PAGE 1/11 Exp. #2-1 : Measurement of the Electrostatic Constant and the Electric Permittivity in Vacuum by Using a Torsion Balance and Understanding of Coulomb's Law Student ID Major Name Team # 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 2/11 1. Objective Student ID Name In this experiment, the electrostatic constant and the electric permittivity in vacuum will be measured by using a torsion balance. In addition, Coulomb's law will be quantitatively understood. 2. Theory (1) Coulomb's law Charges with the same sign repel each other, and charges with the opposite sign attract each other. The magnitude of the electrostatic force or Coulomb force applied between two point charges and separated by a distance is given as the following. (Eq. 1) produced by separated charges. Therefore, it is only possible to keep relatively small amount of charges separated in the laboratory. In this reason, despite that the electrostatic force is extremely larger than the gravitational force, the measurement of the electrostatic force needs a delicate torsion balance whereas the measurement of the gravitational force can be done by a simple spring balance. The torsion balance will provide a direct and precise method in measuring the electrostatic force. If the electrostatic force is inversely proportional to the square of the distance between two objects, it can be shown mathematically that the electric field is zero at all points inside the homogeneously charged conductive sphere. It is well known that this fact is correct based on the measurement with a considerable precision done on the electric field inside a charged conductive sphere. If the electrostatic force is expressed as, is obtained from such an indirect measurement method. Fig. 1. Electrostatic force applied between two point charges. Here, N m C is called the electrostatic constant or Coulomb constant in vacuum, and Fm is called the electric permittivity in vacuum where F C N m is the SI unit of capacitance. The electrostatic force is inversely proportional to the square of the distance between two objects, similar to the gravitational force. Answer the following questions. 1. If protons with a mass g and electrons with a mass g are separated by a distance m, show that the electrostatic force of about N is applied between two. (2) Torsion balance (3) Restoring torque and torsion constant If protons with a mass of g and electrons with a mass of g are separated by a distance of m, the electrostatic force of about N is applied between two. This force corresponds to the gravitational force applied to an object with a mass of about of the Moon on the surface of the Earth. Since an extremely great force is applied between charges with small quantities, it could seem that a delicate torsion balance will not be needed to measure the electrostatic force applied between charged objects in the laboratory. In general, it is difficult to keep charges separated, because the magnitude of the electrostatic force is very large and the size of a proton and an easily mobile electron is very small. Negatively charged electrons repel each other and attract positively charged protons. In addition, if free electrons or ions exist between separated charges, these objects move quickly to decrease the electric field If the restoring torque applied in a torsion balance is and the twist angle of a torsion wire from the zero point is, there is a proportionality relation between them when they are sufficiently small so that the relation between them can be expressed as follows: (Eq. 2) Here, is called the torsion constant. If the torque is given by and the angle between and is, the magnitude of the torque is. Here, is the distance between the rotation axis and the action point of the force, and is the magnitude of the force. Therefore, the relation of and is made so that the torsion constant can be measured by using this relation.
PAGE 3/11 (4) Capacitance of a conductive sphere Consider a capacitor consisting of two conductive spheres with the same centers and radii and ( ). Fig. 2. A capacitor consisting of two conductive spheres with the same centers. One conductive sphere is charged by and the other is charged by. If the potential difference between two conductive spheres is, the capacitance of this capacitor is given by. (Eq. 3) If there is one conductive sphere with a radius, the radius of the other is treated as. Therefore, the capacitance of an isolated conductive sphere with a radius is given by. (Eq. 4) Since the relation between the charge and the potential difference in a capacitor is, the charge of a conductive sphere can be measured by using this relation. (5) Corrected twist angle Since the electrostatic force is applied between two conductive spheres located relatively close in this experiment, a conductive sphere cannot be treated the same way as a point charge. In this reason, the twist angle can be substituted with the corrected twist angle. Here, the correction factor is given by, (Eq. 4) where is the radius of a conductive sphere and is the distance between the centers of two conductive spheres.
