Hall effect. Formulae :- 1) Hall coefficient RH = cm / Coulumb. 2) Magnetic induction BY 2

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1 Page of 6 all effec Aim :- ) To deermine he all coefficien (R ) ) To measure he unknown magneic field (B ) and o compare i wih ha measured by he Gaussmeer (B ). Apparaus :- ) Gauss meer wih probe ) Elecromagne 3) Consan curren source o Pass curren hrough elecromagne 4) Specimen of semi-conducing maerial wih connecing erminals o Pass curren (I )hrough i [Green wire erminals] and o measure he all volage (V ) [Red wire erminals] 5) Consan curren source o Pass curren (I ) hrough semiconducor specimen 6) Milli-ammeer o measure I 7) Volmeer o measure all volage (V ) [5,6 &7 are fixed o all effec board] 8) Connecing erminals. V 3 Formulae :- ) all coefficien R cm / Coulumb I B V ) Magneic inducion B Gauss I R Where V all volage developed beween he upper and lower faces of he specimen (V) I Curren sen hrough he specimen (A) Thickness of he specimen (Disance beween he side faces) (cm) Theory :- As per he saemen of all effec when a magneic field is applied perpendicular o a curren carrying curren conducor, a poenial difference is developed beween he opposie faces of he conducor which is perpendicular o boh curren and magneic field direcions. Consider a uniform hick semiconducor (or) meal srip (specimen) placed wih is lengh parallel o -axis. A curren I is passed hrough he conducor along -axis. A magneic field B is applied along axis, hen he charge carriers experience a force (F) perpendicular o - plane i.e. along Z- axis as per he Fleming s Lef and rule as shown in he figure. If elecrons are he charge carriers, hey accumulae a he upper surface. This surface acquires negaive charge while he lower surface ges posiive charge and some poenial difference is developed beween hese wo surfaces. This is elecrosaic field. This volage is called all Volage (V ) and he Elecric field is called all elecric field (E ). (In his case he all volage V is negaive, his ve sign indicaes he charge carriers are negaively charged i.e. elecrons. If i is +ve he charge carriers are holes.

2 Page of 6 These F and E ac in opposie direcions. i.e. The forces due o magneic field and elecrosaic field on charge carrier ac in opposie direcion. Ulimaely, he ne force on he charge carrier becomes zero. q (V d B ) + q E 0 (or) (V d B ) + E 0 ere V d is he drif velociy of he charge carrier J/nq. Where J Curren densiy q Charge of he carrier n No. of charge carriers/cm 3 ere is anoher physical quaniy called all coefficien which is equal o he reciprocal of he amoun of charge per uni volume. E V allcoefficien R & ( ) nq J B d ( I A) B R V ( d ) ( I d) B V I B Where Thickness of he specimen d eigh A Area of cross-secion This experimen can be used o find ) he naure of he charge carrier ) he all volage 3) curren hrough he specimen 4) applied magneic field 5) Conduciviy of he conducor ec. Bu for he presen i is confined o measure he unknown magneic field. Descripion :- This experimenal se-up consiss of 3 main insrumenal pars. ) Digial Gaussmeer wih all probe :- all probe cable is o be plugged-in o he socke of he digial gaussmeer and he power should be given o he gaussmeer. This probe also operaes basing on he principle of all effec. A small curren sen hrough he all probe develops a small all volage when i is placed in a magneic field and he all volage is amplified by an amplifier whose oupu is calibraed in Gauss which direcly gives he magneic inducion (B) value in he gaussmeer.

3 Page 3 of 6 ) Elecromagne wih consan curren supply :- Two insulaed Copper wires are wound on wo sof iron bars whose faces are facing each oher. When a D.C. curren (in amperes) from a consan curren source is sen hrough he coils, he faces of he iron bars acs as he wo poles of a magne (elecromagne) creaing a magneic field in beween hem. The gap beween poles can be varied, in general, he gap should be cm. 3) all effec board wih all probe semi-conducor specimen mouned on sun mica PCB :- A specimen of recangular semi-conducor slab in which all effec is o be sudied is fixed o a prined circui board (PCB) wih he help of 4 supporing erminals. Ou of 4 erminals, erminals are along he lengh and hese (Middle & green) erminals are conneced o he curren source of he all effec board. The oher erminals are along he widh and hese (Red) erminals are conneced o he Volmeer of he all effec board. The all effec board has uses. A) To pass curren (I ) hrough he specimen & o measure ha curren. B) To measure he all volage (V ) developed across he specimen. To mee hese wo purposes a wo mode swich is arranged o he digial meer of he board. Firs mode is o measure he curren (I ), sen hrough he specimen and he second mode is o measure he all volage (V ) developed across he specimen. Procedure :- This experimen comprises of wo pars ) Measuremen of all coefficien (R ) ) Measuremen of applied magneic field (B y ) by using all effec (Applicaion of all effec) Measuremen of all coefficien (R ) In he s par give he power supply o he gaussmeer. Keep he range swich of he gaussmeer in minimum range and adjus he zero adjusmen such ha he reading in he gaussmeer shows zero. If he gaussmeer does no come o zero, hen keep is value a minimum and ake i as zero error. This zero error is o be correced while aking he final reading of magneic inducion (B ). Now adjus he disance beween he poles of he elecromagne equal o cm & pass A curren hrough he elecromagne from is consan curren source, hen some magneic field (B ) is creaed beween he poles of elecromagne. This magneic field or magneic inducion (B ) is measured by he gaussmeer by keeping is probe beween he poles of he elecromagne. The posiion of he probe is adjused such ha he fla faces of he probe are perfecly verical and perpendicular o he magneic field. Then he gaussmeer shows maximum value.

