Investigating Factors Affecting the Sources of Magnetic Field Using Current in Solenoids and Magnets John Paul Jacosalem, Alyssa Lipura, Min-Roselle Malunhao and Juan Miguel Salonga National Institute of Physics, University of the Philippines, Diliman, Quezon City
Abstract Magnetism has many applications in real life such as in health care, communication and transportation. Magnetism is best described by magnetic fields. In this experiment, we investigate the sources of magnetic fields using coils of current-carrying wires called solenoid attached to a power supply. By comparing a set of varying currents (I) and turns per unit length (n) of the solenoid, we observed its relationship to the magnetic field strength as directly proportional and expressed in the equation: B= μnI = μ(N/L)
(1)
In order to visualize magnetic field and its direction, we put different configurations of magnet bars on the surface of field pattern windows and 3D field tracer.
I. Introduction Magnetic fields in general as a force created by permanent magnet that pulls ferromagnetic materials such as iron and attract/repel other magnet like for example of is the earth’s own magnetic field used in navigation. It is the magnetic influence of electric currents and magnetic materials. Magnetic fields are produced by moving electric charges and intrinsic magnetic moments of elementary particles. However, we are only interested in the movement of charges as a source of magnetic field. Theoretically, a single loop of wire carrying current produces a magnetic field. These loops forms a coil therefore can be considered similar to a bar magnet. When an electric current I flows through a wire, a magnetic field is produced around the wire. As the wire is formed into a loop, the magnetic field near the center is perpendicular to the plane of the loop. As the number of turns, N, of the loop increases, the magnetic field at the center also increases. To produce a strong and uniform magnetic field, we choose the solenoid, a wire tightly wound into a helix of closely spaced turns. It is then produced in the region surrounded by its loops. Magnetic field generated by a solenoid of length and number of turns is dependent on the number of turns per unit length , the permeability of the core material , and the current I flowing through the wire of the solenoid. It is given by the equation, (1) The value of u becomes =4.7 *10-7 T*m/A if the core material inside the solenoid is vacuum. As for this experiment, permeability of free space of air = o is used. The experiment was performed using current carrying solenoid measuring the magnetic field produced using a magnetic field sensor. Also, in this experiment we establish the relationship between the magnetic field due to a solenoid, the current passing through the solenoid and the number of turns per meter of the solenoid using graphical analysis given by the equation, to calculate the value of the permeability of free space , and map the magnetic field of a bar magnet and combination.
II. Methodology The experiment was divided into four parts; magnetic field inside a solenoid, relationship between magnetic field and current, relationship between magnetic field and spacing of turns, and mapping of magnetic field of a bar magnet and combinations of bar magnet. The experimental set-up is shown in Figure 1 where a DC power supply was connected to each end of the slinky that was attached to a meter stick, creating a closed circuit. The connectors were formed like a rectangle because the wire carries magnetic field as well and could change the magnetic field on the edges of the solenoid. It was set up at least 0.25 m away from the power supply to keep the magnetic field induced by the currents of these devices from interfering. The LabQuest was then set up to a duration of 0 s to 10 s in the Meter screen and Duration field. The magnetic field sensor, switched at 6.4mT was connected to the LabQuest and then inserted at the midlength of the solenoid between the turns to get the average magnetic field on the whole length and the center of the 1
circular cross section to get the highest magnetic field. To know which direction the sensor would point, we set up to calibrate the Labquest, turned the power supply on at steady current of 2.0A and Collect. The direction wherein it gave the most positive magnetic field reading was the orientation used for the whole experiment.
Figure 1: Photo of actual set-up used showing the slinky stretched to half a meter with the magnetic field sensor inserted between the turns and in the center of slinky. After the we finished the setup for the experiment, we start by turning off the power supply. While the power supply is off, the set the LabQuest to Zero, went to Graph Screen and pressed Collect button. After 5 seconds, we switched the power supply on and waited another 5 seconds then turned it off. The mean of the portion of the graph where the power supply was on, was then given by the LabQuest. We repeated this steps to get the mean magnetic field for different values of I by adjusting the current value on the power supply as shown in Table 1 . With this, we got the relationship between the magnetic field and current. We used the same setup for the second experiment by changing the length of the slinky however with the current steady at 1.5A. With the increments of 0.25m, the length of the slinky was adjusted and the magnetic field sensor was placed in the middle of the length. To complete the table, we measure the number of turns in the solenoid and recorded it in completion of Table W2. Magnetic field was then measure using the same procedure with varying length and turns. With the use of a field pattern window and a magnetic field model, the form of magnetic field lines for different configurations of bar magnets was mapped. The different configurations were given as: a) a single bar magnet, b) two bar magnets connected end to end, and c) two bar magnets repelling each other due to the south poles close to each other. Also, the field lines within and outside the current-carrying solenoid were traced using a 3D field tracer. The magnetic field sensor was not inserted into the solenoid when the field lines were traced.
III. Results & Discussion These are the completed data gathered from the experiment. Table 1 shows the magnetic field in mT gathered with increasing values of current in 0.5 increments and constant number of turns of 78. Table 1: Magnetic field strength with respect to the current
0.5
0.0536
1.0
0.0953
1.5
0.139
2.0
0.2139
2.5
0.2548
From the data above, we plot the graph showing the relationship between magnetic field strength and current .We set the x-axis to be the current, and magnetic field strength in y-axis to show magnetic field strength as
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a function of current as shown in Figure 2 below. On the graph below was the best fit line and it’s equation in the form of . We got the equation to be .
