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# Class Note for PH 106 at UA-Generl Physics WCalc II

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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Alabama - Tuscaloosa taught by a professor in Fall. Since its upload, it has received 15 views.

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Date Created: 02/06/15

INTERACTION OF A MAGNETIC MOMENT WITH A MAGNETIC FIELD INTRODUCTION A dipole magnetic moment 1 such as that of a permanent magnet will experience a torque when placed in a magnetic eld B The torque 2 is given by 2quot 1x B 1 This torque tends to align the moment along the magnetic eld just as a compass needle tries to line up with the earth s eld If 6 is the angle between 1 and B the magnitude of the torque is r uBsin6 H uBQ 2 The latter equality holds for small values of 6 to within 1 for 6 lt 15 QUESTIONS Here are some things to think about before you go on This experiment involves some rather complicated mathematical expressions and it is important to know ahead of time in a simple way what you are going to do 1 What kind of motion do you expect will result if a dipole is placed in a magnetic eld pushed aside a little and released Consider for example what a compass needle will do if it is frictionless 2 How will the motion change qualitatively if the magnetic eld is increased in strength ie will the motion be faster slower or unchanged 3 How would you expect this motion to depend on the moment of inertia I of this dipole INTRODUCTION CONTINUED Did you gure out that this dipole will oscillate just like a pendulum or a mass on a spring This is true because the restoring torque is proportional to the angular displacement Therefore a magnet suspended in a magnetic eld and disturbed from equilibrium will undergo simple harmonic motion with period T27z 3 Here I is the moment of inertia of the permanent magnet about its center of mass This experiment will explore the interaction of a small permanent magnet with a combination of the earth s eld and the eld produced by a coil of wire of radius R and with N turns of wire The eld of such a coil along its axis is given by B uUNi Rsin uUNi R2 COIL 2 3 2 739 2 2 2 R x y where x is the distance along the axis from the coil plane and r and 4 are de ned in Figure l for x0 g0 N i 2R 4 Figure 1 The apparatus tobe used IS drawn m Flgure 2 Ixugnel coil phm poinlex pmmlcmr coll plane prormclor ln power qrpplv Figure 2 The posltlon othe coll plane wth respect to the earth s magaetro fleld IS adjustable and the angular posltlon ofthe magnet can be determmed by the protraetor The magnet posltlon can also be adjusted along the coll axls to vary x Note that only the horlzontal component ofthe earths magaetro fleld Bzm ls effectlve m produclng a torque on the magnet why7 Hence the total fleld to be used m Equatlons l 2 and 3 IS 1 Bcon BEAR 5 In thls erperlment you wlll flrst of all allgn Boon Wth Baum and measure the perlool othe magiet s osclllatlon as a functlon Ofl and x Thls wlll allow determmatron ofBamnandyermoatron othe funotlonal form oquuaLlon 4 You wlll nert balance out the torque othe earth s eld by means othe coll fleld to explore the yeotorpropertres othe fleld Fmally you wlll determme theyalue ofu andl PROCEDURE Part 1 First choose a spot in the room that is suf ciently isolated from magnetic materials Do this by finding a location such that a compass points to the magnetic north Place the apparatus at this location and align thebase and coil axis in a northrsouth direction Connect the coil to the power source Limit the current you semi through the coil to about 1 ampere Determine T as a iunction of current i between 710 and 10 amperes for about 10 values negative current means Ecoquot opposes 13mm Plot 112 vs currenti You will mm to use Excel for this and subsequent plots Yourplot should look like Figure 3 Figure 3 This plot should be described according to Equations 3 and 4 by 1 u m1 warm 2 2 B 7 2 1 2 T 47 I 87 IR 47 I The cunent 1H the intersection ofthe lines with the i axis corresponds to infinite period which means zero B eld Thus iH can be interpreted as the cunent in the coil necessary to produce a coil eld equal and opposite to 13mm ie N oiH BEARTH BCOIL 6 2R Determine 13mm from Equation 6 and determine the quantity u I from the slopes ofyourplot You should determine uncertainties omeTH from the uncertainties in the slopes ofpans 1 and 2 and you should compare your value to the accepted value namely 5 x 10395T Note In part 1 the two lines may not intersect the abscissa axis at the sane point because of experimental error You must then nd some satisfactory procedure for assigning avalue to lg Part 2 We now wish to demonstrate the vectornature ofB Set the coil axis to some de nite angle from the north 7 let us use 90 Find avalue ofthe coil current such that the magnet angle bisects the coil angle in this example the magnet would be made to point to 45 The magnetic eld ofthe coil will then equal 13mm you should prove this to yourselt From the current in the coil nd 13mm from Equation 6 Turn part1 Excel graph value ofBEARTH part2 value othnerrr Answers to questions on page 1

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