Laboratory Manual Physics_1. Hall effect

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1 AG niversit of Siene an Tehnoog in Crao Department of etronis Laborator Manua Phsis_ Tite: 009 r. a effet periment No. 3

2 . Goa To etermine the sampe onutivit, a oeffiient, mobiit an onentration of arriers.. What to earn? Magneti fie. Magneti fore F. a effet. Current ensit. Drift spee. esistivit. Conutivit. Mirosopi vie of Ohm's a. The reationship beteen the eetri fie an potentia ifferene. etromagnet histeresis. 3. akgroun Consier a semionutor sampe pae in the magneti fie that is in the -iretion (Fig. ). I 0 v - Fig.. Sampe onfiguration in a a measurement set up. A retanguar bok is use as the sampe. Suppose e pass a urrent through that sampe perpeniuar to the magneti fie, sa in the -iretion. The harge arriers are eetrons an the rift ith rift spee v in the opposite iretion.. At the instant shon in Fig. a, an eterna magneti fie pointing out of the pane of the figure has just been turne out. Magneti fore F ats on eah rifting eetron, pushing it toar the eft ege of the sampe.

3 As time goes on, eetrons move to the eft piing up on the eft ege of the strip, eaving unompensate positive harges in fie positions at the right ege. The separation of positive an negative harges proues an eetri fie ithin the sampe pointing from right to eft (Fig. b). This fie ats an eetri fore F on eah eetron tening to push it to the eft. In an equiibrium, the eetri fore F baanes the magneti fore F so as to keep urrent foing aong the -iretion. F q F ev v F ( v ) (,0,0), ( 0,0, ) v q F e, (,0) 0 psurge of the eetria fie in the -iretion is ae a ffet. A a potentia ifferene is assoiate ith the eetri fie aross the sampe of ith as foos: Consiering the baane of fores on the harge arriers e see that : e ev The tota urrent ensit is aoring to the mirosopi Ohm s La ies: e j e ne j j ne j nev hih The a oeffiient is efine as: j ne Note that the sign of iniates if the sampe is n-tpe or p-tpe. When the arriers are eetrons, the a oeffiient is negative. When the arriers are hoes, the a oeffiient is 3

4 positive. The a oeffiient enabes aso estabishing the onentration of the arriers in the sampe n. Carrier onentration is the number or arriers per unit voume. I I - v - F F F Fig.. The iea of a effet etron veoit v is taken to var inear ith the fie : v µ hih is on true uner ohmi onition. The proportionait onstant beteen v an is µ mobiit - an it an be epresse as : µ v j ne j ne j j Votage is ae the onutivit votage i.e. votage beteen the ontats in the iretion of the urrent an is ae the a votage an it is the resutant votage beteen the ontats that are perpeniuar to the iretion of the urrent. The mobiit µ is use to epress onutivit σ neµ. Taking into aount the imensions of the sampe, the tota urrent is reate to the ensit of harge arriers n an their rift veoit v as: I j S j ( env )( ) 4

5 i.e. as the prout of the urrent ensit j an the ross-setiona area of the sampe S. Fina, e obtain the fooing epressions for the : µ σ j I I I σ neµ µ I 4. quipment etromagnet. a probe. Measurement pane ontaining DC poer supp to furnish urrent to a probe, votmeter of high input impeane to measure a votage, votmeters to measure onutivit votage an votmeter to measure votage aross the resistor 000 Ω ±Ω onnete in series ith the a probe. 5. Measurements Fig. 3 shos the measurement set-up. I Z V mv. mv Fig. 3. The measurement set-up. Fig. 4 shos the vie of the front of the measurement pane. eetromagnet. Fig. 5 shos the vie of 5

6 Fig. 4. Measurement pane Knob to set the iretion of urrent in ois Sith on/off Varia to ontro urrent in eetromagnet ois Fig. 5. etromagnet. Turn the measurement pane on (Fig. 4).. Push the knob an then set ith the oer potentiometer on the front of the measurement pane. The instrutor i hoose the ertain vaues of for our eperiment. 6

7 is a votage aross the resistor 000 Ω ±%, hih is onnete in series ith the a probe an it is use to auate urrent I foing through the a probe: I. 3. Turn the eetromagnet on (Fig. 5). Varia to ontro urrent in eetromagnet ois shou be set for ero urrent. 4. Set the iretion of urrent through the eetromagnet ois " to the right" using the knob ith a hite arro on the front of eetromagnet. 5. Push the knob an using the upper potentiometer on the front of the measurement pane set for ero. 6. Set the urrent through the eetromagnet ois for a ertain vaues given b the instrutor. Do not eee eetromagnet urrent of 6A. Aas graua inrease an erease urrent in eetromagnet ois. Large inutive votage surges ma amage the insuation of ois. 7. For ever setting of the urrent measure an votage using votmeters inue in the measurement pane. Push the knob an measure the a votage. Push the knob an measure the votage onutivit. 8. Derease the urrent in eetromagneti ois to ero an hange the iretion of urrent in ois "to the eft" using the knob ith hite arros on the front of eetromagnet. After this hange ajust a votage to ero using the upper potentiometer on the front of the measurement pane. 9. Set the urrent through the eetromagnet ois for the same vaues as in the point 7. For ever setting of the urrent measure an votage. 0. se the eetromagnet harateristi f(i em ) to estabish the magneti fie beteen the eetromagnet poes on the basis of urrent I em in eetromagnet ois (Fig. 6).. Write on the resuts in the Tabe. 7

