Current BalanceWSU-Vancouver PHYS 202Goals1) To explore and verify the right-hand rule governing the force on a current-carrying wireimmersed in a magnetic field.2) To determine the force on the wire...

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Current BalanceWSU-Vancouver PHYS 202Goals1) To explore and verify the right-hand rule governing the force on a current-carrying wireimmersed in a magnetic field.2) To determine the force on the wire when the length of the wire, the magnetic field, and thecurrent flowing in the wire are varied one at a time and to display the relationships graphically.IntroductionElectric charges experience a force when moving through a region of magnetic field. Ifthe charge is stationary, then no force is experienced. Since currents are just electric charges inmotion, current carrying wires can also experience forces when immersed in magnetic fields.The force F on a wire of length L carrying a current I in the presence of a magnetic field ofstrength B is given byF = IL x BNote that the force, wire length, and magnetic field are all vector quantities (the vectordirection of L is in the direction of the current I ). The so-called vector cross product is used tocompute the force. The vector cross product has the property that its magnitude, in this case theforce, is given by ILBsinq, where q is the angle between the length vector and the magnetic fieldvector when the two vectors are placed “tail” to “tail.” The direction of the resulting force vectoris determined by applying the “right-hand rule” as shown in your textbook. In this experimentthe angle θ between the wire and the magnetic field is always 900 making sin θ = 1.The purpose of this experiment is to measure the force on a current carrying wire in thepresence of a magnetic field and to determine how this force depends on magnetic field strength,current, and wire length. You should also be able to apply the right hand rule to predict thedirection of the force on a current carrying wire in a magnetic field.CAUTION: THE LOAD LIMIT FOR THE ELECTRONIC BALANCES IS 200 g. USEAPPROPRIATE CARE SO THIS LIMIT IS NOT EXCEEDED!NOTE: The “red ends” of the small magnets are N poles; the “white ends” are S poles.Our are marked, “N” and “S”.Materials1 each power supply1 each current balance kit1 each electronic balance2 each electrical lead cables1 each metric ruler1 each small ring standExercise 1:Force versus Length1. Setting up the Equipmenta. Using all six of the small magnets, place the magnets and magnet holder on theelectronic balance and tare the balance. Make certain that all the magnets are orientedwith the same polarity so that the magnetic field is maximized.b. Plug circuit sf37 (note that this is the manufacturer’s designation and has no otherpurpose than to identify it) into the ends of the shiny metal bars of the current balanceapparatus mounted on the stand.c. With the power supply off connect it (using the red and black jacks on the front) to thecurrent balance apparatus using the holes provided on the tops of the metal bars.d. Before turning on the power supply, adjust the voltage knob and the current knob totheir full counter-clockwise positions. Adjust the voltage knob to with the whitemark in the 9:00 position (pointing to the left, horizontally). Set the current knob toapproximately the 11:00 position (not quite straight up). This should yield ~ 0.3Vand ~2.0 A.2. Making a Predictiona. Draw a free-body diagram of the magnets (including magnet holder) in equilibriumon the balance with no current flowing through the circuit.b. Draw another free-body diagram of the magnets (including magnet holder) inequilibrium when current is present in the wire that is between the poles of the magnet.You must apply the right-hand rule in conjunction with the magnetic force equation givenearlier to determine the direction of the magnetic force on the wire. Then use Newton’s3rd Law to determine the force on the magnets. Make sure that your diagram andexplanation are very clear here. [Remember that the magnetic field by convention pointsfrom the N pole to the S pole outside the magnet itself. Also recall that current flows outof the red (+) terminal of the power supply and into the black (-) terminal.]c. On the basis of your free-body diagrams predict whether the electronic balance willread a positive value or a negative value.3. Doing the Experimenta. Position the bottom of the U-shaped “wire” on sf40 so that it is centered between thepoles of the magnet sitting on the electronic balance. Align sf40 carefully so that it is nottouching the magnet holder anywhere. You may need to tare the balance again at thispoint before turning on the power supply.b. Turn on the power supply and adjust the current knob clockwise until the ammeterreads 2 A. Check this from time to time during the rest of this exercise since the currentsometimes can drift small amounts as the power supply warms up.c. Compare and comment on the sign of the reading on the balance. If you didn’t get itright the first time, go back and rethink it. Explain in your report how you went wrongand give a corrected explanation.d. Record the balance readings for sf37 to sf42 keeping the current set at 2 A.e. For sf42 only, reverse the direction of the current by switching the connections to theblack and red terminals on the power supply. What happens to the reading given by theelectronic balance? What did you expect to happen? Explain.4. Analyzing the Dataa. Convert all of the balance readings from mass units to forces in newtons.b. For each of the circuits sf37 to sf42 measure the effective length of the wire that wasimmersed in the magnetic field and resulted in a net force on the magnet. See images inCAPSTONE, or use this tableCurrent Loop Length (cm)SF 40 1.0SF 37 2.0SF 39 3.0SF 38 4.0SF 41 6.0SF 42 8.0c. Graph the force on the magnet as a function of the length of the wire immersed in themagnetic field.d. If appropriate, fit a straight line to the data and calculate the magnetic field in tesla (T)for all six magnets. Refer back to the force law given previously for help. Use thepercent uncertainty of the slope to determine the uncertainty of your magnetic field value.Exercise 2: Force versus Magnetic Field1. Setting up the Equipmenta. Plug circuit sf40 into the ends of the current balance apparatus.b. The manufacturer assures us that the magnetic field between the poles of the magnet isdirectly proportional to the number of small magnets used. We have already done ameasurement with sf40 and six small magnets. Now remove one of the small magnetsleaving five. Center the five magnets relative to the magnet poles.c. Align the wire of sf40 relative to the magnet poles as done previously.2. Doing the Experimenta. Set the power supply current to 2A.b. Record the balance reading when current is passed through the wire. Be sure to tarethe electronic balance appropriately.c. Remove one magnet at a time and repeat the measurement. (You should have six datapoints counting the one already done in Exercise 1.)3. Analyzing the Dataa. Make a graph of the magnetic force as a function of the number of magnets.b. Based on your graph what can you say about the relationship between the force andthe value of the magnetic field? If it is linear, find the slope of the graph and calculatethe magnetic field of all six magnets again. (Remember that the field of all six magnets issimply six times greater than the field of a single magnet.) Use the percent uncertainty ofthe slope to determine the uncertainty of your magnetic field value.Exercise 3: Force versus Current1. Setting up the Equipmenta. Replace all the magnets making sure that all the red poles and white poles are alignedcorrectly.b. Plug sf42 into the ends of the current balance apparatus.c. Set the current from the power supply at 3 A.2. Doing the Experimenta. Record the balance reading when current is passed through the wire between the polesof the magnet.b. Lower the current to 2.5 A and repeat the measurement.c. Continue reducing the current in 0.5 A increments until you reach 0.5 A. Record thebalance reading in each case.3. Analyzing the DataGraph the magnetic force on sf42 as a function of the current. What can you say aboutthe relationship between force and current? From this analysis you should be able tocalculate the magnetic field with all the small magnets present. Use the percentuncertainty of the slope to determine the uncertainty of your magnetic field value.4. Compare your three experimental values of the magnetic field of all six magnets. Do theyagree within the experimental uncertainties? If not, are there other measurementuncertainties that you have not included in this analysis (e.g. the fixed parameters in eachexperment)? EXPLAIN YOUR REASONING!ConclusionThe fundamental magnetic force law for current carrying wires in magnetic fields givenin the Introduction makes certain predictions about the dependence of the force on the current,wire length, and the magnetic field. Are your findings from Exercises 1-3 in harmony with theforce law as formulated? Be very specific here and speak to the results of each Exercise. If notin harmony, explain specifically in what way your results differ.It is important to remember that the force law as formulated actually was induced fromexperiments such as you have done today. Thus the law as stated just characterizes how naturebehaves; it doesn’t prescribe beforehand how nature must behave. Nature behaves however shewishes, and we as scientists can only hope to characterize that behavior in simple ways fromtime to time. Of course we often express these characterizations in mathematical terms, theshorthand of science.RUBRIC:(5 pts) (4 pts) (3 pt) (2 pts) (1 pt) (0 pts)IntroductionExercise-1 (Graph,curve fit, analysis)Exercise 2 (Graph,curve fit, analysis)Exercise 3 (Graph,curve fit, analysis,comparisons)Conclusion(Quantitative…)Before you leave the labTurn off the power to all the equipment.Disconnect the power supply and make sure that all six of the small magnets areaccounted for.Straighten up your lab station for the students who follow you.Report any problems or suggest improvements to your lab instructor.
Answered 4 days AfterApr 12, 2022

