Brown University PHYS 0060 Physics Department LAB B Measuring the Earth s Magnetic Field

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1 Measuring he Earh s Magneic Field As is well known he Earh has a small magneic field on he order of 0.5 Gauss. I is an ineresing and challenging lab exercise o ry and measure i. elow we lis 5 mehods wih which you can ry and measure i. (Can you hink of any oher mehods?)since his is a wo week experimen you may have ime o ry several of he mehods oulined below. Make sure you lis which mehods you will ry and exacly wha equipmen you will need in your laboraory proposal. In your lab repor you can compare and conras he differen mehods. Which mehod was he easies, which gave he bes resuls? Accurae measuremen and knowledge of he Earh s magneic field has been hisorically very imporan for navigaion (land, sea, air). Mehod Curren alance: The Sargen Welch and Pasco Scienific curren balances can be wired up o measure he Earh s magneic field. y oriening he curren balance along he eas- wes direcion and passing a large curren hrough he balance (on he order of 0 amperes) he force on he curren balance will be given by: F = IL () Where L is he lengh of he curren balance arm and is he norh- souh componen of he Earh s magneic field, he curren balance will allow you o measure F, I and L, hence he norh- souh componen of he Earh s magneic field is given by: F = (2) IL 40508

2 Furher deails can be found in he Pasco and Sargen - Welch curren balance manuals. Mehod 2 Earh Inducor: The Cenco Earh inducor is simply a 22 cm, 000 urn circular coil designed o roae one half urn hrough eiher he horizonal or verical componen of he Earh s magneic field. y measuring he oal charge produced by he induced emf during he half roaion, he componens of he Earh s magneic field can be calculaed and shown o be: h, v = 2 ε ( ) d 2NA (3) Where h, v is he verical or horizonal componen of he earh s magneic field, ε is he emf induced in he coil during he coil flip, N is he number of urns in he coil, and A is he area of he coil. A derivaion of equaion 3 appears in he appendix of his handou. The inegral of he emf ε appearing in equaion 3 can be measured wih a galvanomeer (see Cenco Selecive Experimens in Physics; The Earh Inducor), oscilloscope (he inegral 2 ε( ) d nay be inerpreed as he area under he volage versus ime race displayed on he oscilloscope), or science workshop (we leave i up o you). Once you measure hand v calculae he dip angle v θ = an and compare i wih an experimenal value ha you can measure wih a dip h needle. Also compare your resuls wih abulaed values of he Earh s magneic field in Providence,RI (available on many websies).noe ha you are making hese magneic field measuremens inside he seel srucure of he arus and Holley building so your measuremens may be differen from acceped values

3 Mehod 3: icycle Wheel Coil/Dip Needle Mehod This is a mehod ha was discovered by surfing he web where he aricle A Simple Mehod of Measuring he Earh s Magneic Field by S. Ganci in he Eur. J. Phys 25 (2004) was found. The mehod is quie simple and elegan. An aluminum bicycle wheel of diameer 0.55m is wound wih 50 urns of wire, i is easy o show ha field a he cener of he wheel is uniform and given by he formula: = Nµ I /(2 ) (4) 0 a where N=number of urns of wire, I is he curren in he wire in amperes, a is he radius of he wheel, and µ 0 is he magneic permeabiliy of free space. The dip needle is aligned along he norh souh direcion in he cener of he bicycle wheel coil and a curren is passed hrough he coil o cancel ou he horizonal and he verical componens of he Earh s magneic field (depending on how you orien he bicycle wheel). For insance when he horizonal componen is cancelled he dip needle will be aligned sraigh up and down. Deermine he horizonal and verical componens of he Earh s magneic field ( hand v ) and calculae he dip angle θ = v an, compare i wih he dip angle measured wih your dip needle. Also compare your h resuls wih abulaed values of he Earh s magneic field in Providence, RI (available on many websies). Noe ha you are making hese magneic field measuremens inside he seel srucure of he arus and Holley building so your measuremens may be differen from acceped values

