PAGE 1/17 Exp. #2-4 : Measurement of Characteristics of Magnetic Fields by Using Single Coils and a Computer Interface Student ID Major Name Team No. Experiment Lecturer Student's Mentioned Items Experiment Class Date Submission Time Submission Place Introductory Physics Office Report Box # Students should write down Student s Mentioned Items at the cover page of Experiment Reports, and then complete Experiment Reports by adding contents to the attached papers (if needed) in terms of the following sections. Contents of the reports should be written by hand, not by a word processor. Instead, it is allowed that figures and tables are copied and attached to papers. Completed Experiment Reports should be submitted to the place due to the time specified by Experiment Lecturers. The Experiment Report score per each Experiment Class is evaluated by max. 50 points (basically 15 points). Solutions of Problems in Experiment Reports are not announced to the public according to the General Physics Laboratory - Administration Rule. If a student permits other students to pirate one s Experiment Reports or a student pirates Experiment Reports of other students regardless of permission of original creators, the corresponding Experiment Report score and Active Participation score will be zero in case of exposure of such situation. Unless Experiment Reports are submitted to the place due to the time specified by Experiment Lecturers, the corresponding Experiment Report score will be zero. If the submission rate of Experiment Reports is less than or equal to two thirds, the grade of General Physics Laboratory will be F level. In order to decide grades of General Physics Laboratory at the end of current semester, the detailed scores of General Physics Laboratory will be announced at Introductory Physics Office homepage. Based on the announcement, students can raise opposition of score error. Since the public evidence is needed for the confirmation of opposition, students should keep one s Experiment Reports completed evaluation by Experiment Lecturers until the Experiment Report score decision If a student is absent from the Experiment Class because of proper causes, the corresponding student should submit documents related to absence causes to Introductory Physics Office regardless of cause occurrence time until the grade decision of General Physics Laboratory. If a student moves the Experiment Class arbitrarily without permission of Introductory Physics Office, it is noted that the total Experiment Scores will be zero. Lecturer's Mentioned Items Submission Time/Place Check Experiment Report Points Evaluation Completion Sign 50
PAGE 2/17 1. Objective Student ID Name Axial components of a magnetic field produced by various single coils are measured in this experiment. 2. Theory (1) Ampere's law The phenomena that a magnetic field is produced near a wire carrying electric currents was discovered by Oersted and can be described by Ampere's law as follows: (Eq. 1) Here, is the magnetic field flux density, NA Hm is the magnetic permeability in a vacuum, and is the electric current passing through a region enclosed by a closed curve. The phenomena that an electric field is produced by a time-varying magnetic field can be described by Faraday's law. Similarly, the phenomena that a magnetic field is produced by a time-varying electric field can be described by Ampere-Maxwell's law as follows: (Eq. 2) Here, is the electric field flux passing through a region enclosed by a closed curve and is given by, where is the electric field. is able to be treated as the electric current and is called the displacement current. For a direct current, the displacement current vanishes so that the phenomena can simply be described by Ampere's law. (2) Magnetic field produced by the circular coil According to Biot-Savart's law, the magnetic field flux density at the position displaced by from the electric current element is given by. (Eq. 3) Here, is the unit vector along the direction of. For a circular coil with radius carrying an electric current as shown in Fig. 1, the magnetic field flux density at the position displaced by along the axis passing through the center of the circular coil can be calculated as the following. The magnitude of the magnetic field flux density at a position displaced by from the electric current element on the circular coil is given by sin. (Eq. 4) The magnetic field flux density can be decomposed into the axial component sin and the radial component cos. However, it can be calculated that the radial component of the magnetic field flux density is zero as the following which is due to symmetry of the circular coil. cos (Eq. 5) The axial component of the magnetic field flux density remains as follows: sin sin (Eq. 6) The magnitude of the magnetic field flux density at a position displaced by from the electric current element on the circular coil is given by sin. (Eq. 4) The magnetic field flux density can be decomposed into the axial component sin and the radial component cos. However, it can be calculated that the radial component of the magnetic field flux density is zero as the following which is due to symmetry of the circular coil. cos (Eq. 5) The axial component of the magnetic field flux density remains as follows: sin sin (Eq. 6) Here, sin and which is the length of the circular coil. Hence, the magnetic field flux density at the position displaced by along the axis passing the center of the circular coil is given by. (Eq. 7) If the number of turns of the circular coil is, the magnetic field flux density will be multiplied by as follows: (Eq. 8) Fig. 1. Calculation of the axial component of the magnetic field produced by a circular coil. From this result, the magnetic field flux density at the center of the circular coil ( ) is given by. (Eq. 9)
PAGE 3/17 (3) Magnetic field produced by the solenoid For a solenoid with radius, length, and the number of turns carrying an electric current, the magnetic field flux density at the position displaced by along the axis passing the center of the solenoid can be calculated as the following. Considering a circular coil with radius, length, and the center displaced by from the center of the solenoid, the position displaced by from the center of the solenoid is displaced by from the circular coil. In addition, the number of turns of the circular coil for the length can be known from the proportionality relation as follows:, (Eq. 10) Therefore, the magnitude of the magnetic field flux density at the position displaced by from the center of the circular coil with radius and the number of turns is given by (Eq. 11) Hence, the magnetic field flux density is given as follows: (Eq. 12) Assuming that the length of the solenoid is sufficiently longer than the radius of the solenoid ( ), the magnetic field flux density at the center of the solenoid ( ) can be given by Here,. (Eq. 13) is the number of turns of the solenoid per unit length. Answer the following questions. 1. Derive (Eq. 12) by direct integral calculation.