PAGE 4/11 3. Experimental Instruments Items Quantity Usage Clean up method Torsion balance 1 set It is used to measure the electrostatic force. It should be placed at the center of the experiment table. Support tube 1 ea. It is used to support the conductive sphere of the torsion balance when measuring the torsion constant. It should be mounted on the torsion balance. Mass 3 ea. Two mg masses and one mg mass are placed on the conductive sphere of the torsion balance when measuring the torsion constant. They should be placed inside the tool box of the torsion balance. Slide assembly 1 set It is used to fix one of the conductive spheres. Conductive sphere 2 ea. Electrostatic force is applied between two conductive spheres. It should be placed at the center of the experiment table. They should be attached to the torsion balance and the slide assembly, respectively. High voltage supply 1 ea. It is used to produce high voltage. It should be placed at the center of the experiment table. High voltage supply -to-wall power connection cable 1 ea. It is used to connect the high voltage supply to the wall power. It should be placed inside the basket of the experiment table. Charging probe 1 ea. It is used to charge two conductive spheres. It should be placed inside the basket of the experiment table.
PAGE 5/11 4. Experimental Procedures (0) Setting before the experiment 1) Place the torsion balance upright and connect the slide assembly to the torsion balance. In order to use the scale of the slide assembly, force the conductive sphere of the torsion balance to stop at the zero point, and slide the conductive sphere of the slide assembly so that it contacts with the conductive sphere of the torsion balance. Since the radii of two conductive spheres are cm respectively, control the position of the conductive sphere of the slide assembly to make the distance between the centers of two conductive spheres be cm. 2) After completing the procedures for using the scale of the slide assembly, move two conductive spheres far away. Set the torsion balance to the zero point by rotating the dial of the torsion balance until the index lines of torsion balance are aligned, and write down the angle of the torsion balance at the zero point. of a conductive sphere obtained from the radius of a conductive sphere and the voltage charging two conductive spheres are known, then the charges and placed on two conductive spheres can be calculated. Note that the actual voltage charging two conductive spheres is the half of the voltage displayed in the high voltage supply. For example, if the voltage displayed in high voltage supply is kv, it is the voltage between terminal and terminal of the high voltage supply so that the actual voltage charging two conductive spheres is kv which is the voltage between the ground terminal and or terminal of the high voltage supply. 3) After confirming that the high voltage supply is off, use a high voltage supply-to-wall power connection cable to connect the high voltage supply to the wall power and keep the high voltage supply off. Connect a charging probe to the right or left terminal of the high voltage supply. Do not connect the charging probe to the middle terminal of the high voltage supply which is the ground terminal. After confirming that the voltage adjust knob of the high voltage supply is set to the minimum, turn on the high voltage supply. 4) Rotate the voltage adjust knob of the high voltage supply to kv. The high voltage supply used in this experiment is a high voltage & low current instrument which makes it not dangerous, but correct manipulation should be done to avoid any electricity accident. 5) By briefly contacting the charging probe with the conductive sphere of the torsion balance, the conductive sphere of the torsion balance will have a charge of. In the same manner, by briefly contacting the charging probe with the conductive sphere of the slide assembly, the conductive sphere of the slide assembly will have a charge of. In principle, the amount of charges placed on two conductive spheres is independent of the time they contact with the charging probe, if this time is sufficiently long. If the capacitance 6) Slide the conductive sphere of the slide assembly so that two conductive spheres are close, and measure the distance between the centers of two conductive spheres by using the scale of the slide assembly. When two conductive spheres are close, the torque due to the electrostatic repulsion applied between two conductive spheres makes the conductive sphere of the torsion balance shift so that it is needed to increase the restoring torque of the torsion wire for restoring the torsion balance to the zero point. Rotate the dial of the torsion balance slowly to restore the torsion balance to the zero point, and write down the angle of the torsion balance. If the torsion constant of the torsion wire, the corrected twist angle obtained from the twist angle, and the distance between the rotation axis of the torsion wire and the center of the conductive sphere of the torsion balance are known, the magnitude of the electrostatic force can be calculated.
