careful with units! Stop! Check the entries in your table with your instructor.
PHYSICS EXPEIMENTS 133 Current Balance-5 Current Balance GOA. To measure the magnetic force between two wires. To experimentally determine the permeability constant, μ 0. To determine the mass of an unknown. EQUIPMENT. Current balance with laser Fractional gram mass set micrometer caliper variable transformer step-down transformer with rated output of 20 amperes at 6 volts AC voltmeter WANING: aser light can damage the retina. Keep the laser level at all times to avoid shining the light into an eye either directly or from a reflecting surface. Note: The apparatus is very sensitive and is easily damaged, handle with care. In this lab we will use a current balance to determine the permeability constant. To do this we are going to use a procedure similar to that analyzed in the Warm-up activity. The current balance consists of a long fixed conducting bar and a parallel movable bar a few millimeters above it. The movable bar is part of a rigid frame balanced on knife edges (the counter-balance acts like the spring in the warm-up); see Figure 1. The same current passes through the fixed and counter-balance moveable wire movable bars in opposite directions causing a repulsive magnetic force. We will measure the equilibrium position. knife-edge fixed wire Then we will add mass which will move the wire away from equilibrium. Then we will increase the current until the wire Fig. 1 End view of current balance moves back to its equilibrium position. Q1. With a carefully drawn diagram show why two parallel wires with currents in opposite directions experience a repulsive force. (Use answer sheet at the end.) You found in the Warm-up that the current in the wire, I, was related to the mass added to the wire, M, the length of the wire,, the distance between the wires in equilibrium,, and the permeability constant, μ 0, (1) I 2πMg μ 0. The added mass is easy to measure. The distance between the wires is a little more difficult because the distances are so small and we cannot just grab this sensitive apparatus and use a ruler. The movement of the upper bar is magnified by the use of a moving mirror that reflects a laser beam onto a piece of paper on the wall; see Figure 2.
Current Balance 6 PHYSICS EXPEIMENTS 133 The distance between wires when in equilibrium is, as measured from center to center. Using similar triangles we can find the separation, s, of the bars of the current balance: (2) s A D/2 B AD or s 2B, MIO B WA D/2 D/2 where A is the distance from the moving bar to the knife edges, B is the distance from the mirror to the wall, and D is the difference between the equilibrium and touching positions of the laser beam on the wall. You also need d, the diameter of the bars (requires using a micrometer to measure). Adding d to the value of s calculated from Eqn. (2) gives, the equilibrium center-to-center distance between the bars: KNIFE EDGE A s laser fixed conducting bar Fig. 2 End view of bars (3) d + AD/2B. I. Measuring the equilibrium distance between the bars Initial adjustment of the apparatus Measure the diameter of the current-carrying wire. Adjust the leveling screws so that the whole balance rests firmly on the table. Adjust the counterpoise (counterbalancing mass) behind the mirror until the frame oscillates freely and comes to rest with the upper bar about 1 millimeter above and parallel to the fixed bar. Adjust the counterpoise below the mirror until the period of oscillation is 1 to 2 seconds. It should come to rest in about 10 seconds when the poles of the damping magnets are about 2 mm apart. Place enough mass on the scale pan so that the bars are in contact (the amount of mass is not important). Carefully align the two bars one above the other; thumbscrews on each post permit either end of the lower bar to be raised or lowered. Similar thumbscrews on the rear of each block permit either end of the upper bar to be moved forward or backward. If the bars are not straight, call this to the attention of your instructor. Determining, the equilibrium center-to-center distance Your current balance is now in adjustment, with the two bars in contact. They are held together due to the mass placed on earlier. Adjust the laser so that its reflection off the mirror is visible on a wall about 2 or 3 meters from the mirror. Tape some paper on the wall at that location and mark the position of the laser spot with bars in contact. Now remove the mass from the weight pan and wait for the oscillations to stop. Mark this "equilibrium" position on the wall (engage the beam lift gently and release it to make sure that the new rest point is reproducible). The difference in spot positions between "bars in contact" and "bars without added mass in equilibrium" is the distance D shown in Figure 1. Using equation (3) determine (the center-to-center distance), this only needs to be done once provided you don't jostle your apparatus. Put the relevant values for the physical quantities in Table 1.
PHYSICS EXPEIMENTS 133 Current Balance 7 II. Measuring the current 1. Connect the circuit as shown in Figure 3 for AC operation. The current is measured using a shunt (a known resistance) and a voltmeter V (be sure it is in AC mode). The shunt is made so that 1.0 A corresponds 1.0 mv. The current through the bars will be measured with the shunt/voltmeter. Fig. 3. Circuit schematic. 2. Start with the bars in the equilibrium position you found above (about 1 mm apart with no current and no added mass). 3. Add 10 mg to the weight pan. (If necessary, each time a mass is added or removed use the bar lift mechanism because of the likelihood of jarring the bar and shifting the knife edges on their bearing posts. Operate the lift mechanism very carefully while raising and lowering the bar.) 4. After adding the 10 mg mass, increase the current by closing the switch until the spot on the wall indicates that the beam has returned to its equilibrium position. 5. Determine the current using the shunt/voltmeter. Be sure you are in AC mode! Do not keep the switch closed. 6. ecord this combination of added mass and current. (Careful with units!) 7. epeat, using successive 10 mg increments in mass, but do not exceed the maximum current allowed by the apparatus, roughly 10 A. Usually this means M total < 150 mg. If you did not get at least 10 points before reaching the limit of 10 A, go back and fill in using other masses. 8. emove the added mass, but do not jostle or modify the apparatus. 9. We now have experimental data relating current and added mass. 10. ook at Equation 1 and notice that, if it correctly describes our experiment, a plot of I 2 vs. M should be a straight line. Make this plot using your data and find the best-fit line. III. Finding the permeability constant. 11. ook at Equation 1 and, assuming a plot of I 2 vs. M, find a symbolic expression for the slope? Q2. What is the expression for the slope when you plot I 2 vs. M? 12. From your best-fit line through the data determine the experimental slope. 13. Now calculate the permeability constant, μ 0. 14. Print out your graph. Q3. What is your experimentally determined value for the permeability constant? What is the percent difference between your value and the accepted value? IV. Determining the mass of an unknown. 115 V AC variable transformer stepdown transformer 15. Obtain an unknown mass from your instructor and record its identifying label. 16. Place the unknown on the current balance and adjust the current until the balance is in equilibrium. 17. ecord this current. 18. Using your plot of I 2 vs. M and I you just measured, determine the mass of the unknown. Q4. ecord the label of your mass, sketch your mass, and show all your work in determining its mass. V shunt A current balance
Current Balance 8 PHYSICS EXPEIMENTS 133 NAME: EPOT. COUSE/SECTION: d A D B Table 1. elevant physical quantities. ANSWES TO QUESTIONS (Q1-4).