PAGE 4/17 3. Experimental Instruments Items Quantity Usage Clean up method Computer 1 set It is used to acquire and analyze data. It should be placed at the center of the experiment table. Sensor shift driver (Computer interface) 1 set It is used to measure the magnetic field produced by the single coils. It should be placed at the center of the experiment table. USB/power connection cable 1 ea. It is used to connect the computer/wall power to the sensor shift driver. It should be mounted at the sensor shift driver. Magnetic sensor 1 ea. It is used to measure the magnetic field produced by the single coils. It should be mounted at the sensor shift driver. Coil support for height adjust 1 ea. It is used to adjust the height of the small coils. It should be placed at the center of the experiment table. Power supply 1 ea. It is used to supply an electric current to the coils. It should be placed at the center of the experiment table.
PAGE 5/17 Items Quantity Usage Clean up method Coils 1 set Magnetic fields are produced by the coils when carrying an electric current. It should be placed inside the basket of the experiment table. Power supply -to-wall power connection cable Power supply -to-coil connection cable 1 ea. It is used to connect the power supply to the wall power. 2 ea. They are used to connect the power supply to the coils. It should be placed inside the basket of the experiment table. They should be placed inside the basket of the experiment table. Measuring scale 1 ea. It is used to measure the size of the coils. It should be placed inside the basket of the experiment table.
PAGE 6/17 < How to Use the Power Supply > [7] In order to prevent an electricity accident, note that one's body must not be in contact with connection parts of the experimental instrument-to-power supply connection cables during the measurement. If the electric circuit becomes open during the measurement, the current will suddenly become zero and the current control indication lamp will turn off. In this case, after rotating all voltage and current adjust knobs to the minimum, turn off the power supply and correct the electric circuit in the same manner of [3]. [1] After confirming that the power supply is off, use the power supply-to-power connection cable to connect the power supply to the wall power and keep the power supply off. Use the experimental instrument-to-power supply connection cables to connect the experimental instrument to and terminals of the power supply. Without special condition, do not connect the ground terminal (GND or COM) of the power supply. [8] After the experiment is finished, turn off the power supply in the way opposite to turning on the power supply. That is, after rotating the current adjust knob to the minimum, rotate the voltage adjust knob to the minimum and turn off the power supply. Note that you must turn off the power supply when all voltage and current adjust knobs are at the minimum, or else a severe electricity accident may be happened. After turning off the power supply, clean up the experimental instruments according to the suggested method. [2] After confirming that all voltage and current adjust knobs of the power supply are at the minimum, turn on the power supply. In some models of the power supply, the power lamp or the voltage control indication lamp (CV) will turn on when turning the power supply on. [3] Rotate the voltage adjust knob (VOLTAGE - COARSE) slowly to increase the voltage. When approaching to a sufficiently high voltage for a normal electric circuit, the current control indication lamp (CC) will turn on. But for an open circuit, no matter how high voltage is, the current will remain zero and the current control indication lamp will be off. In this case, after rotating all voltage and current adjust knobs to the minimum, turn off the power supply and correct the electric circuit. The inspection of the electric circuit must be done only after the power supply is off. [4] In specific experiments that need a current supply, rotate the current adjust knob (CURRENT) slowly to set the desired current while checking if the current control indication lamp is on. [5] Even in properly functional electric circuits, when rotating the current adjust knob to increase the current, it can be observed that the current control indication lamp will suddenly turn off and the nonzero current does not increase any longer. This is caused by an insufficient voltage, which can be solved by rotating the voltage adjust knob more to increase the voltage. After the current control indication lamp turns back on, the current can be increased by rotating the current adjust knob. [6] Note that all voltage and current adjust knobs should be rotated slowly, or else the abrupt change of the voltage or the current may cause an electricity accident. Do not rotate the voltage fine adjust knob (VOLTAGE FINE) unless it is absolutely needed, and keep it at the minimum.
