Expeiment 1 Eleti field and eleti potential Pupose Map eleti equipotential lines and eleti field lines fo two-dimensional hage onfiguations. Equipment Thee sheets of ondutive papes with ondutive-ink eletodes, push pins and wies, a omfot gip voltage pobe with silione insulated, make pen, ule, (15 m), okboad, digital multimetes (DMM), DC powe supply (HY152A). Theoy The magnitude of eletostati foe between two point hages Q and q is given by Coulomb's law: F = k Qq 2 whee is the distane between the hages, k is the Coulomb onstant (k = 9.0x10 9 Nm 2 /C 2 ). The dietions of the foes the two hages exet eah othe ae always along the line joining the two point hages and like hages epel, unlike hages attat. The magnitude of the eleti field is defined as the eletial foe pe unit hage, i.e., E = F/q (N/C), hee q is a test point hage. In the ase of the eleti field assoiated with a single-soue hage Q, the magnitude of the eleti field a distane away fom the soue hage is E = F q = k Q 2 Eleti field is a veto quantity whih is speified by both its magnitude and dietion. Using the unit veto ˆ =, we an wite a veto equation that gives both the magnitude and dietion of the eleti field E due to a point hage Q: E = k Q ˆ 2 The eleti field of a point hage always points away fom a positive hage but towads a negative hage. Figue 1 (a) shows the eleti field vetos fom a positive soue hage. By dawing lines though the points in the dietion of the field vetos, we fom the eleti field lines (Fig. 1 b & ), whih give a gaphial epesentation of the eleti field. (1) (2) (3) Figue 1 9
It an be shown (see you textbook) that the eleti potential at a distane fom the soue hage Q is: Q V k. (4) Eleti potential is a sala quantity whih is speified by its magnitude only. Eleti potential an be eithe positive o negative depends on the sign of the soue hage Q. The eleti potential of two o moe point hages is simply the algebai sum of the potentials due to eah point hage sepaately: N Qi V k, whee N is the total numbe of point hages. (5) i1 i Sine a fee hage moves in an eleti field by the ation of the eleti foe, we say that wok is done by the field on moving a hage fom one point to anothe (e.g. fom A to B in Fig. 1 b). To move a positive hage fom B to A would equie wok supplied by an extenal foe to move the hage against the eleti field. The wok done by an eleti field in moving a unit hage fom point A to point B is alled the potential diffeene between these two points: W = = AB (6) q If a hage is moved along a path pependiula to the field lines, no wok is done, i.e., W = 0, sine thee is no foe omponent along the path. Then along suh a path (Fig. 1b between B and C) V = V AB VA V B WBC V V 0, i.e., V V B C B C. Hene the potential has a onstant value along a path pependiula to the q field lines. Suh a path is alled an equipotential line whih is always pependiula to the field lines. Diffeent equipotential lines have diffeent potential values, theefoe, equipotential lines an neve inteept. An eleti field may be mapped expeimentally by detemining eithe the field lines o the equipotential lines. Equipotential line an be detemined by measuing the potential diffeene between two points. If = 0, the two points ae on an equipotential line. V Caution: Make sue that the " " and " " leads fom the DC powe do not touh eah othe befoe you tun on the powe supply in all the measuements. V ( W AB ) BC Measuement #1: Map equipotential lines fo paallel-plates apaito. 1. Mount the ondutive pape #1 (with pinted side up) on the okboad using two metalli pushpins at the two eletodes whih ae dawn with ondutive ink on the ondutive pape #1. 2. Connet the two eletodes on the ondutive pape #1 to the DC powe supply (HY152A). 3. Connet the blak banana jak (gound) on DMM to the gound (blak banana jak) on the DC powe supply (HY152A). Connet the ed banana jak on DMM to a omfot gip voltage pobe with silione insulated. Selet voltage sale of 20 V on DMM. 4. Tun on the DC powe to 10 V. 5. To measue the voltage at a point on the ondutive pape #1 in Fig. 2, just let the tip of the voltage pobe touh that point. The tip of the voltage pobe should be pependiula to the ondutive pape at the touh point (in Fig. 2). 6. Attention: To edue measuement eo, at eah labelled oss in Fig. 2, say 1A, measue thee voltages at thee positions along the vetial line of the oss. Make the same 3-position-voltage measuements at eah labelled oss (fom 1A to 5E) in Fig. 2. Reod the data in Table 1. 7. Tun the voltage to 0V befoe shut down the DC powe (HY152A). 10
1E 2E 3E 4E 5E E 1D 2D 3D 4D 5D D 1C 2C 3C 4C 5C 10 V 1B 2B 3B 4B 5B 1A 2A 3A 4A 5A Figue 2 Condutive pape #1 Table 1 Data of 3-position-voltage measuements at eah labeled oss (fom 1A to 5E) in Fig. 2. Voltage (V) A B C D E 1 2 3 4 5 Ave. Data Analysis 1 1. Daw equipotential lines on Fig. 2 using a ed pen. Daw field lines (fom high to low voltage) using a blue pen. 2. Ae the field lines pependiula to the equipotential lines? 3. Use a ule to measue x on the ondutive pape. Reod x value in Table 2. 4. Calulate the magnitude of the eleti field E fo the paallel plate onfiguation using fomula E V / x. Reod the data in Table 2. 11