4 Mehod 4: Exension Cord Jump Rope/Oscilloscope Mehod This experimen is similar o mehod 2. You simply make a jump rope ou of an exension cord and aach i o an oscilloscope. y swinging his jump rope perpendicular o he norh- souh componen of he Earh s magneic field you will be changing he flux hrough he loop formed by he exension cord and hence by Faraday s law a volage will be induced in he wire of he exension cord which can be measured by he oscilloscope. The induced emf can be shown o be: da( ) 2π 2π ε ( ) = = A0 cos( ) (5) d T T where A 0 is he area of he swinging loop, T is he duraion of one full swing. This is similar o how elecriciy is generaed in a power plan, by roaing large coils of wire in srong magneic field (a 60 Hz in he U.S.). Noe ha signal produced by his is mehod is raher small and noisy (abou a millivol) so you will probably have o use an amplifier (amplify he signal by abou a 00) o ge a good signal on he oscilloscope. For furher deails see Esimaing he Earh s Magneic Field Srengh wih an Exension Cord, The Physics Teacher vol. 4 5/2003, p Mehod 5: uild Your Own Magneomeer: This mehod may appeal o fuure professional and amaeur scieniss. There are elecronic designs available ha allow you o build a fluxgae magneomeer (essenially a precision ransformer) fairly cheaply. This is an exremely sensiive magneomeer ha has many scienific applicaions (eg (.)you can deec small seasonal variaions in he Earh s magneic

5 field due o he Sun s solar flares and sunspo aciviy, (2.) a scienific biological sudy of fish whose ears have buil- in magnes was done wih a fluxgae magneomeer, see Magnes in guiarfish vesibular recepors, Experenia v.37 (98) p ). Some simple elecronic designs can deec changes in he Earhs magneic field as small as Gauss (or 20 nanoeslas)! Warning: building, esing, and calibraing his scienific equipmen may ake longer han 2 lab periods so eiher plan o spend a weekend or more of your own ime building/debugging he apparaus or if you can ge i o work be prepared o explain in your repor in deail how your magneomeer works, exacly wha you ried, wha you would ry if you had more ime, ec. If you choose his mehod he following references may be helpful:.) Fluxgae Magneomery, R. Noble, Elecronics World + Wireless World (Sep. 99) vol. 97, p ) A Review of Magneic Sensors, J.E. Lenz, Proc. IEEE 78(6) 990 p ) Recen Advances in Fluxgae Magneomery, D.I. Gordon, R.E. rown, IEEE Trans. Magneics v. MAG- 8,,972 p ) Earh s Field Magneomery,W.F. Suar, Repors on Progress in Physics,972,vol. 35, p ) Magneic Measuremens Handbook, J.M. Janicke, Magneic Research Press 2 nd ediion

6 Appendix: Here we derive equaion 3. Recall ha Faraday s law of inducion saes ha when he magne φ hrough a coil of wire changes wih ime an elecromoive force (emf) is induced in he flux ( ) coil which is given by: dφ ε = N (a) d Inegraing equaion 5 wih respec o ime yields: 2 2 dφ ε ( ) d = N d N( φ ( 2 ) φ ( ) ) = (2a) d Here N = he number of urns of wire and φ ) φ ( ) is he change in flux hrough he loop. ( 2 This change in flux can be caused by changing he magneic field in ime, roaing he loop, moving he loop away from a magne, ec. For he case of he earh inducor we are changing he flux hrough he loop by roaing he loop 80 degrees in a consan magneic field (he of he Earh s magneic field). If we flip he coil such ha he norh souh componen ( ) Earh s magneic field is perpendicular o he plane of he loop he change in flux hrough he loop ( φ ) φ ( )) is given by: ( 2 φ ) φ ( ) = NA( cos( 0) cos(80) ) = 2NA (3a) ( 2 Plugging his ino equaion 2a yields:

7 2 ε ( ) d = 2NA (4a) If we orien and hen flip he coil so ha he verical componen of he earh s magneic field ( v ) is perpendicular o i hen similarly we find: 2 ε ( ) d = 2NA (5a) v For a very complee and horough discussion of Faraday s law of inducion see E. Purcell, Elecriciy and Magneism 2 nd ediion,( chaper 7 )