PARALLEL-PLATE CAPACITATOR

Transcription

1 Physics Department Electric an Magnetism Laboratory PARALLEL-PLATE CAPACITATOR 1. Goal. The goal of this practice is the stuy of the electric fiel an electric potential insie a parallelplate capacitor. In the first part, we will etermine the relation between the electric fiel insie the capacitor an the voltage applie to the plates an the separation between them. In the secon part, we will stuy the electric potential in the space between the capacitor plates. 2. Overview. A capacitor is an electronic component capable of storing electric charge. Capacitors consist of two conuctors at ifferent electric potentials. The net total charge store in a capacitor is zero since each conuctor stores the same charge but with ifferent signs. The capacitance of a given capacitor is efine as: is a reasonably general moel for electric fiels, without electric circuits. An ieal capacitor is characterize by a constant capacitance C, efine as the ratio of charge ±Q on each conuctor an the voltage V between them. Q C [1] V where Q is the charge store on each plate an V is the potential ifference between them. The SI unit for capacitance is the Fara name after the great physicist Michael Faraay an is enote by F. The parallel-plate capacitor consists of two parallel conucting plates of surface S separate a istance between which there is a potential ifference V (figure 1). V Figure 1: Sketch of a parallel-plate capacitor. The capacitance of a parallel- plane capacitor epens on its geometry an is given by: 1

2 S C 0 [2] Where 0 is the permittivity of vacuum, an has a value of C 2 /Nm 2, S is the area of each capacitor plate an is the istance between them. When the plate separation istance is much smaller than the plate imensions ( ) the electric fiel insie the capacitor is approximately constant (ege effects can be neglecte) an is given by: S E r [3] 0 E Figure 2: Electric fiel insie a parallel-plate capacitor. where is the surface charge ensity on the plates of the capacitor an is given by: Q [4] S The electric fiel [3] is an iealization which is only accurate in the central area of the capacitor since electric fiel lines begin to curve as we approach to the eges. In the central part of the capacitor the electric fiel expression can be written as the variation of the potential in just one irection: V V E r r V [5] x x that ue to the homogeneity can be further simplifie as: V E [6] 2

3 Thus, the electric fiel insie the capacitor is not only constant but proportional to the applie potential between the plates an inversely proportional to the istance between them. Since the electric fiel is constant insie the capacitor it is easy to obtain the electric potential integrating equation [5] an imposing the bounary conitions: V(x) V 0 V 1 V 0 x [7] Where V 0 an V 1 are the potentials at the capacitor plates an V(x) is the potential at a istance x from the plate 1 (see Figure 3). E V 0 V 1 x V x Figura 3: Potential variation insie a capacitor parallel-plate. 3. To learn more... Bibliography: - TIPLER P.A. y MOSCA, G., Physics 4 th eition E W.H Freeman an company o Chapter 31. Pages In Internet: 1) In Spanish: ) In English:

4 4. Material. 1. Parallel-plate capacitor. 2. Electric Fiel Meter. 3. Potential probe. 4. Butane gas burner. 5. Grauate ruler. 6. Power supply multimeters. 8. Connectors.(10) 9. Screwriver. 10. Lighter. 11. Potential probe aapter Figure 4: Material to be use in practice. 5 4

5 5. Experimental proceure. 5.1 Electric fiel intensity as a function of istance between plates. Assemble the circuit as shown in Figure 5. You shoul take special care to properly fee the electric fiel meter. The input of the electric fiel meter is foun to the left an is marke with V-IN. These two entries nee to be connecte the output of the power supply situate at leftmost position (output 0-12 V) taking special care to respect the polarization. Output - (Blue) from the power supply must be connecte to the IN (Black) an the output meter + (Re) from the source to the re socket of the meter. Once the connections are mae, rotate the power regulator to the maximum value of 12 V. Figure 5: Schematic view of the assembly for measuring the electric fiel insie the capacitor. 5

6 Figure 6: Photograph of the assembly for measuring the electric fiel insie the capacitor. Capacitor plates must be fe using the secon outlet from the power supply (0-50 V output). The measurement of electric fiel intensity will be mae with the help of a multimeter connecte to the OUT (± 10 V) electric fiel meter. Set the multimeter input to measure potential (V) an select the 2 to 4 volts range. For the fiel meter use the scale of 10kV/m that can be selecte by pressing the "Range" button. In this way the multimeter lecture will correspon to the electric fiel intensity between the parallel-plate capacitor in kv/m units. Before oing any measurement make sure to set the electric fiel meter to zero. When no potential ifference is applie to the plates the electric fiel shoul be zero an therefore the electric fiel meter shoul inicate zero. If the meter lecture is not zero use the electric fiel meter gauge until the multimeter measurement signals a zero. At the first part of the practice we will stuy the electric fiel intensity as a function of istance between plates. To o this, apply a voltage of 50 volts (as measure by the multimeter) between the capacitor plates, an measure the electric fiel intensity as a function of plate separation istance between 2 to 12 centimeters every centimeter. It is important to keep the plates as parallel as possible before each measurement Plot the electric fiel strength (E) as a function of the istance between plates (). Plot also the theoretical values obtaine from equation [6] Discuss the results of the plot Calculate Ln() an Ln(E) from the measurements taken in section Make a least square fit an compare the results with equation [6]. What is the meaning of each fitting parameter? 6