Figure 2: Graph of Magnetic Field Strength
as a function of current including equation of the best fit line.
The shape of the plot in Figure 3 is an increasing straight line, which shows positive linear relationship between the magnetic field and the current through the solenoid. As the current passing through the solenoid increases, the strength of the magnetic field induced also increases. We plotted the data points and determined the best-fit line that would represent this relationship. The regression value of the best fit line is equal to 0.9884, which is a good indication that the linear relationship is well-represented, while the equation of the best fit line is given by Comparing this to the equation of magnetic field strength versus current through a solenoid given by equation (1) above, where μ is the permeability of the material inside the solenoid and n is the number of turns per unit length, we can say that the coefficient of the current I in Equation (1) equal to μ(N/L), is represented by the slope of the best-fit line. The y-intercept of the best-fit line should be close to zero since Equation 1 suggests that a zero value of current would result to zero magnetic field strength, and would only account for the experimental deviation. Data recorded on Table 2 below shows the number of turns , in terms of mT, and turns per unit length depending on the value of length with increments of 0.25 m and steady current of 1.5 A. Table 2: Magnetic field strength with respect to the number of turns per unit length. Length, (m)
Number of turns,
(mT)
Turns per unit length, (m-1)
0.25
78
0.5858
312
0.5
78
0.3065
156
0.75
78
0.220
104
1.0
78
0.1454
78
1.25
78
0.1227
62.4
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Figure 3: Graph of magnetic field strength as a function of turns per unit length The shape of the plot in Figure 3 is also an increasing straight line, which indicates positive linear relationship between the magnetic field and the number of turns per unit length of the solenoid. This means that an increase in the number of turns in a unit length of solenoid would increase the magnetic field strength. The regression value of the best-fit line is equal to 0.995, which indicates a well-represented linear relationship. The equation of the best-fit line is given by y = 0.001x + 0.012. Comparing this to Equation (1), we can see that the coefficient of the unit number of turns equal to μI is represented by the slope of the best-fit line. Again, the yintercept of the best-fit line is close to zero as it only accounts for the experimental deviation. Given the equations of the best-fit line, we get the slope of each line in Figures 2 and 3 to be and respectively. We, therefore we calculate for the experimental given the two equations; 1) and 2) , and got; 1) 1.33e-6 and 2) 6.67e-7 respectively. Compared to the theoretical value of , it is close however with a very large percent deviation of 6% to 47% which is not acceptable.
Figure 4: Images of magnetic field lines of a large bar magnet (left) and a slinky (right) As seen from Figure 4, the bar magnet and the slinky exhibited similar magnetic field lines. Although the slinky produces a magnetic field around each loop, magnetic field lines never intersect. They instead interact with each other and produce a net magnetic field that resembles the magnetic field lines in a bar magnet.
Figure 5: Images of magnetic field lines of two small bar magnets aligned at North and South (left) and South to South (right)
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From Figure 5, we can see that the magnetic field lines always point from North to South. When the magnets are aligned at North and South, the magnetic field lines point from the inner North towards the inner South, resulting in the two magnets becoming attracted to each other. The South to South set-up on the other hand, produces magnetic field lines that go from the respective Norths of the magnet to the South, but never from the two South sides of the magnets facing each other. This results to the magnets in the configuration repelling each other.
III. Conclusion Based from the experiment conducted, we were able to investigate how magnetic fields are produced in solenoids, the factors that affected the magnetic field and how magnetic fields interact with other magnetic fields. We were able to show that currents produced magnetic fields due to the electrons moving and generating a net magnetic field. Knowing this, increasing the amount of electrons, therefore increasing the current, will also increase the net magnetic field generated. This was shown when we determined the linear relationship between the current and the magnetic field as shown in Figure 2. Passing a current through the wire shaped in a loop produced a magnetic field that can be determined using the right hand rule. Putting many loops together resembles the slinky, and becomes a solenoid when current is passed through it. Since magnetic fields are vectors, each magnetic field generated by a loop will interact with each other and eventually create a net magnetic field. The relationship between the turns or number of loops and the magnetic field created is linear as shown in Figure 3. Lastly, magnetic field lines interact with other magnetic field lines, causing either attraction or repulsion. Using the different magnet set-ups, we were able to see that first, magnetic field lines pointed away from North and towards the South. Similar to this, set-ups involving two or more magnets will show different interaction of different magnetic fields. Magnetic field lines can be used to determine whether there will be attraction or repulsion.
References [1] H. Young, R. Freedman, F. Lewis, “Magnetic Field and Magnetic Forces”, University Physics, 12th ed., Pearson Education South Asia PTE. LTD., Philippines (2009), pp. 916-917. [2] H. Young, R. Freedman, F. Lewis, “Sources of Magnetic Field”, University Physics, 12 th ed., Pearson Education South Asia PTE. LTD., Philippines (2009), pp. 976-977. [3] Experiment 4, Sources of Magnetic Field, @2014 Lab manual authors
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