Induction Kit 8 Thursday 12-2pm
Ni Feng (z5162408) Rebecca Tran (z5208589) Shannon Turner (z5045864) Tajaswini Dhadge (z5207558)
August 2018
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Contents
1 Aims:
2 Introduction:
3 Experimental Procedure:
3.1 Basic…………………………..
3.2 Standard………………………..
3.3 Extended………………………..
4 Results:
4.1 BasicExperiment…………………..
4.2 StandardExperiment………………..
4.3 ExtendedExperiment……………….
5 Discussion of Results:
5.1 Basic…………………………………… 10 5.2 Standard………………………………… 11 5.3 Extended………………………………… 12
6 Conclusion: 13
7 References: 14
8 Acknowledgements: 14
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1 Aims:
Generally, the aim of the experiments required an observation on the induction of EMF; enabling for the practical use of Faraday’s equations, Faraday’s law and Lenz’s law. For purposes of this section, the aims of the experiments are specified below:
Basic – To determine the effects of a varying resistor on the strength of an EMF produced by a solenoid; and whether more coils on a solenoid produce a stronger EMF.
Standard – To observe how the velocity of a changing magnetic field affect the in- duction of EMF in a coil.
Extended – To observe the effects of a current-induced magnetic field on an oscil-
lating spring.
2 Introduction:
A British scientist named Michael Faraday first introduced the principle of induction in 1831. He performed two experiments such as the ‘moving magnet experiment’, depicted in Figure 1. This has led to Faraday’s law, which demonstrates the relationship between magnetic flux and the in- duction of EMF.
Figure 1: Faraday’s moving magnet experiment inducing EMF
The experiment requires one to move a magnet in and out of a solenoid, which is connected to a galvanometer. Initially it was observed that “no current was registered in the galvanometer when the bar magnet was stationary” (1). However, when relative motion occurred between the solenoid and the magnet, current was induced where “the galvanometer deflects when the magnet approaches the loop, and the opposite way as it moves away”(1). This shows there was some form of current present.
The induction of EMF in the galvanometer without a power source allowed Faraday to confirm his hypothesis- that a change in magnetic flux generates electrical current through a closed loop resulting from the induction of EMF. This hypothesis is widely known as Faraday’s law.
Furthermore, Faraday’s attentiveness saw that “the magnitude of EMF induced in the coil is proportional to the rate of flux through time linked with the coil” (6).This can be mathematically explained using the equation below:
EMF αN∆Φ ∆t
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Russian physicist Heinrich Friedrich Emil Lenz extended on Faraday’s law by conjuring a formula to further explain the phenomenon of electromagnetic induction. The equation is expressed below:
EMF =−N∆Φ ∆t
He built upon Faraday’s law and hypothesized that “an electromagnetic field interacting with a conductor will generate electrical current that induces a counter magnetic field that opposes the magnetic field generating the current.” (3) Hence, the negative sign in the formula shown above. The formulation of such expression not only enabled for a clarified explanation of the phenomenon of electromagnetic induction, ”but also enabled Lenz to win a Nobel Prize.” (6)
To physically articulate Lenz’s formula, a French scientist named Dominique Arago developed the “swinging magnet experiment”. It requires a piece of magnet attached to the string and a slab of metal. The magnet is then allowed to swing above the piece of metal. Refer to Figure 2 below for reference.
Figure 2: Arago’s swinging magnet experiment to explain Lenz’s law
“It can be seen that the swing of the magnet is dampened when the conductor is in close proximity”(3), compared to its motion with the absence of the metal; which swung consistently and without delay. Such observation validates Lenz’s hypothesis, where the relative motion between the magnet and metal causes a change in flux. Hence, EMF is produced to counteract this resulting in a dampened swing of the magnet.
Additional principles were utilised in the experiments to explain the trend and relationship of testing variables. Such principle included Ohm’s law. It states that electrical current is propor- tional to the voltage applied, as well as inversely proportional to the resistance in the circuit. It is given by the formula:
V =IR
Other formulas include Ampere’s law. It states that the magnetic field strength is proportional to the electric current flowing through the main source of what produces the EMF. It can be mathematically described using the formula:
This prior knowledge has enabled for the creation of experiments with varying difficulty, resulting for a deeper exploration of the concept.