4 Page 4 of 6 Keep he mode swich of he curren source of he semiconducor specimen in he curren mode (ere also he zero error and zero correcion are o be made) and pass 0.5 ma (or) ma curren (I ) hrough he specimen. Place his specimen beween he poles of he elecromagne such ha he faces of he specimen are perfecly verical and noe he volage (V ) developed beween he upper and lower faces of he specimen afer urning he mode swich of he curren source of he specimen in o volage mode. Now reverse he posiion of he specimen (up side down and vice versa) and keep i beween he poles once again and measure he volage (V ) developed beween he upper and lower faces of he specimen. ( V ~ ) Now calculae he all volage V V Noe he values of I, V, V in he able and calculae V. Repea he experimen for differen values of I by increasing is value in equal inervals of 0.5 ma. Graph :- Draw he graph by aking he curren hrough he specimen I on - axis and all volage V on - axis. This gives a sraigh line passing hrough he origin. Take a paricular value of I and noe is corresponding value of V Noe he hickness () of he specimen which was noed on he board of he specimen. Subsiue he values of I, V, and B in he formula and calculae all coefficien (R ) Measuremen of applied magneic field (B y ) In he nd par of he experimen keep he curren hrough he semi-conducor specimen (I ) a consan value of ma and pass A curren hrough he elecromagne and measure he volages V and V by placing he specimen beween he poles of he elecromagne & from ha calculae he all volage V (as measured in he s par). Also measure he magneic inducion (B ) wih gaussmeer by placing is probe beween he poles of elecromagne. Subsiue he values of I, V, and all coefficien R (as calculaed in s par ) in he formula and calculae value of applied magneic field (B ). The experimen is repeaed by increasing he curren hrough he elecromagne (i means by changing he magneic field B ) in equal inervals of 0.5 A. Noe he values in he able. In he nd par he experimen he magneic field B is measured wih gaussmeer as B and also measured by using he all effec as B. These wo are compared in he able. Precauions :- ) Elecromagne power supply should be conneced o a 3 pin main socke having good earh connecion. ) Swich ON or OFF he power supply a zero curren posiion. 3) Adjus he disance beween he poles of he magne nearly cm, hen only he gaussmeer shows correc reading. Resuls :-

5 Page 5 of 6 Table - Thickness of he semi-conducor specimen Curren hrough he Elecromagne A cm. Applied magneic field measured wih gaussmeer B S. No Curren hrough The specimen I (ma) Measuremen of all Volage V (V) ( V ~ ) V I V V V S. No Curren hrough he elecromagne (A) Table - Curren hrough he semi-conducor specimen I ma Measuremen of all Volage V (V) V I V V ( V ~ V ) Magneic inducion measured wih all V effec B I R (Gauss) Magneic inducion measured wih gaussmeer (B ) (Gauss)

6 Page 6 of 6 More accurae mehod o measure V :- In he above wo pars of he experimen i.e. while measuring R and B he all volage (V ) shall be measured firs. In measuring V, he following is he accurae mehod. Firs some curren (A) is sen hrough he elecromagne o creae he magneic field beween he poles of he magne. Now he curren I (ma) is sen hrough he semiconducor specimen and pu he specimen beween he poles and measure he volage (V ) developed across he specimen (afer swich over he mode swich in o volage mode) as said above. Now he curren in he specimen is reversed by inerchanging he curren leads of he specimen and measure he volage (V ). Then all volage V (V ~V )/. Now reverse he curren direcion in he elecromagne by inerchanging is curren leads. Once again measure he volages (V 3 & V 4 ) developed across he specimen by placing he specimen beween he wo poles, before and afer reversing he curren direcion in he specimen by iner changing is curren leads. Now he all volage V (V 3 ~V 4 )/. Then he all volage V ( V + V ) The above mehod is o be adoped while measuring V.