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Current Balance 7. Current Balance* Objective: The objective in this set of experiments is to explore the way a magnetic field exerts a force on a wire that carries an electric current. You know an electric current is a flow of charge. You know too that an ampere is a coulomb per second. You will learn from your reading that, in fact, the ampere is a more fundamental unit than the coulomb and is defined by force measurements. The learning objectives are the following: 1. To know the relationship between charge and current. 2. To know how an ammeter is placed in a circuit in order to measure current through a specified branch. 3. To be able to use the right-hand rule to predict direction of a magnetic field in a coil, given the direction of current flow. 4. Similarly, to be able to figure out the direction of magnetic force on a current carrying wire when the direction of current flow and direction of magnetic field are given. 5. To get experience with a circuit in which there are two, parallel branches. 6. To learn to solve a problem involving forces and torques caused by electric currents. (These concepts are described in your textbook.) Pre-lab reading assignment: Before coming to lab, read the following: Everyone: Go to the National Institute of Standards Technology (NIST) website and find the official definition of the Ampere in terms of a force measurement. Review the sections on Magnetic field due to current especially in a solenoid, force on current carrying wire in magnetic field , magnetic fields and forces. In all of this, pay attention to the righthand rule discussion. This is your vector sign convention for magnetic fields. Serway and Vuille (212): 19.3 Magnetic Fields, 19.4: Magnetic Force on a Current-Carrying Conductor , 19.5 Torque on a Current Loop and Electric Motors, 19.6 Motion of a Charged Particle in a Magnetic Field 19.7 Magnetic Field of a Long, Straight Wire and Ampère's Law Serway and Jewett (252): 29.1 Magnetic Fields and Forces, 29.2 Magnetic Force Acting on a Current-Carrying Conductor, 29.3 Torque on a Current Loop in a Uniform Magnetic Field , 29.4 Motion of a Charged Particle in a Uniform Magnetic Field, 29.5 Applications Involving Charged Particles Moving in a Magnetic Field Pre-lab assignment: Do the following before coming to lab. You must complete your assigned reading and exercises before entering joining your group in the laboratory. Your TA will check this as you enter. 1. The ampere, which is the SI unit of electric current, is actually defined by a measurement recipe. What is the definition of the ampere, according to NIST? ______________________________________________________________________________ *© William A Schwalm 2012 7-1 Current Balance 2. How is the ampere related to the Coulomb? From this relation, suppose when charging a capacitor, a steady 2.5 amp current flows for .0012 Sec. onto one of the plates. If the plate were initially uncharged, how much charge would accumulate on each plate, including the sign? 3. Two electric currents flow in two parallel wires twenty centimeters apart, as shown. 10 A 5A . (a) Calculate the magnitude and direction of the forces acting on the upper wire due to the lower wire. Explain carefully in words how you have figured out the direction of the force using the right-hand rule. (b) Similarly, what is the magnitude and direction of the force on the lower wire due to the upper one? 4. A current of 3.2 mille amperes flows through the wire winding of a solenoid, as shown. The radius of the coil is .75 cm and the length is 2.0 cm. (a) What is the magnitude and direction of the magnetic field at the center of the solenoid? (Get N and n from the picture, assuming only one layer of wire.) (b) Explain how you know the direction of the field. (Just writing “right-hand rule” will not be enough.) 5. The following circuit is one in which there are two parallel branches. Current in one branch flows around a solenoid. In the other branch, the current flows along a wire around the edge of a plastic teeter board. Current entering from the wall receptacle separates at P and recombines at Q. 7-2 Current Balance (a) If the ammeter A1 reads .15 amps, how much current flows through A2 and in which direction? (b) Explain how you would have to put an ammeter A3 into the circuit so that it would measure the whole current coming from and back to the wall socket. A1 Switch Rheostat 1 .4 amp P Q Solenoid .4 amp A2 Rheostat 2 7-3 Current Balance Problem Your team has to solve the following physics problem, and then make laboratory measurements to see how well you can verify your solution in the lab. A small mass m providing counterweight B Teeter totter with its end inside a solenoid A small teeter totter made of plastic is pivoted at its center and one end is situated