B ds = μ0I
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3 Experimental Procedure: 3.1 Basic
Equipment: 200, 400, and 800 turn solenoids, magnetic field sensor, lab pro, a multimeter, set of leads, 2V DC power supply, a rheostat, retort stand, masking tape
Method:
1. Connect the magnetic field sensor to the LabQuest
2. Setup the equipment as shown in the figure below
3. Mark an outline of where the solenoid is positioned underneath the magnetic field sensor using the masking tape.
4. Measure the magnetic field of the environment and record as offset for final results.
5. Use the multimeter to set the varying resistance with the rheostat (0.6, 12 and 26.8 Ω) and measure the magnetic field of the 200 coiled solenoid.
6. Repeat steps 1-5 for the 400 and 800 coiled solenoid.
3.2 Standard
Equipment: 400 solenoid, magnet, wires, perspex rod, voltage probe, retort stand, 2 clamps, 2 bossheads, protractor, blu-tack, LabQuest, computer
Method:
1. Attach the voltage probe to LabQuest
2. Setup the equipment as shown in the figure below
3. Set perspex rod at angle of 40 degrees
4. Press record on the computer as soon as the magnet is dropped in and stop recording when it comes out of the perspex rod.
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5. Time the duration of the magnet sliding using the stopwatch. 6. Calculate and record the average speed of the magnet
7. Record the highest peak of the graph obtained as the voltage 8. Repeat steps 2-7 two times
9. Repeat steps 2-8 at 50 and 60 degrees.
3.3 Extended
Equipment: Retort stand, spring, clamp, String, Piece of metal (iron), solenoid, wires, perspex rod, powerpack
Method:
1. Set up equipment as shown without the solenoid
3. Extend the spring to an appropriate length that will allow for spring oscillation within the length of the plastic tube.
4. Record the length of extension and apply it for every oscillating process.
5. Start timer after first oscillation of spring and record the time it took to decelerate to rest.
6. Repeat steps 1-5 with the solenoid and a current of 1A, 2A and 3A 3 times each.
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4 Results:
4.1 Basic Experiment
Figure 3: Theoretical results using Ampere’s law
Figure 4: Resistance vs. EMF
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Figure 5: No. of Turns vs. EMF
4.2 Standard Experiment
Figure 6: Velocity vs. Voltage
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Figure 7: The pathway of EMF induced by magnet travelling through perspex tube
Figure 8: Above is how the results was interpreted by LabQuest device, information such as the peak potential voltage and time taken for the magnet to travel through the rod was extracted to generate table 3 and graph 3.
4.3 Extended Experiment
Figure 9: ”Model plots of induced voltage vs distance from coil”(5)
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Figure 10: The theoretical results of the spring damping due to the strength of the EMF induced opposing the springs relative motion making it decrease overtime. EMF would keep opposing this motion until there is no more relative motion left in the spring.(2)
5 Discussion of Results: 5.1 Basic
The experiment utilised a constant DC voltage of 2V, resulting in the current applied to be de- pendent on the varying resistance. ”When this current flows through a solenoid, it is then able to produce a magnetic flux through the open space of a solenoid” (4).
Since Ampere’s law states that the magnetic field strength is proportional to the electric cur- rent flowing through the main source of what produces the EMF, then the obtained results satisfy the formula:
B ds = μ0I
Hence, referring to Figure 3 – Resistance vs. EMF – the decline in the strength of the electro- magnetic field is inversely proportional to the increase in resistance in the circuit, satisfying the hypothesis of a reduced current decreasing the strength of a magnetic field.
As for the third variable from the basic experiment, number of turns in a solenoid, which we would change to prove Faraday’s Law with:
EMF =−N∆Φ ∆t
Faraday’s law suggests that if an induced magnetic flux is changing through a number of turns in a solenoid, then the total EMF is the sum of each turned wire with a magnetic flux. But results appeared inconclusive to this law, hence when referring to Figure 4 – No. of Turns vs. EMF – there is a decline in strength of the produced EMF as the number of turns in a solenoid has increased. To counteract this, equipment saturation was considered. Hence, a variable resistor was added to reduce the current to reduce saturation of junk results. This was done in consideration of the maximum Tesla reading of the magnetic sensor, which was 8.5 mT. Figure 10 below depicts an example of saturated results, where the peak to peak waves had different shapes.