Table 2 Potential diffeene between two vetial lines with indies 1, 2,.5 labeled in Fig. 2. V V V V V V V V x = V E V / x 5. Ae the E values lose eah othe? 12 1 V2 23 2 V3 34 3 V4 45 4 V5 6. Is it tue that E1A E1 B... E5E? Why? Measuement #2: Map equipotential lines fo a point hage with guad ings. 1. Mount the ondutive pape #2 (with pinted side up) on the okboad using two metalli pushpins at the two eletodes whih ae dawn with ondutive ink on the ondutive pape #2. 2. Connet the two eletodes on the ondutive pape #2 to the DC powe supply (HY152A). 3. Connet the blak banana jak (gound) on DMM to the gound (blak banana jak) on the DC powe supply (HY152A). Connet the ed banana jak on DMM to a omfot gip voltage pobe with silione insulated. Selet voltage sale of 20 V on DMM. 3C 2C 1C 3D 2D 1D 1B 2B 3B 10V 1A 2A 3A Figue 3 Condutive pape #2 12
4. Tun on the DC powe to 10 V. 5. Attention: To edue measuement eo, the tip of the voltage pobe should be pependiula to the ondutive pape at the touh point. 6. Measue voltages at all the points labeled in Fig. 2. Reod the data in Table 3. 7. Tun the voltage to 0V befoe shut down the DC powe (HY152A). Table 3 Measued voltages at all the points labeled in Fig. 3 (ondutive pape #2). Voltage (V) A B C D 1 2 3 Data Analysis 2 1. Based on the data in Table 3 daw equipotential lines on Fig. 3 using a ed pen. Daw field lines (fom high to low voltage) using a blue pen. Ae the field lines pependiula to the equipotential lines? 2. Theoetially, should the points 1A to 1D be on an equipotential line? Ae the measued voltage values at points 1A to 1D vey lose eah othe? If not, what is the main soue of eo? Measuement #3: Map equipotential lines fo two-point-hage onfiguation (at 10V and 0 V espetively). 1. Mount the ondutive pape #3 (with pinted side up) on the okboad using two metalli pushpins at the two eletodes whih ae dawn with ondutive ink on the ondutive pape #3. 2. Connet the two eletodes on the ondutive pape #3 to the DC powe supply (HY152A). 3. Connet the blak banana jak (gound) on DMM to the gound (blak banana jak) on the DC powe supply (HY152A). Connet the ed banana jak on DMM to a omfot gip voltage pobe with silione insulated. Selet voltage sale of 20 V on DMM. 4. Tun on the DC powe to 10 V. 5. Attention: To edue measuement eo, the tip of the voltage pobe should be pependiula to the ondutive pape at the touh point. 6. Measue voltages at all the points labeled in Fig. 4. Reod the data in Table 4. 7. Tun the voltage to 0V befoe shut down the DC powe (HY152A). Table 4 Measued voltages at all the points labeled in Fig. 4. Voltage (V) A B C D E 1 ------- 2 ------- 3 4 ------- 5 ------- 13
Data Analysis 3 1. Based on the data in Table 4 daw equipotential lines on Fig. 4 using a ed pen. 2. What is the main ause fo the diffeene in shape of the equipotential lines between Fig. 3 and Fig. 4? 3E 2C 4C 3D 1C 5C 2D 1D 1B 2B 3C 4D 5D 5B 10V 1A 5A 3B 2A 4A 3A Figue 4 Condutive pape #3 4B Wok to be done: 1. Chek that the DC powe (HY152A) is off. If not, tun voltage to 0V then shut it down. 2. Let you TA hek you data pages. If they ae OK, you TA will sign them. 3. Clean up you benh. 14
Lab epot on Expeiments 1 1. You lab epot should be in the equied fomat desibed in the Intodution of the lab manual. 2. Figues 2, 3 and 4 with eoded data should be inluded in you lab epot. 3. Tables 1 to 4 should be inluded in you lab epot. 4. It is equied that the answes to the questions listed in eah data analysis and in Questions and Exeises should be inluded in you lab epot. 5. You an tea those pages out of the lab manual as a pat of you lab epot, whih ontain measued (aw) data and analyzed data, answes to questions. The data sheets must be heked and signed by you lab TA. Questions and Exeises The following thee eletostati hage onfiguations ae in thee sepaated spaes. (1) (2) (3) a Q -Q a a b b b 1. Use ule to daw veto aows with label Ea, Eb, E on eah diagam to indiate the eleti field lines though points a, b, espetively in eah of the thee hage onfiguations. 2. Let Ea, Eb, E be the magnitudes of Ea, Eb, E espetively. Use smalle (<), geate (>) and equal (=) signs to desibe the elationships among E, E, E in the onfiguations: onfiguation (1):.. a b onfiguation (2):.. onfiguation (3):.. 15
3. The eleti potentials at points a, b, ae denoted V a, V b and V espetively. Use smalle (<), geate (>) and equal (=) signs to desibe the elationships among V a, V b and V in: onfiguation (1):.. onfiguation (2):.. onfiguation (3):.. 4. Now a negative point hage q ( ) q Q is plaed at point a. Use ule to daw a veto aow (with a label ) on eah diagam to indiate the dietion of the motion of q in eah of the thee hage onfiguations. F a 16