inside a coil or a solenoid carrying a current. The coil provides a constant, uniform magnetic field in the direction shown. A wire around one end of the teeter board can carry a current, provided by a battery as shown. When there is no counterweight (that is, when m = 0) and no current, the teeter balances. The length of the teeter board is L and the width is W. Suppose the magnitude B of the magnetic field is known. Parts (a) and (b) are sort of preliminary. (a) How much current must flow through the wire to balance the teeter with a counterweight m in place? (b) Where would you have to place a resistor in the circuit to limit the current through the teeter wire? Show in a sketch. (c) Your team has to devise a way, using the equipment provided, to see whether this predicted “theoretical” solution actually works. You need to produce a graph showing current in the teeter circuit versus the counter weight and discuss the results. At the NIST laboratories, this method is used to make extremely accurate current measurements. An important practical consideration will be: What factor limits the accuracy of this measurement concept in your lab set-up? 7-4 Current Balance In-class activities: A set-up that can be used for this experiment is shown below: The teeter is shown in the center, one end stuck into a solenoid. There are two ammeters, corresponding to A1 and A2, two rheostats (variable resistors) and a switch. The connections to the wall receptacle are shown at the right. 1. Locate and mark on the figure above the two points P and Q where the two circuits merge. 2. The variable resistors work as shown below. The slide on top makes contact with the resistance wire at a variable point. One connection is made to the slider and the other is made to the end of the resistance. By moving the slider you can control the resistance, and hence control the amount of current flow. Make a drawing to show how the picture of an actual variable resistor corresponds to the usual circuit diagram for a rheostat, as shown on page 3. This much of the resistance active. (Lower resistance, larger current.) This much of the resistance active. (Higher resistance, less current.) 7-5 Current Balance 3. The part of the circuit that carries current I around the edge of the teeter could be drawn separately as follows. Frankenstein switch Rheostat 2 + I Balanc e A2 Ammeter Using a red colored pencil, indicate the path of this circuit on the figure on page 5. If you want more current to flow through this circuit, would you push the slider to the right, or to the left? 4. The circuit that feeds current through the coil is drawn separately here. Using a blue colored pencil, indicate the path of this current on the photo on 5. B + Solenoid To and from current source A1 A Rheostat 1 1 Ammeter 7-6 Current Balance 5. According to the manufacturer’s the number of turns N in the solenoid is 540. Explain how you can use this to relate the magnetic field inside the solenoid to the current that flows through it. (The explanation should include a formula.) 6. As the mass m used as counterweight for the current balance, you will need some rather small, rather accurate masses. One way to get these is to use lengths of string which you can hang on the tab at the end of the teeter board. Given a good supply of fairly uniform string, how could you prepare a set of small, rather accurate masses? Measurement plan: In consultation with your group, outline a plan for comparing the force on the outside end of the teeter, as measured using the string masses, against what you compute for the magnetic force on the other end of the teeter. Some details you need to include are the linear density (mass per length) of the string, and hence the mass of each string weight, the current in the solenoid coil, the other current around the edge of the teeter board. A data table might look something like this: Isolenoid B Ibalance FB 1 2 3 4 5 7-7 # of unit counter weights Fg Current Balance Write your measurement plan here and explain how you will use the data to assess the validity of your prediction for FB. Regarding how which current values to use in the coil or in the current balance, you may have to figure this out as you go along. (See warnings below.) Record your plan here. Implementation of Plan: Put your plan into effect and gather data. Record the data and notes here. Analysis: Analyze your data as described in your plan. Of course you need to make it clear to the reader what you are doing. Include some estimate of the maximum error, which you need to explain, as always. Conclusion: There will be a brief summary discussion of how the objectives are addressed by the laboratory activities. Write a summary of the class discussion here, adding your own conclusions as appropriate. 7-8

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