There was also the occurring issue of an oscillating magnetic field in the LabQuest results, which made no sense considering that only DC was supplied. Supposedly, according to Faraday’s law, there should be a reading of a constant magnetic field.The failing results prompted for the testing of all equipment, to ensure no faulty equipment was used. For example,the magnetic field sensor was tested on a rare earth, static magnet. The magnetic field sensor displayed accurate results of a straight line.
Conclusively, equipment was tested to be not faulty. However, results displaying a sine curve could not be explained.
Due to Ampere’s law, the number of turns on a solenoid did not factor into the change of results. Rather, it was hypothesised that the change in current due to varying resistance is proportional
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Figure 11: Saturation of results when resistance was not varied in the circuit
to the magnetic field detected. Regardless, the declining trend of a reduced EMF as resistance is increased of the theoretical and practical results are very similar in Figures 3 and 4.
5.2 Standard
The experimental results obtained from the standard experiment did prove the hypothesis: ’the induced voltage potential within the solenoid will increase, as the velocity of the magnet increases’ to be correct. The hypothesis was made according to the velocity equation and Faraday’s law:
v = x − x0 ∆t
EMF =−N∆Φ ∆t
In the above formulas, the change in time is inversely proportional to the both the the velocity and the EMF. Thus, as the time decreases, both the velocity and the EMF should be increasing theoretically. So the experimental results should prove that as velocity increases, the EMF induced should increase accordingly.
Within the standard experiment there were two variables measured: the velocity of the mag- net and the induced potential within the solenoid. The initial method measured the velocity of the magnet with a motion detector, which was set up parallel to the Perspex rod. The motion detector gave inaccurate measurements of the magnet’s velocity. This is a result of the mechanics of the motion detector such that it emitted sound and hit the ends of the perspex rod instead of the magnet. Hence measuring the velocity of the rod instead.
By recalling the fundamental formulas of physics, the velocity of the magnet instead calculated
using the formula:
v = x − x0 ∆t
Whereby, the velocity of the magnet was calculated to be the length of the perspex rod over the time the magnet took to travel this length. The length of the perspex rod was measured with a ruler represented in millimeters, minimising uncertainty to 0.05cm. The time was recorded on LabQuest when measuring EMF to prevent human reaction errors with a stopwatch. The velocity was altered by changing the angle of elevation of the perspex rod. As a result, uncertainties of the velocities were between ±4.2% – ±17.6%depending on the angle.
The results were graphed as potential voltage vs. time, with results recorded at angles 40, 50 and 60 degrees. The results in Figure 7 were very similar such that when the magnet entered the solenoid, voltage increased as EMF was induced. When the magnet was inside the solenoid the voltage returned to its equilibrium state, however when it exits the solenoid the voltage potential increased in the negative direction with the same magnitude as in the positive direction. This produced a graph similar to a sine curve.
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This is due to the direction of magnetic field lines of the magnet, hence causing the solenoid to experience a changing magnetic field as it slides through it. When the magnet has fully exited the solenoid, the voltage goes returns to its equilibrium position.
According to the results graph in Figure 5, the voltage within the solenoid increased, as the velocity of the magnet was increased by altering the angle of elevation. The average velocity for the perspective angles 40, 50 and 60 degrees is 0.0996m/s, 0.362 m/s, and 0.455m/s. From the measurements on LabQuest, the average voltages for the perspective angles 40, 50 and 60 according to the graphs produced is 0.107 ± 0.012V, 0.187 ± 0.020V and 0.275 ± 0.014V .The experimental results validate Faraday’s law “the induced EMF is proportional to the rate of change of magnetic flux through the coil”. This can be mathematically expressed as:
EMF αN∆Φ ∆t
The equation shows that the EMF induced within the solenoid is proportional to the rate of change in magnetic flux. This thus proves the proportionality of velocity and EMF produced and hence our result satisfies the equation.
