An Investigation of the Relationship Between Current in an Electromagnet vs Force of Repulsion
Physics Internal Assessment
By Paige Lawton
Research Question: How does the current flowing through an electromagnet affect the force of repulsion?
Introduction | Method | Data | Conclusion | Evaluation | Links | Bibliography | Return to Research
For as long as I can remember, I have been fascinated by computers. I have always been curious about how the components work and what allows each part to function. Participating in IB Physics has given me the opportunity to research further into this area. It has provided me with the necessary tools to understand and explore my curiosities. Through more research, I have learned that electromagnets play a huge role in making computers function. Electromagnets are everywhere in computers from hard disk drives to cooling fans. Electromagnets allow hard disk drives to process data because they can reverse their polarity by changing the direction of their current. Hard disk drives read data in 0s and 1s and magnets can easily represent these values with north and south poles. The computer circuit can tell if there is a current flowing and can process data accordingly. Electromagnets have been useful for as long as they have been around.
The first electromagnet was invented in 1825 by British electrical engineer, William Sturgeon. An electromagnet is a piece of metal wrapped with a coil around itself many times. Sturgeon loosely wrapped a coil around a horseshoe-shaped piece of iron and ran a current through the coils to magnetize the electromagnet. He controlled the electromagnet’s strength by regulating the electrical current he would allow to flow through the coil. Without the addition of the electrical current, the electromagnet would not be magnetized. Introducing the current produces a magnetic field around the coil, thus magnetizing the metal core.
One
big discovery in the world of magnetism was Ampere’s Law, which states that
when you have a current, there will be a magnetic field that encircles the
current. That magnetic field multiplied by the length of the circulation is
proportional to the current flowing. Ampere’s Law provides a way to calculate
the relationship between magnetic fields and electric currents. You can
determine the magnetic field that is produced from an electric current flowing
through a wire by using his equation: 
In a uniform magnetic field there is no repulsion because both poles will feel the same magnetic force in opposite directions since their charges are also opposite. Magnets only repel when there is a gradient in the magnetic field. When there is a non-uniform magnetic field, such as one with two magnets, the pole experiencing the larger magnetic field will experience a larger force and it will, in turn, have a net force. If the magnets are oppositely aligned, then one magnet will be repelled by the higher magnetic field.
A solenoid is a specific type of electromagnetic that has an iron core and creates a controlled and uniform magnetic field. The direction of the current determines the direction of the magnetic field within the solenoid. A solenoid essentially acts as a permanent magnet, a magnet that holds its magnetic properties without a current, that can be turned on and off. The core of a solenoid usually has two components two it, the stationary core and the moveable core. If the solenoid did not have a core, it would just be a standard electromagnet.
The purpose of this investigation is to determine the relationship, if any, between an electromagnet’s current and its force of repulsion. Current is defined as a stream of electrons flowing through the magnet and repulsion is the force at which the magnets repel each other. The current(A) will be the independent variable in this experiment. The force of repulsion(N) is the dependent variable as it is dependent on the current(A). The controlled variable in the experiment is the distance between the electromagnet and the fixed magnets.
Hypothesis:
I believe that as more current(A) is flowing through the electromagnet the force of repulsion will also increase because as more current(A) flows through the wire the magnetic field becomes stronger. With a higher gradient in the magnetic field the electromagnet is stronger. A stronger magnetic field means a larger force of repulsion. This relationship will portray itself in a linear fashion on a graph as the two variables should have a positive correlation.
Materials:
A solenoid was used as the electromagnet and was held above the fixed magnets by a buret clamp. Two permanent magnets were the magnets being repelled. A triple beam balance was used to measure the force of repulsion. An ammeter, not pictured in the diagram, was used to measure the current(A) through the solenoid.
Diagram:
Method: Top
In order to gather the most accurate data possible, I followed the same procedure for every data point I recorded. Before I started each trial I began by making sure my experiment had not been altered from its original set up and that the distance between the solenoid and the fixed magnets had not changed. I then turned on the ammeter and set the current(A) to my first value of 0.250A. Next, I used the triple beam balance to measure the mass, by moving the sliding weights along the beams until it was balanced. After measuring the mass, I recorded it in my datatable. Once the data point was recorded, I increased the current(A) on the ammeter by 0.250A for the next variation and followed the same procedure I used to gather the previous data point. Each trial consisted of 20 variations ranging from 0.250A to 5.00A increasing by 0.250A each data point. I conducted three trials using the same values in each trial. By going up by 0.250A I was able to get a substantial amount of data for each trial without surpassing too high of a current(A). If the current(A) were to exceed 5.00A the solenoid would become too hot to continue the experiment. By conducting three trials I was able to gather a sufficient amount of data and could confidently compare the results of the trials to come to a solid conclusion.
