Electromagnetic Induction: Changes in Magnetic Flux Coursework

Introduction

This report describes an experiment conducted to test the effect of electromagnetic induction. More specifically, it tests whether the change in magnetic flux caused by the change in relative speed of the ordinary magnet towards the coil of copper wire results in the change of the direct current generated in the wire. Changes in the amount of current are measured using a sensitive multimeter at the moment when the magnet passes within the coil at different speeds and recorded by a digital camera for precision.

Electromagnetic induction is a process in which a dynamic interaction of a magnetic field and an electrical conductor produces an electromotive force. Several types of interaction, collectively described as a change in magnetic flux, result in the generation of the current. The most common ones include the change in the position of the conductor relative to the source of the magnetic field and the change in the power of the field. The latter served as a basis for the discovery of the phenomenon by Michael Faraday, who noticed the relationship between the change in the readings of galvanometer and the process of connecting and disconnecting an electromagnet to a power source (Hammond 233). The process was later mathematically described by Maxwell as Faraday’s law of induction via the following formula:

ℰ

Here, ℰ is an amount of electromotive force generated in the coil, N is a number of loops in a coil, Φ is the amount of magnetic flux involved, and t is time. Importantly, the change in the flux can be created mechanically rather than electrically, with faster movement resulting in greater voltages.

Literature Review

Electromagnetic induction was discovered by Michael Faraday in 1831 (Hammond 233). By that time it was established that a coil carrying an electric current could generate a magnetic field. Faraday hypothesized that the opposite process is possible, i.e. it is possible to generate an electric current by placing a coil within the magnetic field. He soon observed that such process indeed takes place, but only under the condition of a changing magnetic field, the phenomenon termed magnetic flux. The initial experiment established the presence of a current generated in the moment of connection of a power source to the coil, and another manifestation during the moment of disconnection. Soon other conditions were discovered under which the current could be generated. First, the magnitude of the current directly depended on the strength of the magnetic field. Second, a direct relation was observed between the generated voltage and the speed at which the magnetic field moved either towards or away from the coil. Since all of the described effects can be attributed to the change in magnetic flux, the generated voltage is proportional to the rate of change of the flux (Sahay 61).

It was later discovered that the induced current could generate additional magnetic flux in the coil which is opposite to change in external flux. This dependence, known as Lenz’s law, can be used to determine the direction of the current or, conversely, the direction in which the flux is changing relative to the coil (i.e. the direction in which a magnet passes through it) (Bakshi and Bakshi 3-8).

Relevance of the Experiment

Since its introduction, the principle of magnetic induction found a wide range of applications. Most notably, the premise behind the generation of a current via moving a magnet relative to the coil is a central principle in the construction of electric generators. In addition, electric transformers utilize the principle of alternations in the flux of the coil to induce the current in a second coil, situated within reach of the first coil’s magnetic field. It is, therefore, necessary to have a thorough understanding of the phenomenon. First, it will allow me to gain comprehension of the principles behind the function of the relatively widespread technology. Second, it will provide us with potential limitations of the existing technology and enhance the understanding of the external factors which can influence the functionality of the said equipment and necessary safety precautions resulting from them. For instance, can voltage output of a consumer electric transformer be changed in the range of a magnetic field? Are these changes significant enough to create hazards? We surmise that the results of this experiment may illustrate not only the potential risks but also determine the approximate likelihood and magnitude of these events, e.g. the necessity to avoid the presence of magnets in consumer electronics.

Variables

In our experiment, the velocity of the magnet at the moment when it passes through the coil fixed in a constant position is an independent, or experimental, variable. The amount of voltage induced by the change in magnetic flux resulting from the movement of a magnet relative to the coil and measured in volts is a dependent, or response variable. The external variables are the length of the wire as well as the number of loops in the coil, the power of the magnetic field, and the distance traveled by the magnet before the passage through the coil. The first two variables will be controlled by using the same coil and magnet, respectively. The third one will be controlled by using four tubes with predetermined and measured length and a ruler to assure the equal distance between the lower end of the tube and the surface.

