Investigating Magnetic Field and its Relationship with Current and Number of Turns per Meter of the Solenoid Acelar, Hazel, Atienza, Ailyn and San Diego, Annamarie* College of Engineering University of the Philippines, Diliman, Quezon City *Corresponding author:
[email protected]
Abstract The strength of a magnetic field inside a solenoid was measured using a magnetic field sensor. The relationship between magnetic field, current, and spacing of turns in a solenoid was established. By graphical analysis of the experimental data, it was found that magnetic field strength is dependent on the permeability constant of the material, the number of turns per unit length, and the current passing through the wire. The permeability constant was calculated from the slope of the trendline. The magnetic field lines of a solenoid, bar magnet, and combinations of bar magnets were mapped. Through this experiment, quantitative and qualitative descriptions of magnetic field arising from bar magnets and solenoids were obtained.
1. Introduction A magnetic field is defined as the area of influence around a moving charge or a currentcarrying conductor. It is in this region that magnetic forces act on charges in motion. The presence of a magnetic field cannot be confirmed by mere sight or touch, but it can be demonstrated by its effects on certain objects like magnetic metals or currentcarrying coils of wire. Magnetic field is a vector and has SI unit Tesla (T). This experiment focuses on one source of magnetic field—the solenoid. A solenoid consists of a wire wound to form a helix. This configuration allows a uniform magnetic field to be generated in the solenoid's interior. The net magnetic field can then be obtained by the vector sum of the fields arising from all the turns of the wire. Ampere's Law is used to find the magnetic field produced in highly symmetric geometries, which includes the solenoid. In 1825, AndréMarie Ampère established the quantitative relationship between the magnetic field and the electric current that generates it. The general statement of Ampere's Law is that the line integral of the magnetic field around a path is directly proportional to the algebraic sum of the currents enclosed by that path. From this law, an expression to compute for the interior magnetic field of a solenoid can be obtained. The strength of the magnetic field inside a solenoid is given by the equation: B = μ0nI (1) Magnetic field strength can be computed given the current I passing through the wire, permeability of free
space μ0 = 4π × 10 −7T ∙ m/A , and the number of turns per unit length n = N /L where N is the number of turns and L is the length of the wire. The objective of this experiment is to measure the magnetic field inside a solenoid and find out how characteristics of the loop affect field strength. It also aims to qualitatively describe the magnetic field of a bar magnet using field line mapping. The study of magnetic field sources has significant applications to science and technology, as well as other industries. Solenoids are employed for many purposes: from doorbells, to automotives, to medical imaging equipment, to tall cranes used for transporting heavy materials. Measurement of field strength is therefore crucial in creating controlled magnetic fields that will fit for different practical applications.
2. Methodology The materials used for the experiment are: PASCO DC power supply, Vernier magnetic field sensor, Vernier Labquest 2.0, slinky, meter stick, connectors, tape, compass, bar magnets (2 small, 1 big), field pattern window, magnetic field model, and 3D field tracer. The slinky was placed and stretched to about 1 m in length on a meter stick. Tape, a nonconducting material, was used to hold the slinky in place. The Vernier Magnetic Field Sensor was connected to the LabQuest and the switch on the sensor was set to HIGH x200 or 6.4 mT. The slinky was connected to a power supply to form a circuit. The alligator cables and banana plugs used as connectors were kept far from the slinky to avoid interference with measurements, as these devices also create currentinduced magnetic field. The power supply was set to steady current 2.0 A. The sensor was inserted in the center of the slinky. It was rotated as the LabQuest collects data to find the direction of the most positive magnetic field reading. That orientation was used for the rest of the experiment. The power supply was turned off and the meter screen of LabQuest was calibrated to zero.