PAGE 7/17 < How to Use the Sensor Shift Driver > [1] Connect the computer/wall power to the USB/power connection terminal located at the back face of the sensor shift driver. Connect the magnetic./optic sensor mounted at the sensor shift driver to the magnetic/optic sensor connection terminal located at the back face of the sensor shift driver. [2] After turning on the computer, open the SensorLab program. After selecting Motor Driver as a device, click the Connect button of the SensorLab program. [3] Sensor shift speed selection switch located at the front face of the sensor shift driver can be set to one of Low Mid High positions, and sensor shift direction selection switch located at the front face of the sensor shift driver can be set to one of Left 0 Right positions. By using these switches and the SensorLab window, place the sensor at the center of the measuring object. If the above procedure is completed, place the sensor at the one edge of the sensor shift driver again. [4] Magnetic sensor range/optic sensor selection switch located at the top face of the sensor shift driver can be set to one of 5G 50G 500G OPT positions, and zero adjustment knob (ZERO ADJ) located at the top face of the sensor shift driver can be adjusted. By using these switches and the SensorLab window, adjust the zero status. [5] Set the sensor shift speed selection switch to the proper position. Start the sensor shift by using the sensor shift direction selection switch, and click the Start button of the SensorLab program to start the measurement. Check if the acquired data is displayed in the screen. [6] If the data is acquired, stop the sensor shift by using the sensor shift direction selection switch, and click the Stop button of the SensorLab program to stop the measurement. Repeat this procedure to acquire the correct data. [7] Save the data in the computer by selecting File Save ******.txt in the menu of the SensorLab program and copy the text files to a USB memory prepared beforehand. [8] After the experiment is finished, close the SensorLab program and turn off the computer. Clean up the experimental instruments according to the suggested method.
PAGE 8/17 4. Experimental Procedures (0) Setting before the experiment 1) After confirming that the power supply is off, use a power supply-to-wall power connection cable to connect the power supply to the wall power and keep the power supply off. Use power supply-to-coil connection cables to connect the power supply to the coils. (1) Measurement of the characteristics of the magnetic field produced by a circular coil 1) Measure the magnetic field produced by circular coils having the same radii but different numbers of turns. Draw the graphs of the experimental value of the magnetic field flux density to compare the results. 2) Connect the computer/wall power to the USB/power connection terminal of the sensor shift driver. After turning on the computer, open the SensorLab program. After selecting Motor Driver as a device, click the Connect button of the SensorLab program. 2) Similarly, measure the magnetic field produced by circular coils having the same numbers of turns but different radii. Draw the graphs of the experimental value of the magnetic field flux density to compare the results. 3) By using the sensor shift speed/direction selection switch and the SensorLab window, place the magnetic sensor at the center of the coil. Use the coil support for height adjustment of small coils. If the above procedure is completed, place the magnetic sensor at the one edge of the sensor shift driver again. 4) Set the magnetic sensor range selection switch to 50G position. Make sure no electric current is carried by the coil. By using the zero adjustment knob (ZERO ADJ) and the SensorLab window, adjust the zero status. 5) After confirming that all the voltage and current adjust knobs of the power supply are set to the minimum, turn on the power supply. Rotate the voltage adjust knob slowly to increase the value of the voltage sufficiently and rotate the current adjust knob slowly to set the value of the current near A. In order to prevent an electricity accident, note that one's body must not be in contact with the connection part of the power supply-to-coil connection cable during the experiment. 6) Set the sensor shift speed selection switch to High position. Start the sensor shift by using the sensor shift direction selection switch, and click the Start button of the SensorLab program to start the measurement. Check if the acquired data is displayed in the screen. 7) If the data is acquired, stop the sensor shift by using the sensor shift direction selection switch, and click the Stop button of the SensorLab program to stop the measurement. Repeat this procedure to acquire the correct data. 8) Save the data in the computer by selecting File Save ******.txt in the menu of the SensorLab program and copy the text files to a USB memory prepared beforehand. 9) If the measurements for a certain coil are completed, confirm that all the voltage and current adjust knobs of power supply are set to the minimum and turn off the power supply. After changing to another coil, repeat the experimental procedures. 3) The magnetic field flux density at the center of the circular coil with radius and the number of turns is given by,. Using this formula, calculate the average value of the magnetic permeability in vacuum from the magnetic field flux density at the center of the circular coil and compare it to the reference value. (2) Measurement of the characteristics of the magnetic field produced by a solenoid 1) Measure the magnetic field produced by solenoids having the same radii but different numbers of turns (different lengths). Draw the graphs of the experimental value of the magnetic field flux density to compare the results. 2) Similarly, measure the magnetic field produced by solenoids having the same numbers of turns (the same lengths) but different radii. Draw the graphs of the experimental value of the magnetic field flux density to compare the results. 3) The magnetic field flux density at the center of the solenoid with radius, length, and the number of turns is given by (if ) Using this formula, calculate the average value of the magnetic permeability in vacuum from the magnetic field flux density at the center of the solenoid and compare it to the reference value.