Risk Assessment:
There are no major risks within this experiment other than the heat that is generated from the electromagnet at the higher currents(A). Keeping a good distance between the electromagnet can help ensure safety and prevent one from burning themself. Allowing the electromagnet to cool between trials also offers a safer execution of the experiment. Overall, there are no ethical or environmental issues with this experiment.
Data and Analysis: Top
Table 1: Raw data illustrating current(A) and recorded mass(g) values.
|
Current(A) |
Mass(g) |
||||
|
+/- .005 |
grams |
||||
|
Amps |
Trial 1 |
Trial 2 |
Trial 3 |
Average |
Uncertainty |
|
0.00 |
28.0 |
28.0 |
28.0 |
28.0 |
+/- 0.00 |
|
0.250 |
28.3 |
28.2 |
28.3 |
28.3 |
+/- 0.05 |
|
0.500 |
28.6 |
28.6 |
28.8 |
28.7 |
+/- 0.10 |
|
0.750 |
28.9 |
29.1 |
29.1 |
29.0 |
+/- 0.10 |
|
1.00 |
29.4 |
29.6 |
29.5 |
29.5 |
+/- 0.10 |
|
1.25 |
29.8 |
30.0 |
30.0 |
29.9 |
+/- 0.10 |
|
1.50 |
30.3 |
30.2 |
30.4 |
30.3 |
+/- 0.10 |
|
1.75 |
30.6 |
30.7 |
30.7 |
30.7 |
+/- 0.05 |
|
2.00 |
31.0 |
31.1 |
31.1 |
31.1 |
+/- 0.05 |
|
2.25 |
31.4 |
31.6 |
31.6 |
31.5 |
+/- 0.10 |
|
2.50 |
31.8 |
31.9 |
32.0 |
31.9 |
+/- 0.10 |
|
2.75 |
32.3 |
32.2 |
32.4 |
32.3 |
+/- 0.10 |
|
3.00 |
32.6 |
32.7 |
32.8 |
32.7 |
+/- 0.10 |
|
3.25 |
33.0 |
33.1 |
33.0 |
33.0 |
+/- 0.05 |
|
3.50 |
33.4 |
33.6 |
33.6 |
33.5 |
+/- 0.10 |
|
3.75 |
33.8 |
34.0 |
34.1 |
34.0 |
+/- 0.15 |
|
4.00 |
34.2 |
34.4 |
34.4 |
34.3 |
+/- 0.10 |
|
4.25 |
34.6 |
34.7 |
34.7 |
34.7 |
+/- 0.05 |
|
4.50 |
35.1 |
35.1 |
35.2 |
35.1 |
+/- 0.05 |
|
4.75 |
35.6 |
35.5 |
35.7 |
35.6 |
+/- 0.10 |
|
5.00 |
36.5 |
36.0 |
36.2 |
36.2 |
+/- 0.25 |
Data file: Text
Data Processing:
Once all the data from the three trials is gathered, each variation is averaged. To calculate the average of one variation, calculate the sum of all three trials and divide that by the number of trials.
Average of one variation:
Then subtract the mass of the two fixed magnets with no current(A) flowing from the averaged mass. This ensures the calculations are the increase in force, not just the force. Subtracting the initial mass acts as a zero error. The initial mass of the two fixed magnets was 28.0g.
Measured mass minus initial mass:
= 1.50g
The dependent variable was measured in grams because a triple beam balance was used to gather the measurements. In order to accurately evaluate the data, convert each averaged data point into force of repulsion(N). The averaged apparent increase of mass, due to the repulsion, was divided by 1000 to convert it to kg. Once the mass was converted to kg, use F=mg to convert it to force: F is equal to force, m is equal to the mass, and g is equal to the gravitational acceleration of the planet the experiment was conducted on. On earth, the gravitational acceleration constant is 9.81 ms-2.
Mass (g) converted to Mass (kg):
Take this value and multiply it by Earth’s gravitational acceleration constant.
Mass (kg) converted to Force (N):
0.0015kg
9.81
-1
= 0.0147N
This same process of averaging, subtracting the initial mass, and converting the data to Newtons was repeated for each variation.
