Problem 1: The Earth s Horizontal Magnetic Field

Transcription

1 Eperimentl competition Problem 8 April 009 Pge of 4 Problem : The Erth s Horizontl Mgnetic Field This is to determine the horizontl component of the Erth s mgnetic field H using smllmplitude oscilltion of cylindricl br mgnet. The mgnet is to oscillte in the combined sttic fields of the Erth nd tht due to squre coil. Y supporting string Z O squre coil of sides nd N turns P mgnet of length L nd rdius r X i i Figure The eperiment is to be done in three sections. Section is derivtion of formule to be used in Section. Apprtus Ech student is provided with pprtus s shown in Figure :. squre coil of resistnce 5. ± 0. Ω nd 30 turns. smll cylindricl mgnet of mss 5.0 ± 0. g with nylon strings. 3. voltmeter (for mesuring the potentil difference cross the coil only) 4. power supply (plced under the tble to void the interference of its mgnetic field) 5. wooden stnd 6. stop wtch 7. ruler 8. protrctor 9. white lbel (you cn write on it) 0. color cly. grph ppers. n electricl cord

2 Eperimentl competition Problem 8 April 009 Pge of Pltform not used DO NOT chnge these connections. Figure Wrning Use the multi-meter to mesure only the voltge difference of the coils. Using the multi-meter in other modes cn destroy the power supply!!!

3 Eperimentl competition Problem 8 April 009 Pge 3 of 4 Section [ point] i P t is given here tht the mgnetic flu density P t perpendiculr distnce from the middle of stright current element i is Figure 3 P = μ0i π ( ) +.. (i) 7 where μ0 = 4π 0 henry per metre, the permebility of free spce. Use this epression to show tht the epression for the mgnitude of the mgnetic flu density from the squre coil t point P in Figure is given by p μ 0 in = π (ii) t is lso given here tht the period of smll-mplitude oscilltion of the mgnet in the net mgnetic field is T = π.. (iii) m where m is the mgnetic moment of mgnet with mss M, nd is its moment of inerti bout the is through its centre of mss L r = M (iv)

4 Eperimentl competition Problem 8 April 009 Pge 4 of 4 Section [0.8 point] For the eperiments in Section you hve to lign the mgnet in the position s shown in Figure. f the length of the string is too smll, the torsion of the string cnnot be neglected in the oscilltion of the mgnet. Perform pproprite mesurements (sy, oscilltion of mgnet in Erth s mgnetic field lone) to justify tht we cn ignore the torsion of the string. You re not required to plot grph. Section For the following eperiments (in, b, nd c), you hve to lign the mgnet in the position s shown in Figure. Mesure nd write down the vlue of the distnce between the centre of the mgnet nd the top surfce of the pltform. [0. point] ) Coil s mgnetic field nd Erth s horizontl mgnetic field in the sme direction [5 points] Wrning Plese connect the coil to the power supply nd leve it on for t lest 5 minutes. Mesure periods of oscilltion for different vlues of the combined field strength when the coil s mgnetic field nd Erth s mgnetic field re in the sme direction. Drw stright line grph nd compute the vlues of their errors. H nd the mgnetic moment m from this grph nd estimte b) Erth s mgnetic field only [ point] Use the vlue of m from () nd the period of oscilltion of the mgnet br in the bsence of the Coil s mgnetic field from Section to clculte gin the vlue for error. H nd estimte its c) Coil s mgnetic field nd Erth s horizontl mgnetic field in opposite directions [ points] y reversing the connection t the power supply, find the equilibrium position 0 long the X- direction between Erth s mgnetic field nd the opposing mgnetic field from the coil. Use the vlue of 0 to clculte gin the vlue for H nd estimte its error. ********************

5 Eperimentl competition Problem 8 April 009 Pge of 5 Problem : Oscilltion of Wter-Filled Vessel The student is required to perform non-destructive mesurements in order to determine the thickness t of n luminium vessel whose cvity is completely filled with wter. The luminium vessel is composed of cylinder nd two end pltes. The cylinder is of length L nd outer rdius R. The totl length of the vessel is h. The thickness of both end pltes is 0.60 cm (see Figure ). You cn neglect the error of this thickness. n this problem, plese use grmme nd centimetre s units for mss nd length, respectively cm Y R L wter O h X g 0.60 cm CM mss M Figure t cm Figure Figure shows the so-clled bifilr suspension of mss M. The two strings re ech of equl length. The period T of smll-mplitude oscilltion of M is T = π g M.. (i) where is the effective moment of inerti bout the verticl is through the centre of mss of M nd g is the ccelertion due to grvity t ngkok ( g 978 cm s ) =. This eperiment consists of two prts. Section concerns derivtion of formule nd Section concerns the ctul eperimenttion.

6 Eperimentl competition Problem 8 April 009 Pge of 5 Apprtus Ech student is provided with:. wter-filled vessel. stnd 3. stop wtch 4. ruler 5. nylon string 6. protrctor 7. msking tpes 8. knife (not shown in the figure below)

7 Eperimentl competition Problem 8 April 009 Pge 3 of 5 Section [.0 points] The student is to derive epressions in terms of R, Lt, nd the density ρ of luminium of the following quntities, [see Figure ] i) mss ( m ) of the cylindricl body of the vessel, ii) mss ( m ) of ech end plte, iii) mss ( m 3 ) of wter in the whole cvity, iv) the totl mss ( M ) of the wter-filled vessel, nd v) the effective moment of inerti, y, bout the Y-is, of this wter-filled vessel (see Figure ), ssuming tht the wter is idel fluid. Then perform mesurements of R, h, L. y substituting the vlues, derive epressions in terms of t for the quntities i)-v) bove. The luminium density ρ =.70 g/cm 3 nd the wter density is.00 g/cm 3. Hint: L m R Y R O m X = m R + R = m R 4 + R ( ) y ( ), L = m Thin rod of length L Thin cylinder of inner rdius R nd outer rdius R Figure 3

8 Eperimentl competition Problem 8 April 009 Pge 4 of 5 Section Figure 4 Figure 5 ) Angulr oscilltion bout the is of symmetry [4.0 points] For one fied vlue of, perform precise mesurements of the period T y for smll-mplitude oscilltion s in Figure 4. Then compute the vlue of the thickness ( t ) of the cylindricl wll. Estimte the eperimentl error Δ t for the thickness. Compute lso the vlues of m, m, m3, nd M using this vlue of t.

9 Eperimentl competition Problem 8 April 009 Pge 5 of 5 b) Angulr oscilltion bout the centrl is perpendiculr to the length [.8 points] Chnge the bifilr suspension of the vessel to tht of Figure 5 nd mke similr mesurements s in (). Then use the vlue of the period of oscilltion just found together with the vlues of tm,, m3, M found in () to compute the vlue of the effective moment of inerti X-is (see Figure nd Figure 5). Compute lso the theoreticl estimte of the vlue of Ep of the vessel bout the Theo bsed on the vlue of t found in () ssuming tht the whole of the computed mss of wter found in () is now constrined to tke prt in the oscilltory motion of the vessel. c) Compring eperimentl nd theoreticl vlues of the moment of inerti Wht is the difference ( Δ ) between the vlues of Theo nd Ep? [. points] Do you consider this difference sttisticlly significnt? Estimte the percentge of the mss of wter tht tkes prt in the oscilltory motion in (b), ssuming this wter to be circulr discs dhering to the end pltes. Hint: ( ) ( 0.6 cm) 0.6cm ( ) Theo L R + R t R L L R t = m m m *********************