PAGE 9/17 4) If all the measurements are finished, confirm that all the voltage and current adjust knobs of the power supply are set to the minimum and turn off the power supply. Close the SensorLab program and turn off the computer. Finally, clean up the experimental instruments according to the suggested method. Answer the following question. 2. Semiconductor devices with known number density of electrons are contained in the probe measuring the magnetic field. Describe the physical principle about the probe measuring the magnetic field.
PAGE 10/17 5. Experimental Values (1) Measurement of the characteristics of the magnetic field produced by a circular coil 1) Variation of the magnetic field flux density produced by a circular coil along the -axis Electric current carried by the circular coil (A ) [Set near A ] Formula : Magnetic field flux density produced by the circular coil [Use Hm.] Length (mm) Radius (mm) Circular coil #1 Circular coil #2 Circular coil #3 Circular coil #4 Circular coil #5 1 Draw the graphs of the experimental for all the circular coils. (Distinguish the circular coils by changing the color or shape of points and lines showing experimental values.)
PAGE 11/17 2 For circular coils with the same radii, how does the magnetic field depend on the number of turns? Circular coil Radius (mm) [Constant] Exp. magnetic field flux density at the center (mt) #1 #2 #3 Slope mt -intercept -intercept mt 3 For circular coils with the same numbers of turns, how does the magnetic field depend on the radius? Circular coil [Constant] Radius (mm) (mm ) Exp. magnetic field flux density at the center (mt ) #3 #4 #5 Slope mt mm -intercept -intercept mm mt
PAGE 12/17 2) Calculation of the magnetic permeability in vacuum from the magnetic field flux density at the center of the circular coil Exp. Circular coil Electric current (A ) (A ) Length (mm) Radius (mm) magnetic field flux density at the center (mt) (T m ) #1 #2 #3 #4 #5 Slope Hm -intercept -intercept A T m Magnetic permeability in vacuum Reference value (Hm ) Experimental value (Hm ) Error (%)
PAGE 13/17 (2) Measurement of the characteristics of the magnetic field produced by a solenoid 1) Variation of the magnetic field flux density produced by a solenoid along the -axis Electric current carried by the circular coil (A ) [Set near A ] Formula : Magnetic field flux density produced by the solenoid [Use Hm.] Length (mm) Radius (mm) Solenoid #1 Solenoid #2 Solenoid #3 Solenoid #4 Solenoid #5 1 Draw the graphs of the experimental for all the solenoids. (Distinguish the solenoids by changing the color or shape of points and lines showing experimental values.)
PAGE 14/17 2 For solenoids with the same radii, how does the magnetic field depend on the number of turns or the length? Solenoid Length (mm) per unit length (mm ) Radius (mm) [Constant] Exp. magnetic field flux density at the center (mt) #1 #2 #3 Slope mt mm -intercept mm -intercept mt 3 For solenoids with the same numbers of turns or the same lengths, how does the magnetic field depend on the radius? Solenoid [Constant] Length (mm) [Constant] per unit length (mm ) [Constant] Radius (mm) Exp. magnetic field flux density at the center (mt ) #3 #4 #5 Slope mtmm -intercept mm -intercept mt
PAGE 15/17 2) Calculation of the magnetic permeability in vacuum from the magnetic field flux density at the center of the solenoid Exp. Solenoid Electric current (A ) (A ) Length (mm) Radius (mm) magnetic field flux density at the center (mt) (T m ) #1 #2 #3 #4 #5 Slope Hm -intercept -intercept A T m Magnetic permeability in vacuum Reference value (Hm ) Experimental value (Hm ) Error (%)
PAGE 16/17 6. Results and Discussions (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents should be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.) Write down contents in terms of the following key points. 1. Explain the relation between the magnetic flux density and the number of turns of the circular coil, while the radius of the circular coil keeps constant. 2. Explain the relation between the magnetic flux density and the radius of the circular coil, while the number of turns of the circular coil keeps constant. 3. Explain the relation between the magnetic flux density and the number of turns per unit length of the solenoid, while the radius of the solenoid keeps constant. 4. Explain the relation between the magnetic flux density and the radius of the solenoid, while the number of turns per unit length of the solenoid keeps constant. 5. Calculate the theoretical for all the circular coils and all the solenoids, and compare them to the experimental.
PAGE 17/17 7. Solution of Problems (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents should be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.) 8. Reference