PAGE 6/11 7) While rotating the dial of the torsion balance, two conductive spheres are frequently discharged and the force between two conductive spheres becomes attractive or zero. If the conductive sphere of the slide assembly is discharged, it can be simply solved by keeping contact between the charging probe and the conductive sphere of the slide assembly. On the contrary, if the conductive sphere of the torsion balance is discharged, it is impossible to keep contact between the charging probe and the conductive sphere of the torsion balance. Therefore, it is necessary to contact the charging probe with the conductive sphere of the torsion balance each time the conductive sphere of the torsion balance seems to be discharged. Since the discharging time depends on the humidity of the laboratory, the operation of the air conditioner in the laboratory gives better experimental results. However, the torsion balance is sensitive to the air flow so that the direction of the air flow coming from the air conditioner should be controlled. Answer the following questions. 2. Explain why the attractive force is applied between charged and uncharged conductive spheres. (1) Measurement of the electrostatic force vs. the distance 1) While keeping the voltage displayed in the high voltage supply constant as kv, change the distance between the centers of two conductive spheres to cm and repeat the experimental procedures. 2) By using a proper program, draw the magnitude of the electrostatic force vs. graph and confirm the proportionality relation between two quantities. (2) Measurement of the electrostatic force vs. the charge 1) While keeping the distance between the centers of two conductive spheres constant as cm and cm respectively, change the voltage displayed in the high voltage supply to kv and repeat the experimental procedures. 2) By using a proper program, draw the magnitude of the electrostatic force vs. graph and confirm the proportionality relation between two quantities. 3) If all the measurements are finished, confirm that the voltage adjust knob of the high voltage supply is set to the minimum and turn off the high voltage supply. Finally, clean up the experimental instruments according to the suggested method. (3) Calculation of the electrostatic constant and the electric permittivity in vacuum From the former experimental results, complete the table of the magnitude of the electrostatic force vs.. By using a proper program, draw the magnitude of the electrostatic force vs. graph and confirm the proportionality relation between two quantities. Find the electrostatic constant and the electric permittivity in vacuum from the slope of the graph and compare them to the reference values.
PAGE 7/11 5. Experimental Values (1) Measurement of the electrostatic force vs. the distance Radius of the conductive sphere (cm) Capacitance of the conductive sphere (F) [Use Fm.] Angle of the torsion balance at the zero point Torsion constant of the torsion wire (N mdeg) Distance between the rotation axis of the torsion wire and the center of the conductive sphere of the torsion balance (cm) Voltage displayed in the high voltage supply (kv) Charges placed on two conductive spheres (C) Distance between the centers of two conductive spheres (cm) (m ) Correction factor Angle of the torsion balance Twist angle Corrected twist angle Magnitude of the electrostatic force (N ) Note that the actual voltage charging two conductive spheres is the half of the voltage displayed in the high voltage supply. Slope -intercept -intercept N m m N
PAGE 8/11 (2) Measurement of the electrostatic force vs. the charge Radius of the conductive sphere (cm) Capacitance of the conductive sphere (F) [Use Fm.] Angle of the torsion balance at the zero point Torsion constant of the torsion wire (N mdeg) Distance between the rotation axis of the torsion wire and the center of the conductive sphere of the torsion balance (cm) Voltage displayed in the high voltage supply (kv) Charges placed on two conductive spheres (C) Distance between the centers of two conductive spheres (cm) (C ) Correction factor Angle of the torsion balance Twist angle Corrected twist angle Magnitude of the electrostatic force (N ) Note that the actual voltage charging two conductive spheres is the half of the voltage displayed in the high voltage supply. If the former experimental setup continues, the experimental values for kv are the same as the former experimental values. cm cm Slope NC NC -intercept C C -intercept N N
PAGE 9/11 (3) Calculation of the electrostatic constant and the electric permittivity in vacuum Measurement Voltage displayed in the high voltage supply (kv) Charges placed on two conductive spheres (C) Distance between the centers of two conductive spheres (cm) (C m ) Magnitude of the electrostatic force (N ) Measurement of the electrostatic force vs. the distance Measurement of the electrostatic force vs. the charge Slope N m C -intercept -intercept C m N Electrostatic constant in vacuum Reference value (N m C ) Experimental value (N m C ) Error (%) Electric permittivity in vacuum Reference value (Fm ) Experimental value (Fm ) Error (%)
PAGE 10/11 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 why the capacitance is given by for the isolated conductive sphere with radius. 2. Explain the relation between the magnitude of the electrostatic force and the distance between the centers of two conductive spheres, while the charges placed on two conductive spheres keep constant. 3. Explain why the distance between the centers of two conductive spheres keeps constant as cm and cm instead of other values. 4. Explain the relation between the magnitude of the electrostatic force and the charges placed on two conductive spheres, while the distance between the centers of two conductive spheres keeps constant. 5. Describe the physical principle about the role of the magnet and coils mounted on the torsion balance.
PAGE 11/11 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