8 6. Data haning. Write on the resuts in the Tabe. Dra the reationships: f( ), f( ), f( ) for eah that orrespons to I em,.5,,.5, 3.0, 3.5, 4.0 A, respetive. 3. For eah reationship fin the "best fit" straight ine through the ata using the inear regression metho, fin the regression oeffiients of the ine a an b an the unertainties of oeffiients a an b. 4. Fin the arrier mobiit µ, a oeffiient an onutivit σ of the a probe using the reationships: µ σ an the proper inear regression equations. e arefu: use the one parameter inear regression (b0) 5. Fin the onentration of arriers n on the basis of the reationship 6. Cauate the unertainties µ,, σ, n.. ne Literature:. aia, esnik Funamentas of Phsis - 8 th eition, John Wie 007, 8

9 Tabe. esuts [V] I em [A] [Wb/m] [mv] [mv] [mv] [mv] [mv] [mv] 4,5,5 3 3,5 4 5,5,5 3 3,5 4 6,5,5 3 3,5 4 +, + Dimensions of the a probe: (3,7 ± 0,) 0 3 m, (,7 ± 0,) 0 3 m, (,5 ± 0,) 0 3 m, 0 (,4 ± 0,) 0 3 m. 9

10 etromagnet harateristi f(i em ) 0,45 0,4 0,35 0,3 [Wb/m ] 0,5 0, 0,5 0, I em [A] Fig. 6. etromagnet harateristi 0

11 6. ints to the report.. f( ) for onst. On the basis of Tabe reate the sub-tabe: I em [A] A [mv] [mv] µ [...].. Wb/m µ [...] µ Dra the pot f( ). Fin the regression oeffiient a an the unertaint σ a for these ata. se the one parameter inear regression (b0) Compare the sopes: a µ a µ µ a [ m] m m Fin the unit of µ: [ µ ] Wb Wb Vs m m Cauate the unertaint µ/µ using the metho of ogarithmi erivative: µ a Cauate ogarithm of the both sies of the equation: n µ n a + n n n Derivate both sies of the equation: µ µ a a here: a σ a is the unertaint of the regression oeffiient a 3 3 0, 0 m, b 0, 0 m are the geometria unertainties of the probe,

12 is the unertaint of the estabishe on the basis of the eetromagnet harateristi. ui-up suh sub-tabes for eah vaues of I em,.5,,.5, 3.0, 3.5, 4.0 A an respetive. Cauate µ an µ/µ in eah ase an oet the resuts in one fina tabe [Wb/m] µ [...] µ [...] µ.. f( ) for onst. On the basis of Tabe reate the sub-tabe: I em [A] A [mv] [mv] Η [...].. Wb/m [...] Dra the pot f( ). Fin the regression oeffiient a an the unertaint σ a for these ata. se the one parameter inear regression (b0). Compare the sopes: a a a Fin the unit of. Cauate the unertaint of / using the metho of ogarithmi erivative: ui-up suh sub-tabes for eah vaues of I em,.5,,.5, 3.0, 3.5, 4.0 A an respetive. Cauate an / in eah ase an oet the resuts in one fina tabe

13 [Wb/m ] [...] / [...] 3. f( _average ) On the basis of Tabe reate the subtabe: I em [A] A [mv] [mv] σ [...].. Wb/m σ [...] σ Dra the pot f( ). Fin the regression oeffiient a an the unertaint σ a for these ata. se the one parameter inear regression (b0) Compare the sopes: a σ a σ a σ Fin the unit of σ. Cauate the unertaint of σ /σ using the metho of ogarithmi erivative: ui-up suh sub-tabes for eah vaues of I em,.5,,.5, 3.0, 3.5, 4.0 A an respetive. Cauate an / in eah ase an oet the resuts in one fina tabe [Wb/m ] σ [...] σ /σ[...] 3

14 4. n e emember: e C. Determine the unit of n. Cauate the unertaint n using the tota ifferentia metho: n δn δ Coet the resuts in the fina tabe: [Wb/m ] n [...] n [...] pate: , b arbara Diuria 4

Chapter 2: One-dimensional Steady State Conduction

Chapter 2: One-dimensional Steady State Conduction 1 Chapter : One-imensional Steay State Conution.1 Eamples of One-imensional Conution Eample.1: Plate with Energy Generation an Variable Conutivity Sine k is variable it must remain insie the ifferentiation