II. Equipment. Magnetic compass, magnetic dip compass, Helmholtz coils, HP 6212 A power supply, Keithley model 169 multimeter

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1 Magntic fild of th arth I. Objctiv: Masur th magntic fild of th arth II. Equipmnt. Magntic compass, magntic dip compass, Hlmholtz s, HP 6212 A powr supply, Kithly modl 169 multimtr III Introduction. IIIa. Magntic fild of th arth. Th arth bhavs lik a larg magnt which crats a magntic fild around th plant. This larg magnt has its south pol approximatly at th gographic north pol of th arth. A schmatic of th arth magntic fild is givn in Fig.1. Th magntic fild lins mrg from th south gographic pol, surround th arth, and sink into th arth north gographic pol. Th rd arrow indicatd th dirction of th magntic fild at a location in th north hmisphr. Th prsnc of th arth magntic fild is attributd to th prsnc of a moltn iron cor at th cntr of th arth. From Fig.1 it can b sn that th magntic fild can b dcomposd into a horizontal and a vrtical componnt at any location on th arth such as uffalo. In Fig.2 w show th top viw of a magntic compass. This is a prmannt magnt in th form of a ndl that can rotat about a vrtical axis. Th magntic ndl will align itslf and bcom paralll with th horizontal componnt of th arth magntic fild h. Thus th axis of th ndl points along th south-north axis. Th dg of th ndl markd N points to th gographic north pol of th arth. This proprty was discovrd by th Chins, was usd for navigation and contributd to th grat discovris of th 15 th cntury. A scond typ of compass is calld a dip ndl and it is a prmannt magnt in th form of a ndl that can rotat around a horizontal axis which is prpndicular to th arth magntic fild. Th sid viw of such a dip ndl is shown in Fig.3. Undr ths circumstancs th dip ndl with align itslf with arth magntic fild as shown in Fig.3. Th angl btwn th magntic fild and th horizontal is known as fild inclination or mor simply as dip angl. In Fig.4 w show a schmatic of th dcomposition of th arth magntic fild into a horizontal componnt h and a vrtical componnt v IIIb. Hlmholtz s. Ths ar shown in Fig.5. Each has a diamtr D and consists of N turns of wir. Thy ar positiond so that thy hav a common axis and th distanc btwn th cntrs is adjustd so that it is qual to half th diamtr D. Undr ths conditions th Hlmholtz s gnrat a magntic fild along th common axis of th s which is uniform in th vicinity of th midpoint btwn th cntrs. Th magntic fild is givn by th quation: 16 Ni D (qs.1) 1

2 Hr th currnt i is masurd in Amps, is masurd in tsla, D m, N 320, and 0 is a constant qual to T.m/A If w substitut th numrical valus for 0, D, and N w gt th quation: 6 in Tsla i in ma (qs.2) Th Tsla is a vry larg unit, much largr than th magntic fild of th arth. For this rason in this xprimnt w will us th smallr unit of Gauss baring mind that 1 Tsla = 10,000 Gauss 2 in Gauss i in ma (qs.3) IIIc Masurmnt of th horizontal componnt th total magntic fild of th arth. h of th arth magntic fild and Th stup for th masurmnt of h is shown in Fig.6. A magntic ndl is placd at th cntr of a pair of Hlmholtz s. Th Hlmholtz s ar connctd to a powr supply which provids th currnt. Th s currnt i is masurd by th ammtr in th circuit. Th Hlmholtz s ar orintd so that th plans of th two s ar paralll to th north-south dirction. Th magntic fild gnratd by th Hlmholtz s and th horizontal componnt of th arth s magntic fild h, as wll as th nt magntic fild nt ar shown in Fig.6. Ths filds ar also shown sparatly in Fig.7. Th magntic ndl at th cntr of th Hlmholtz s always aligns its axis with th nt magntic fild. Whn th s currnt is zro w hav that 0 and thus nt h nt. As a rsult, th magntic ndl is alignd along th north-south dirction. If w pass a currnt i through th s th ndl will align its axis with nt and th ndl axis will now form an angl with th north-south dirction, as shown in Fig.6. If w rfr to Fig. 7 w hav that: tan. If w solv this quation for h w gt: h h (qs.4) tan caus quation 4 involvs th tangnt of th angl, th stup of Fig.6 is known as h th tangnt compass. Rfr now to Figur 3. In this cas w hav: cos, whr is th nt magntic fild of th arth. If w solv this quation for w gt: 2

3 h (qs.5) cos IV. Procdur IV1. Align th plans of th Hlmholtz s so that thy ar paralll to th north-south dirction as shown in Fig.6. IV2. With zro currnt in th s, rotat th cas of th compass so that th ndl point to th zro rading. IV3. In this sction w will masur th avrag currnt that rsults in a dflction of 30 dgrs. a. Choos th currnt polarity so that th ndl dflcts to th right by 30 dgrs. ring th currnt to zro. Rpat 5 mor tims. Rcord your data in tabl 1 b. Rvrs th currnt dirction so that th ndl dflcts to th lft by 30 dgrs. ring th currnt to zro. Rpat 5 mor tims. Rcord your data in tabl 2. IV4. In this sction w will masur th avrag currnt that rsults in a dflction of 60 dgrs a. Choos th currnt polarity so that th ndl dflcts to th right by 60 dgrs. ring th currnt to zro. Rpat 5 mor tims. Rcord your data in tabl 3 b. Rvrs th currnt dirction so that th ndl dflcts to th lft by 60 dgrs. ring th currnt to zro. Rpat 5 mor tims. Rcord your data in tabl 4. IV5. Align th dip ndl so that it points along th north-south dirction. Masur th dip angl. V. For th rport V1. From tabls 1 and 2 find th avrag valu of th currnt i that producs a dflction of 30 dgrs. Us quation 3 to calculat th magntic fild. Us quation 4 to dtrmin th horizontal componnt of th arth s magntic fild V2. From tabls 3 and 4 find th avrag valu of th currnt i that producs a dflction of 60 dgrs. Us quation 3 to calculat th magntic fild. Us quation 4 to dtrmin th horizontal componnt of th arth s magntic fild. h. V3. Us quation 5 to dtrmin th nt magntic fild of th arth. h 3

4 Fig. 1 Fig.2 N h S Magntic compass (top viw) 4

5 Fig.3 S horizontal Dip magntic ndl (sid viw) N Fig.4 v h 5

6 Figur 5 Fig.6 north (top viw) nt Hlmholtz θ Hlmholtz h θ ndl south Powr supply Ammtr 6

7 Fig.7 nt h Top viw 7

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