Table 2: Current(A) vs. Force (N)
This table represents all of the fully processed data points from all three trials.
|
Current(A) +/- .005 |
Force (N) |
Uncertainty |
|
0.00 |
0.00 |
+/- 0.00 |
|
0.25 |
0.0026 |
+/- 4.91*10-4 |
|
0.50 |
0.0065 |
+/- 9.81*10-4 |
|
0.75 |
0.0101 |
+/- 9.81*10-4 |
|
1.00 |
0.0147 |
+/- 9.81*10-4 |
|
1.25 |
0.0190 |
+/- 9.81*10-4 |
|
1.50 |
0.0226 |
+/- 9.81*10-4 |
|
1.75 |
0.0262 |
+/- 4.91*10-4 |
|
2.00 |
0.0301 |
+/- 4.91*10-4 |
|
2.25 |
0.0347 |
+/- 9.81*10-4 |
|
2.50 |
0.0383 |
+/- 9.81*10-4 |
|
2.75 |
0.0422 |
+/- 9.81*10-4 |
|
3.00 |
0.0461 |
+/- 9.81*10-4 |
|
3.25 |
0.0494 |
+/- 4.91*10-4 |
|
3.50 |
0.0543 |
+/- 9.81*10-4 |
|
3.75 |
0.0585 |
+/- 1.47*10-3 |
|
4.00 |
0.0621 |
+/- 9.81*10-4 |
|
4.25 |
0.0654 |
+/- 4.91*10-4 |
|
4.50 |
0.0700 |
+/- 4.91*10-4 |
|
4.75 |
0.0746 |
+/- 9.81*10-4 |
|
5.00 |
0.0808 |
+/- 2.45*10-3 |
The uncertainty of the force(N) is the uncertainty of the trials in grams converted to force(N).
Graph 1: Using the data in Table 2, this graph Force(N) vs Current(A) can be charted.
Each data point has individually calculated error bars. To calculate an error bar, take the maximum value for a variation and subtract the minimum value in that same variation. Since the initial data is in grams, converting the difference to Newtons is needed. In order to convert to Newtons, the same steps from the prior data processing were followed.
Error bar calculation for one variation:
29.6g - 29.4g = 0.200g
Converting the
Difference:
(0.200g / 1000) * 9.81Nk
-1 =
0.001962N
These steps were followed for each variation of the data.
The slope of the line of best fit is calculated through the graphing program, but the uncertainty of the slope must be manually calculated. To calculate the uncertainty, both a steepest possible line and a least steep line were drawn on the graph; these lines go through all of the error bars of the data. The slopes of these lines were calculated, the difference of the two slopes was found, and then divided by 2 to calculate the uncertainty.
Maximum and Minimum Slope Values:
Maximum: 
Minimum: 
0.0153
Slope Uncertainty: 
0
Line of Best fit slope = 0.0159 +/- .000450
Conclusion: Top
The purpose of this experiment was to determine the relationship, if any, between the current flowing through an electromagnet and its force of repulsion. The data gathered clearly supports my hypothesis, increasing the current in the solenoid resulted in an increase in force. This repulsion is due to the gradient in the magnetic field:
In the diagram above, the blue curve represents the magnetic field due to the coil, pictured on the left. On the right is the permanent magnet I used to generate a repulsive force. The magnetic field is stronger closer to the coil and weaker further away.
The north side of the permanent magnet is closer to the coil and so it is being repelled quite strongly. Whereas, the south pole being farther away is in a weaker magnetic field and is therefore being attracted with less force. So the net overall force is that of repulsion. This force of repulsion was my dependent variable.
The force of repulsion is increasing with more current(A) because the gradient in the magnetic field is also increasing:
The graph on the left represents less current and the graph on the right represents more.
With less current there is less of a field difference from one end of the magnet to the other, so therefore less repulsive force. When the current is more, the gradient increases also widening the disparity between repulsive and attractive forces resulting in a greater force of repulsion. Since the gradient of this field increases in proportion to the overall magnitude I would expect it to be a linear relationship.
Evaluation: Top
The use of a triple beam balance to measure the masses provided some level of error in the results. Manually moving the sliding weights provided a level of inaccuracy to the dependent variable data that was gathered. Since the current(A) was increased by only 0.250A each variation, the data points had very small differences. The distance to move the sliding weights was very small each time and quite hard to execute without flaw. In order to counteract this, doing more trials would be able to help eliminate this source of error. In addition to more trials, a digital scale would be a very precise option. If the distance could remain constant, a digital scale would eliminate the possible human error that comes with moving the sliding weights. The small increase in current(A) would not be an issue for the digital scale as it would have no issue with changing the reading by a small amount.