Figure 1. Experimental setup
Using the Graph Screen, data was collected, then the power supply was turned on for five seconds. The mean for the portion of the graph where the power supply is on was recorded as the magnetic field strength. Using these methods, the magnetic field strength was measured for different current values; 0.5 A, 1.0 A, 1.5 A, 2.0 A, and 2.5 A. The number of turns of the slinky was counted and recorded. Loops that stick together were counted as one. To find the relationship between magnetic field and spacing of turns, the current was fixed to 1.5 A and the length of slinky was varied from 0.25 m to 1.25 m with 0.25 m intervals. For each setup, the number of turns of slinky was counted. The same procedures as before were used for getting their respective magnetic fields. Magnetic field lines of a bar magnet and combinations of bar magnet were mapped using field pattern window. For the slinky stretched to 0.50 m length at a steady current of 2.0 A, 3D field tracer was used.
3. Results and Discussion The data gathered from the experiment were used to establish the relationship between magnetic field and current.
Figure 2. Magnetic field strength vs current through the solenoid
The magnetic field strength vs current graph behaves linearly. The equation of the trendline is y = 0.1034x 0.0107, where y represents magnetic field, x represents current, the yintercept 0.0107 is equal to the value of magnetic field when current is zero, and the slope 0.1034 is the value of μ0n from equation (1). Since n = 85 m−1 , we can deduce that μ0 = 0.1034/85m−1 = 1.22 × 10−3mT ∙ m/A
Figure 3. Magnetic field strength vs number of turns per unit length of solenoid
Similarly, the magnetic field vs number of turns per unit length of solenoid graph is also linear. The equation of the trendline is y = 0.0021x 0.0521, where x represents the number of turns per unit length of solenoid, y represents the magnitude of magnetic field, the yintercept 0.0521 is the magnitude of magnetic field when there are no turns, and the slope 0.0021 is equal to the value of μ0I from equation (1). Since I = 1.5 A, we can deduce that μ0 = 0.0021/1.5A = 1.4 × 10−3mT ∙ m/A . The magnetic field lines of solenoid, bar magnet, and combination of bar magnets were mapped this way:
(a) (b) Figure 4. Sketches of magnetic field lines of (a) large bar magnet (b) slinky
(a) (b) Figure 5. Sketches of magnetic field lines of two small bar magnets aligned and connected at (a) North and South (b) South and South
Based on Figure 4, the direction of magnetic field lines of bar magnet and slinky are the same in terms of the direction and flow of lines. In both cases, field lines flow from North pole to South pole. It is evident on Figure 5 that opposite poles attract and like poles repel.
4. Conclusion From the gathered data and results, the direct relationship that magnetic field has with current and the number of turns per unit length of the solenoid, that is the coil density. The equation B = μ0nI has been proven and is clearly shown by the linear behavior of the graphs of both the magnetic field versus number of turns per unit length of solenoid, and the magnetic field versus the current through the solenoid. This just goes to show that for every increase and decrease in the current and/or the number of turns per unit length, there is a corresponding change in the magnetic field in the same direction, whether increasing or decreasing. Moreover, for the magnetic bars and the combination of such, regardless of the orientation of the magnet, especially for the combination of magnets, the field is always directed away from the North pole and into the South pole. Also, it has been proven through the observation of field lines the opposite poles attract and like poles repel.
Acknowledgment The researchers would like to express their deepest gratitude and appreciation to the University of the Philippines Diliman National Institute of Physics for providing the necessary resources and materials, and to their laboratory instructor, Ms. Arianne Lacaba for the knowledge imparted and guidance throughout the whole experiment. This experiment will not be possible without their help.
References 1. 2. 3. 4. 5.
Influence of Permanent Magnets With Network Cabling Siemon. (n.d.). Retrieved March 10, 2015, from http://www.siemon.com/uk/white_papers/060501magnets.asp Magnetic Field in a Slinky. (n.d.). Retrieved March 10, 2015, from http://physics.ham.miamioh.edu/LabPages/MagFieldSlinky/Magnetic_Field_in_SlinkyS14.htm Solenoid. (n.d.). Retrieved March 10, 2015, from http://hyperphysics.phyastr.gsu.edu/hbase/magnetic/solenoid.html Resnick, R., & Halliday, D. (2002). Chapter 30. In Physics (5th ed.). New York: Wiley. Young, H., & Freedman, R. (2012). Chapter 28. In University physics (13th ed.). Reading, Mass.:
AddisonWesley.