Hypothesis

Judging from the work done by Faraday and the overview of the electromagnetic induction effect, the amount of magnetic flux that goes through the loop induces a certain amount of current in the wire (Sahay 58). The amount of current depends on the rate of change in the flux which, in turn, can be changed by altering either the relative speed of the source of the flux towards the coil or the magnitude of the magnetic field (Sahay 58). While the speed cannot be controlled directly using the means available to me, it is expected that the difference in the distance which is traveled by the magnet during the free fall within the tube of measured length results in specific speed correlated to the tube’s height. Based on this information, I hypothesize that by changing the speed of the ordinary magnet at which it passes through the coil I will generate a measurable difference in the amount of the current induced in the process, and that a direct relation will be observed between the independent and dependent variables, i.e. the increase in speed will lead to the respective increase in voltage.

Materials and Methods

To conduct the experiment, I used the following materials:

• 1 digital multimeter with adjustable DC output measuring capability
• 1 digital camera with high recording frame rate of 240 fps to control the results of the observations
• 1 coil of copper wire with 100 loops
• 4 plastic tubes with an outer diameter which allows inserting them into the aperture of the coil and lengths of 25 cm., 50 cm., 100 cm., and 200 cm., respectively.
• 1 ordinary magnet with a diameter that allows passing it through the inner aperture of the plastic tubes
• 1 adjustable stand rod with a vise for fixing the tubes in upright position
• 1 roll of duct tape for fixing the coil on the tubes
• 1 plastic ruler with mm increments

I set up my experiment as follows:

The coil is placed on the table vertically with its loops oriented parallel to the table’s surface.

1. The digital multimeter is connected to the ends of the wire and set in the DC mode with the highest available sensitivity (200 mV.)
2. The camera is positioned on a tripod in front of the multimeter to record the readings of the instrument and set to the highest frame rate (240 fps).
3. The camera is set to record mode.
4. One side of the magnet is marked with an arrow to ensure that it is inserted in the same manner each time, and a line in the middle to eliminate the possible difference in the height of release.
5. The smallest tube (25 cm.) is inserted into the coil’s aperture, positioned vertically, fixed to the tube by the duct tape, and then fixed vertically in the vise of the standing rod.
6. The vise holding the tube with the attached coil is raised 15 cm. above the table’s surface to allow the magnet to be removed after each session without disturbing the installation. The height is measured and controlled using the plastic ruler.
7. The marked side of the magnet is inserted into the upper end of the tube up to the mark in the middle and released.
8. During the fall, the magnet creates a change in magnetic flux which is registered by the multimeter and recorded by the camera.
9. The magnet is retrieved from under the coil, and the procedure is repeated three more times to compensate for the limitations of the measuring equipment (e.g. the inability to remember the highest reading) and eliminate irregularities in the procedure.
10. The tube is unmounted from the vise and the coil is separated from the tube by removing the duct tape. The procedure is performed carefully not to damage the wire or the connection with the measuring equipment.
11. The 20-cm tube is replaced with a 50-cm one, which is fixed to the coil and a standing rod in the same manner. The longer distance traveled by the magnet before it reaches the coil allows it to attain greater velocity and induce a more powerful current in the wire. The procedure (step 6-11) is repeated four times in consistency with the previous session.
12. The procedure (step 6-11) is repeated for a 100-cm. tube with the same amount of repetitions.
13. The procedure (step 6-11) is repeated for a 200-cm. tube with the same amount of repetitions.
14. The video recording is retrieved from the camera and reviewed to obtain the measurements. The high frame rate allows recording the slightest changes in readings. The video is slowed down during the controversial readings and watched frame-by-frame whenever required.

Replication

During each session of the experiment, market by the length of the used tube, the procedure was performed four times. The maximum accuracy of the used multimeter used for measurements was one digit after the decimal point (20 mV considering the selected sensitivity). All of the readings were recorded with the exact same accuracy and averaged to equalize the irregularities and the inertia of the instrument. Table 1 presents the unprocessed data retrieved from the experiment.

Table 1. Readings of the multimeter as shown on the display of the instrument

Since the readings were scaled by the instrument, they were converted to millivolts by multiplying the obtained numbers by 200 and then converted to volts since all measurements were larger than 1000.

Table 2. Measurements obtained during the experiment, V.

