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Force on Conductors in Magnetic Fields 3309ENG Engineering Electromagnetics February 20, 2015 1 Before Lab (1 1 2 hours) Conductors which carry an electric current through a magnetic field experience a force which is related to: (a) the strength of the current, (b) the length of the conductor, (c) the strength of the field, and (d) the angle between the current and the field. Read Wentworth §3.6 Magnetic Forces [1] and complete the following tasks before you come to the lab: (1) Write down the Lorentz force equation. Define all of the symbols and the SI units for the physical quantities they represent. (2) Write down the equation for the force F on a wire of length ℓ carrying current I at an angle θ to a magnetic field with flux density B. Define the SI units for the physical quantities the symbols represent. (3) Write down the equation for the force F on a mass m in the earth’s gravitational field g. Give the value for the earth’s gravitational field g in SI units. 2 During Lab (2 hours) The experiment uses a current balance set up as shown in figure 1. When a current from the power supply (C) is passed through the circuit board (D) sitting in the magnetic field from the magnet (E) the force created is transferred to the balance (F). The force can be determined by adjusting the balance to measure the effective weight in units of mass (grams g) and then using the equation from task (3) in section 1 to convert the weight into force. A stand B arm C power supply (5A DC) D PCB or coil E magnet (2 types) F balance A B C D E F Figure 1: Current balance set up. 1 Aim The aim of the experiment is to determine the relationship between force and each of the parameters (a), (b), (c) and (d) listed in section 1. Method The method is to: (1) fix three of the parameters to the values given in the next section, (2) measure the force while varying the remaining parameter, and (3) plot the variation of force against the parameter. Hints ⊲ You have to repeat the method four times – once for each of the parameters. ⊲ See appendix A for notes on how to vary each parameter and how to use the equipment safely. ⊲ Be careful not to exceed the currents specified since that can damage the equipment. Results Tabulate your results as follows: current variable 0 – 4 amps length 40 millimetres field 6 magnets angle 90◦ current X measured weight magnet weight effective weight force Y (amps A) (grams g) (grams g) (grams g) (newtons N) 0 1 2 3 4 current 2 1 2 amps length variable 0 – 80 millimetres field 6 magnets angle 90◦ length X measured weight magnet weight effective weight force Y (millimetres mm) (grams g) (grams g) (grams g) (newtons N) 0 20 40 60 80 current 2 1 2 amps length 40 millimetres field variable 0 – 6 magnets angle 90◦ field X measured weight magnet weight effective weight force Y (magnets) (grams g) (grams g) (grams g) (newtons N) 0 2 4 6 2 current 2 1 2 amps length 40 millimetres field 6 magnets angle variable −90◦ – +90◦ angle X measured weight magnet weight effective weight force Y (degrees ◦ ) (grams g) (grams g) (grams g) (newtons N) −90 −60 −30 0 30 60 90 3 After Lab (1 1 2 hours) Plots (a) Plot column Y against column X for each of your tables. (b) Label all axes with numbers, units and a name. (c) Label all plots with a title. Interpretation (a) From the shape of each of your plots write a relationship (i.e. an equation) between force and the parameter you have varied. Define all of the symbols you use and give the SI units for the quantities they represent. (b) Combine four your equations into one single equation which is consistent with all of the separate equations. Application From the equation you have deduced, answer the following questions: (1) How does the force change if you double the current? (2) How does the force change if you halve the field and double the length at the same time? (3) How does the force change if you change the orientation from 0◦ to 45◦ ? From your general knowledge of electrical machinery: (a) Name two types of electrical machine which use forces on conductors in magnetic fields. (b) Describe the purpose of each machine. References [1] S. M. Wentworth. Fundamentals of Electromagnetics with Engineering Applications. John Wiley & Sons, 2005, §3.6 pp 126–131. 3 A Notes on Equipment ⊲ Adjust the current on the power supply (C) by using the supply’s current limiting facility as follows. (1) Adjust the voltage control to 5V. (2) Short circuit the DC output with one of the leads. (3) Use the current adjust control to set the maximum current to 1 amp. (4) Remove the short circuit. (5) Connect the circuit for the experiment. (6) Use the current adjust control to set the chosen current. (7) Don’t change the voltage control. ⊲ Adjust the length of the conductor by exchanging the PCB current loops (D) at the end of the arm (B). The printed circuit boards are quite a tight fit. They need to be tight because they carry high current. Be careful connecting and disconnecting them from the arm. Use a ruler to measure the bottom section of the loops. Some loops are double sided, which doubles the effective length. ⊲ Adjust the magnetic field strength by sliding the plastic retainer out of the magnet assembly (E) and removing some magnets. Replace the plastic retainer. Weigh the magnet assembly each time. When replacing the magnets match the north/south poles (red/white) to the same colours on the magnet assembly. ⊲ Adjust the orientation of the conductor by using the wire-wound current loop (D) and the magnet assembly (E) with the wide air gap. Vary the angle from one extreme with the conductor perpendicular to the field, through 180 degrees to the other extreme with the conductor again perpendicular to the field but in the opposite direction. Adjust (rotate) the plastic marker to read zero degrees when the conductor is parallel to the field. Remember to reduce the current to 1 amp before using the wire-wound current loop. B List of Equipment 1 5A DC power supply Frederiksen 3630 1 pair of high current leads — 1 15cm clear plastic ruler — 1 tripod stand Pasco SF8607 current balance kitset 1 arm Pasco SF8607 current balance kitset 1 set of 6 PCB current loops Pasco SF8607 current balance kitset 1 assembly of 6 magnets Pasco SF8607 current balance kitset 1 current loop with angular adjustment Pasco SF8608 current balance kitset accessory 1 assembly of 2 magnets Pasco SF8608 current balance kitset accessory 1 0.01 gram mechanical balance Ohaus Cent-o-gram model 311 4 ENG 3309 LAB 1 Force on Conductors in Magnetic Fields Equipment 1 5A DC power supply Frederiksen 3630 1 pair of high current leads — 1 15cm clear plastic ruler — 1 tripod stand Pasco SF8607 current balance kitset 1 arm Pasco SF8607 current balance kitset 1 set of 6 PCB current loops Pasco SF8607 current balance kitset 1 assembly of 6 magnets Pasco SF8607 current balance kitset 1 current loop with angular adjustment Pasco SF8608 current balance kitset accessory 1 assembly of 2 magnets Pasco SF8608 current balance kitset accessory 1 0.01 gram mechanical balance Ohaus Cent-o-gram model 311 Label ENG 3309 ⋄ LAB 1 Force on Conductors in Magnetic Fields 5

GRIFFITH UNIVERSITY GOLD COAST GRIFFITH SCHOOL OF ENGINEERING 3309 ENGINEERING ELECTROMAGNETICS REPORT NUMBER 3 ‘Force on Conductors in Magnetic Fields’ The report represented is the sole work of the author. None of this report is plagiarised (in whole or in part) from a Fellow student’s work, or from any un-referenced outside source. Student Name: Albert Lee Student Number: S2802138 Due Date: 5 May, 2013 Aim “The aim of the experiments is to determine the relationship between force and each of the parameters (a), (b), (c) and (d) listed in section 1.” Preliminary 1.)