5.3 Extended
The extended experiment explores Lenz’s hypothesis of electromagnetic induction: “a changing magnetic field will affect the relative motion of a spring by producing opposing EMF.” In this experiment, the time it takes for the spring to stop oscillating was measured while the number of coils were controlled. This experiment was conducted at a range of varying currents to further investigate the proportionality of EMF produced to the change in magnetic field (Faraday’s Law); as well as explaining the negative sign in Lenz’s formula.
EMF =−N∆Φ ∆t
The results were predicted to show a trend, such that an increase in current would have a smaller amount of time on slowing down the oscillation of the spring to a stop. This can be explained through Lenz’s law and Faraday’s equation.
When a current is applied from the power pack to the solenoid, it creates an uniform magnetic field through the solenoid. This magnetic field is disturbed when the metal from the spring is oscillates near it with close proximity. Whereby the change in magnetic field due to a relative motion between the spring and solenoid will cause for an induction of EMF to oppose this relative motion. Consequently counteracting the springs oscillating motion and forcing it to slow down to a stop. Thus, supporting Lenz’s law of how the direction of the EMF induced in a solenoid opposes the relative motion of the source disturbing it’s magnetic field. This also satisfies the law of conservation of energy.
The strength of the EMF induced is proportional to the change in magnetic flux, hence EMF should increase when there is an increase in the input current. Therefore the increase in current influences the strength of the magnetic field. This makes the change in flux to be greater, produc- ing more EMF to oppose the springs motion. Therefore the time measured for the spring to come to a rest decreases with increasing current.
The strength of the EMF induced is proportional to the change in magnetic flux, shown in the EMF equation below, hence EMF should increase when there is an increase in the input current. Linking this to Amperes law, we have that magnetic field is proportional to current. Hence the increase in current means there is an increase in magnetic field and therefore the change in flux from a certain area would increase. From Faraday’s law a change in flux means an EMF will be induced.
∆φ = ∆βA
B ds = μ0I
Therefore the increase in current influences the strength of the magnetic field. This makes the change in flux to be greater, producing more EMF to oppose the springs motion faster. Hence the time measured for the spring to come to a rest decreases with increasing current.
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If time was permitted, the experiment would have been revised so that the solenoid will be attached to the voltage probe and LabQuest. This would produce expected results in a visual manner and comparisons can be easily made. The expected graph of the EMF produced in the solenoid should look similar to Figure 9, where the polarity of the EMF changes to oppose motion. Due to the nature of the spring to stop oscillating, the the magnitude of the voltage potential should slowly oscillate to zeroes depicted in Figure 10.
Figure 12: The opposing nature of EMF, hence describing Lenz’s law
6 Conclusion:
In conclusion, Faraday and Lenz’s law of electromagnetic induction, as well as related formulas: magnetic flux, Ohm’s law and Amperes, was explored through the revision of Faraday’s ”moving magnet experiment” as well as the creative write-up of the extended experiment. It has deepened the understanding of the basics of Faraday’s hypothesis on the induction of EMF and its relation- ship to current, time and no. of turns on a coil.
Furthermore, the extended experiment embraces all the theoretical elements supported by the standard and basic experiment with the addition of Lenz’s law and formula.
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7 References: References
[1] Anon. Chapter 10 faraday’s law of induction. url = http://staff.ustc.edu.cn/ bjye/em/mit-7- 1.pdf.
[2] Anon. Physics reference. url = http://physics-ref.blogspot.com/2014/11/physics-9702-doubts- help-page-20.html.
[3] NDT Resource Center. Experiments to demonstrate lenz’s law. url = https://www.nde- ed.org/teachingresources/ndttips/lenzlaw.htm.
[4] David Halliday and Robert Resnick. The fundamentals of physics, 10th edition. pg.848-850.
[5] Robert Kingman, S. Clark Rowland, and Sabin Popescu. An experimental observation of faraday’s law of induction. url = https://physlab.lums.edu.pk/images/3/33/faraday2.pdf.
[6] Clil Lesson. Faraday laws of electromagnetic induction. url = https://www.liceocutelli.it/attachments/article/338/lesson-faraday.
8 Acknowledgements:
Group Induction Kit 8 would like to thank all of the physics tutors in the physics lab: Thursday 12-2pm. Group Induction 8 would also like to thank each member for completing their required tasks to produce this project.