University of Illinois at Urbana-ChampaignDepartment of PhysicsPhysics 401 Classical Physics LaboratoryExperiment 67HALL PROBE MEASUREMENT OF MAGNETIC FIELDSTable of ContentsSubjectPageIntroduction. 2Magnetic Fields Due to Current Loops. 2Experimental procedureA. Measurement of the Helmholtz Coil Field.9B. Measurement of the Solenoid Field. 13Calculations and Discussion. 15Report. 15Appendix I Theory of the Hall Effect .16Revised 3/2006.Copyright 2006 The Board of Trustees of the University of Illinois. All rights reserved.

Physics 401 Experiment 67Page 2/31Hall Probe Measurement of Magnetic FieldsIntroductionJGWhereas no convenient technique exists for measuring arbitrary electric fields E , severalJGtechniques are available for the practical measurement of magnetic fields B . These include theobservation of the force exerted on a current-carrying wire, the emf induced in a rotating coil, thefrequency at which certain atomic or nuclear systems exhibit resonant absorption, and the Hallvoltage induced in a current-carrying conductor. The latter technique utilizing the Hall effecthas the advantage of requiring only a very small probe and very simple instrumentation. Duringthis laboratory, you will use a Hall probe to study the magnetic field distributions produced byboth a Helmholtz coil and a solenoid. The physical mechanism of the Hall effect is discussed inAppendix I.Magnetic fields from single and multiple current loopsThe magnetic field due to a single circular current loop at an arbitrary point in space isshown in Fig. 1. It is a rather complicated function of the coordinates.Figure 1. Field lines for a single, circular current loopOn the axis of the loop, however, a simple expression may be found for the field due to therotational symmetry of the system.Consider a loop of radius a whose axis lies along the z axis and whose center is at theorigin, as shown in Fig. 2 below.

Physics 401 Experiment 67Page 3/31Hall Probe Measurement of Magnetic FieldsFig. 2. Geometry for the calculation of the B field on the axis of a circular current loopWe apply the Biot-Savart LawJJG GJG μd A ξ0B I4 π v ξ 3G G GGGwhere ξ r r ′ , and r and r ′ specifiy the field and source points, respectively. Due toJGrotational symmetry, only the z component of B survives the integration. In cylindricalGJJGJJG Gcoordinates, d A a dφ φ and ξ z ′ z a ρˆ , so d A ξ z a 2 dφ . Thus(dB z )μ o I a 2 dφ.4πξ3As ξ remains constant as we integrate around the loop, we findJG μo Ia 2B 21(3z2 a2 2)z .

Physics 401 Experiment 67Page 4/31Hall Probe Measurement of Magnetic FieldsUsing this result, we may now find the expression for the field on the axis of both aHelmholtz coil and a solenoid. A Helmholtz coil consists of two identical circular current loopsof radius a, each having N turns. The coils are parallel and coaxial, and separated by distance a,as shown in Fig. 3.Figure 3. Geometry of the Helmholtz coilThe same current I flows through both coils. As was the case for a single current loop, the fieldfrom a Helmholtz coil for an arbitrary point in space is shown in Fig. 4, a complicatedFigure 4. Field lines for a Helmholtz Coil

Physics 401 Experiment 67Page 5/31Hall Probe Measurement of Magnetic Fieldsfunction of the coordinates, but rotational symmetry simplifies the calculation on the field of theaxis. To find the axial magnetic field due to a Helmholtz coil, we first note that, bysuperposition, the field from each loop of N turns is simply N times the field due to a coil of asingle turn.We choose the z axis along the axis of the coils, and choose the origin at the midpointbetween the coils, as shown in Fig. 3. By superposition, the total field from the Helmholtz coil isthe sum of the fields from each coil may be obtained from our expression for the single loop byapplying the coordinate transformation z z aafor the right hand coil, and z z for the22left hand coil. Thus the axial field is given by JG μ0 N Ia 2 11 B z 33 22222 a a 2 z a 2 z a 2 2 (1) μ0 I N 11 z 33 2a 2222 z 1 z 1 1 1 a 2 a 2 and shown in Figure 5 below. N is the number of turns per coil.Bz on axis of Helmholtz pair of radius a0.005Bz (T)0.0040.0030.0020.0010210z/a1Figure 5. Magnetic field along the axis of a Helmholtz coil.2