Quantitative Analysis

The amount of voltage induced during each session was averaged:

The result was rounded to two digits after the decimal point.

Results

The table and graph below illustrate the results of the experiment. The data indicates that as the height at which the magnet is released in the tube increases, the amount of the voltage induced by the effect of electromagnetic induction is increased respectively. The lowest average reading was 1.53 volts at 20 cm. of traveling distance while the highest reading was 2.78 volts resulting from 120 cm. traveling distance. The direct relationship between the length of the tube determining the distance traveled by the magnet and the resulting voltage is illustrated in the graph below.

Table 3. Average amount of voltage induced by the magnet passing through the coil at different speeds

Conclusion

Based on the results obtained during the experiment it is apparent that there exists a direct relationship between the speed at which the magnet passes within the coil and the amount of voltage induced in the wire as a result of this event. While the experiment did not produce data which would confirm the assumption that the difference in height produced sufficient difference in velocity, the findings are consistent with the hypothesis. Finally, the graph clearly shows the direct relationship between the height of the tube and the amount of generated current, where greater height invariably results in higher amount of voltage. Therefore, my hypothesis is fully confirmed by the experiment. For the most part, the obtained results surpassed my expectations, with one notable exception. First, the change in the voltage produced during different sessions was significant enough to form a distinctive pattern on the graph. This was counterintuitive since the amount of current generated in this way is usually relatively small and may not have registered on the equipment I selected. In addition, the multimeter is poorly suited for registering peak values because it does not have the function of memorizing the results. Fortunately, the camera was helpful in overcoming the latter limitation, and the values obtained during the first three sessions aligned in a characteristic upward curve. The readings from the fourth session, on the other hand, were visibly less aligned with the trend, which can be seen on the right of the graph. The comparative lack of difference between the voltage generated in the two last sessions can be attributed to two things. First, no preliminary calculations were made that would allow me to conclusively predict the gradual increase in the readings based on the twofold increases between the sizes of tubes. Second, and, perhaps, more important, was the level of accuracy of the multimeter. While the instrument was sensitive enough to register even the lowest readings involved in the experiment, it likely did not have the refresh rate high enough to register rapid changes occurring at the later stages where the magnet passed the coil faster. This suggestion is partially confirmed by the discrepancies within sessions, which on two occasions reached the difference of 0.24 volts. Since no concrete evidence exists to back this explanation, further experimentation may be required to confirm the validity of the dynamics with the help of the more suitable measuring tools (e.g. the oscilloscope).

The obtained results confirm the theoretical basis of the Faraday’s law. Given the assumption about the relationship between the height of the tube and the resulting change in magnetic flux is correct, the results align with the formula

ℰ

The formula suggests that the change in magnetic flux is altered using the increase in relative speed which results in greater electromagnetic force generated. Since these results were observed, the experiment confirms the basic physics principle described above.

The obtained results suggest the possibility of practical application. The most evident one is the use of mechanical energy for generation of electrical energy, creating a concept of an electrical generator. Besides, if the suggested reason for discrepancy between the data obtained in first three sessions and the final session can be confirmed, the effect can be reversed, e.g. it is possible to measure the speed of the object which is a source of magnetic field by measuring the amount of voltage it induces by passing through the loop of known size. Finally, the results offer insights into the risks posed by the effect to the equipment dependent on the power sources which use this principle and exposed to the external influence of magnetic fields. However, before any of the named applications could be developed

However, before such changes can be implemented, several follow-up studies are recommended to enhance the understanding of the issue.

1. Is there a pattern in the relationship between the speed of a magnet with a constant magnetic field and an amount of electromagnetic force generated in the wire which would allow us to predict the voltage for certain speeds prior to the testing procedure?
2. Is the pattern displayed in the graph consistent with any given strength of the object’s magnetic field?
3. How do the number of loops in the coil and the material used for the wire (e.g. steel) influence the obtained readings and the pattern displayed in the graph?

Works Cited

Bakshi, Uday, and Mayuresh Bakshi. Magnetic Circuits and Transformers. Technical Publications, 2008.

Hammond, Percy. Applied Electromagnetism. Elsevier, 2013.

Sahay, Kuldeep. Basic Concepts of Electrical Engineering. New Age International, 2006.