Another flaw in the method of this experiment was the inconsistency of the ammeter’s readings. Once the current(A) was set for one variation, the reading would fluctuate around the set current(A). This inconsistency in current(A), while minimal, can definitely affect the accuracy of the data gathered. Since a triple beam balance was used, the mass was not immediately found. The sliding weights needed to be adjusted to the new current(A) and this can take up to a minute with the fluctuating current(A) and tediousness of the minimal increase in mass. During this time, the current(A) would deviate from the intended current by as much as +/-0.100(A). This value is almost half of 0.250A, the difference between each variation, which poses a significant source of error in the data. To counteract this fluctuation, more trials would need to be done. With more trials the impact of errors is minimized because the more times you collect data, the closer the average is to the true value. More trials allow more confidence in the results of the data when supporting or not supporting a hypothesis.
The temperature of the solenoid also played a role in the accuracy of the results. As the current(A) flowing through the solenoid reached around 4.00A, the temperature of the solenoid began to increase rather quickly. The solenoid reached high enough temperatures to produce a burning aroma in the area where the experiment was conducted. To create a safer environment while gathering data of higher currents(A), the flow of the current was stopped in between the variations 4.00A and 5.00A for 1-5 minutes to allow the solenoid to cool down to a reasonable temperature. This definitely could have caused discrepancies in the data as the current flowing was not a constant current throughout the entire experiment. To counteract this error, using a solenoid with more windings of coil would allow more current(A) to flow through the coil without the temperature getting too high. With more windings, there is more wire for the current(A) to flow through allowing the solenoid to stay cooler longer. However, even when using a solenoid that could withstand more current, allowing the solenoid to cool down between each trial would be a great preventative measure to ensure that it does not overheat.
Further Research Suggestion:
If I were to perform this experiment again, it would be interesting to see how different the results would be with more precise instruments and minimizing the sources of error. In addition to doing the same experiment again, having different distances between the solenoid and the permanent magnets and analyzing the effect of distance on the force would be a fun twist on the experiment. With my extended knowledge of the results of this experiment, being able to see the effect that distance has on the force of repulsion would be fascinating and give me more insight into magnetic fields on a greater scale. While I’m not quite sure how I could conduct an experiment involving electromagnets and computers, that would be a very fun experiment to conduct. Combining my love for physics and computers would be the best of both worlds.
Links: Top
https://www.thoughtco.com/who-invented-the-electromagnet-1991678 - This website talks about the invention of the first electromagnet.
https://science.howstuffworks.com/electromagnet.htm#:~:text=Electromagnets%20create%20a%20magnetic%20field,it%20were%20a%20permanent%20magnet – This website has great background on electromagnets and how they work.
https://qmagnets.com/magnetic-field-gradients/#:~:text=Magnetic%20field%20gradients%20are%20the,or%20Sodium%20ions%20(Na%2B). – This website explains magnetic field gradients.
https://www.physicsclassroom.com/class/estatics/Lesson-3/Coulomb-s-Law - This website gives background information on forces.
https://www.britannica.com/science/magnetism/Repulsion-or-attraction-between-two-magnetic-dipoles - This website explains repulsive and attractive forces between magnetic dipoles.
Bibliography: Top
Bellis, Mary. “William Sturgeon and the Invention of the Electromagnet.” ThoughtCo, ThoughtCo, 23 Feb. 2019, https://www.thoughtco.com/who-invented-the-electromagnet-1991678.
Brain, Marshall, and Chris Pollette. “How Electromagnets Work.” HowStuffWorks Science, HowStuffWorks, 7 Sept. 2021, https://science.howstuffworks.com/electromagnet.htm#:~:text=Electromagnets%20create%20a%20magnetic%20field,it%20were%20a%20permanent%20magnet.
C, Andrew. “Do Electromagnets Get Hot? (and How to Cool It?) [2022].” Simply Magnet, Simply Magnet, 11 Feb. 2021, https://simplymagnet.com/do-electromagnets-get-hot/.
“Electromagnet Invented 1825 by William Sturgeon.” Intriguing History, Intriguing History, 4 Mar. 2015, https://intriguing-history.com/1825-invention-of-the-electromagnet/.
Kopot, Andrey. “Ampere's Law.” Aklectures.com, Ak Lectures, 12 Dec. 2013, https://aklectures.com/lecture/ampere's-law-biot-savart-law-and-solenoids/amperes-law.
Suckling, Eustace E. “Ferromagnetism.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 28 July 2016, https://www.britannica.com/science/magnetism/Ferromagnetism.