7 Calculate the capacitance an the surface charge ensity for a plate separation of 3 cm. Develop the calculation. Do not forget to measure the area of the plates. 5.2 Electric fiel intensity as a function of the applie potential ifference between the capacitor plates. Using the same setup as in the previous section an with a plate separation of 5 cm measure the electric fiel intensity as a function of the applie potential ifference between the capacitor plates between 0 an 50 volts every 5 volt Plot the electric fiel strength in terms of tension between plates Make the least squares fit of the points on the plot. What is the meaning of each fitting parameter? 5.3 Potential insie a capacitor plane-parallel plate. For this stuy it is necessary to prepare the assembly shown in Figure 7. We will make use of the potential probe an the thir capacitor plate. Unscrew the plate that is in the fiel meter an replace it with the other plate. Install the potential aapter tip in the fiel meter as shown in Figure 7. Connect the potential probe to the re input. Groun the fiel meter through the support structure as inicate in the sketch of Figure 8 (Gn). Figure 7: Scheme of the assembly for measuring electrical potential insie the capacitor. 7

8 To avoi the isturbing influence of surface charges, the air aroun the tip of the probe is ionize with a flame. Try to use the smallest possible flame to avoi excessive fluctuations in the potential measurement. Since the measurement often vary consierably the best practice is to estimate a maximum an minimum values an take an average value as a result of the measure. In this assembly you shoul not change the connection of the multimeter nor the multimeter fiel scale (10kV/m). The result of the electrical potential is obtaine by multiplying by 10 the value given by the meter an its units are volts (V). To measure the electric potential, in terms of istance from the capacitor plate connecte to the positive output of the power supply, we will separate the plates a istance of 10 cm an apply a voltage of 50 V between them. Then, keeping fixe the istance between plates to 10 cm, the electric potential is etermine with the help of the potential probe by varying the istance between the probe an the positive plate from 1 to 9 cm in 1 cm steps. Ensure that the probe is in the central region of the capacitor to avoi ege effects. Figure 8: Photograph of the assembly for measuring electrical potential insie the capacitor Plot the potential insie the capacitor as a function of probe position with respect to the plate connecte to the positive output of the source Calculate the least squares fit of the ata an compare the result with equation [7]. What is the meaning of each fitting parameter? Comment the above results. Base in your experimental results, o you think that the electric fiel insie the parallel-plate capacitor is approximately constant? IMPORTANT: All plots must be accompanie by a table with the ata represente. Inclue in the tables all units an uncertainties of the measurements. 8

9 6. Appenix: Multimeter Multimeter is an electronic measuring instrument that combines several measurement functions in one unit. A typical multimeter may inclue features such as the ability to measure. o Current an voltage at stationary regime, DC= irect current, AC alternating current. o Resistors o Capacitors o Electric Continuity o Hybri parameters of transistors 6.1 How to measure with a igital multimeter (DMM). Measuring Voltage: 1. Set the DMM selection ial to rea DC volts (V). Insert one wire into the socket labele 'V' an a secon wire into the socket labele 'COM'. 2. Set the selection ial of the DMM to the highest voltage measurement setting. Connect the two wires from the DMM to the two points between which you want to measure the voltage, as shown below. To measure voltage, the DMM must be place in the circuit so that the potential ifference across the circuit element you want to measure is the same as the one across the DMM. 3. If no number appears, try a ifferent measurement scale. Start at the highest voltage scale an work your way own the scales until you get a satisfactory reaing. Measuring Current: 1. Set the selection ial of the DMM to the highest current measurement setting (10 or 20 amps). Insert one wire into the socket labele '10A' an a secon wire into the socket labele 'COM'. 2. Attach the DMM into the circuit as shown below: To measure current, the DMM must be place in the circuit so that all the current you want to measure goes through the DMM. 9

10 3. If no number appears while the DMM is at the 10A (or 20A) setting, move the wire from the 10A socket to the 200mA socket an then turn the selection ial to the largest setting. If there is still no reaing, change the ial to a smaller setting, etc. 4. When you have taken your measurement, return the DMM selection ial to the highest current setting (10 amps) an move the wire back to the 10A socket. 10