Solution

Dr Shweta answered on Apr 16 2022
11 Votes
Solution
Exercise 1: Force versus Length
2. Making a Prediction
a. Draw a free-body diagram of the magnets (including magnet holder) in equili
ium on the balance with no cu
ent flowing through the circuit. Nva
Solution: when no cu
ent is flowing:
At equili
ium, N=Mg
Where, M = mass of the magnets
N = Normal force exerted on the magnets by the balanceMg
. Draw another free-body diagram of the magnets (including magnet holder) in equili
ium when cu
ent is present in the wire that is between the poles of the magnet. You must apply the right-hand rule in conjunction with the magnetic force equation given earlier to determine the direction of the magnetic force on the wire. Then use Newton’s 3rd Law to determine the force on the magnets. Make sure that your diagram and explanation are very clear here. [Remember that the magnetic field by convention points from the N pole to the S pole outside the magnet itself. Also recall that cu
ent flows out of the red (+) terminal of the power supply and into the black (-) terminal.]
Solution:
Here, l = total length of the wire,
= Force is upward if the cu
ent flowing in the loop is clockwise
Thus, we get two cases:
Case I = cu
ent is clockwise = force on the wire is upward
Case II = cu
ent is anticlockwise = force on the wire is downward
Now, using Newton’s third law which states every action has equal and opposite reaction
Thus, we get two cases:
Case I = force on the magnet is downward
Case II = force on the wire is upward
With magnitude F =IBlN
Thu, Case I = Case II =F
N
Mg
F
Mg
c. On the basis of your free-body diagrams predict whether the electronic balance will read a positive value or a negative value.
Solution: Since, the magnet is initially balanced,
Thus, Case I = Extra downward force = positive value on the balance
Case II = Extra upward force = negative value on the balance
3. Doing the Experiment
d. Record the balance readings for sf37 to sf42 keeping the cu
ent set at 2 A.
Solution:
    Trial
    SF
    Mass(g)
    Mass(kg)
    Volt
    Ampere
    check
    37
    0.21
    0.00021
    0.3
    1.95
    1
    40
    0.14
    0.00014
    0.4
    1.98
    2
    37
    0.24
    0.00024
    0.3
    1.99
    3
    38
    0.42
    0.00042
    0.4
    1.98
    4
    39
    0.35
    0.00035
    0.3
    1.98
    5
    41
    0.7
    0.0007
    0.4
    1.98
    6
    42
    0.96
    0.00096
    0.4
    1.97
    6 reversed
    42
    -0.96
    -0.00096
    0.4
    1.97
e. For sf42 only, reverse the direction of the cu
ent by switching the connections to the black and red terminals on the power supply. What happens to the reading given by the...
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