Physics 401 Experiment 67Page 6/31Hall Probe Measurement of Magnetic FieldsHelmholtz coils are frequently used in the laboratory because they provide a reasonably largeregion free of material in which there is a uniform magnetic field (the region midway betweenthe coils and along the axis). The calculated field on the axis of a Helmholtz coil with 145 turnsper coil and with a radius a 10.8 cm and at a current of 3.0 A is shown in Fig. 5 below. On thehorizontal axis the coils are at z a 2 ( z a 1 2 ).The solenoid is another current distribution which provides a region of uniform field.The magnetic field distribution for a solenoid whose length is equal to twice its diameter isshown in Fig. 6.Figure 6. Lines of B for a solenoid whose length is equal to twice its diameter.For the same total number of ampere-turns of a given of a given radius and occupying the sameoverall length, the uniformly wound solenoid gives a somewhat higher field at the center than theHelmholtz coils. The field of the Helmholtz coils at its center is, however, more uniform thanthe field for the solenoid at its center. The solenoid has the experimental difficulty that theuniform field region is accessible only from the ends of the solenoid while for the Helmholtz coilthe uniform field region is accessible from the side as well. To calculate the B field for a point Pon the axis we establish the coordinate system shown in Fig. 7. The origin is chosen at point P,and the solenoid extends from z z1 to z z2 . If the solenoid has n turns per unit length, thenin a length dz there is a current n I dz flowing, and the field at the point P due to the length dzis given by

Physics 401 Experiment 67Page 7/31JG μo n IdzdB 2Figure 7.a2(32 22z a)Hall Probe Measurement of Magnetic Fieldsz ,Geometry for the calculation of the B field on the axis of a solenoid.and the axial field due to the whole solenoid is given by the integralJG μo n Ia 2B 2z2 z1dz(3z 2 a2 2)z .Making the changing variables z a tan θ givesJGμo n I θ 2 μo n I [ cos θ cos θ ] z ,B sinθdθz122 θ 2(2)1where cos θ1 z1a 2 z12 and similarly for cos θ 2 . Hence, the on-axis field of a solenoid isproportional to the difference in cosines of the angles subtended by the ends. The angles forfield points both exterior and interior to the solenoid are shown in Figure 8 below.

Physics 401 Experiment 67Page 8/31Hall Probe Measurement of Magnetic FieldsFigure 8. Angles subtended by the ends of the solenoid for exterior and interior field points.The calculated field from a solenoid with 245 turns, a radius of a 5.1 cm and length 2b 20.3cm with a current of 3.1 A is shown in Figure 9 below. On the horizontal axis the points z b 1 represent the ends of the solenoid.Figure 9. Magnetic field along the axis of a solenoid.One can obtain a little more information about the magnetic field of a solenoid withoutsolving for the field everywhere. If one applies Amperes circuital law to a path containing anJG Gedge of the solenoid, as shown in the Figure 10 below, one obtains: v B d A μo N I .Figure 10.Integration path for Ampere’s law.

Physics 401 Experiment 67Page 9/31Hall Probe Measurement of Magnetic FieldsHere, N is the number of turns of wire contained by the integration loop. We suppose that thecontribution to the line integral along the radial paths is negligible. Then evaluating the integralgives Bz ,inside Bz ,outside A μo N IorΔ Bz Bz ,inside Bz ,outside μo n I . (Recall that n N A .)(3)Thus the difference in the z-components of the magnetic field is proportional to the currentdensity. In fact, this result is true for any shape current sheet; it is only necessary to remain closeto the sheet.For our last consideration we want to relate the rates of change of a transversecomponent and the z-component of the magnetic field of a solenoid. To this end we use the factthat any magnetic field has zero divergence, i.e.JG JG B By Bz B x 0 . x y zUtilizing the symmetry of the solenoid we have, on-axis, Bx1 Bz . x2 z By y Bxhence x(4)On the axis of the solenoid the transverse component is zero, but it has a rate of change withdistance off-axis that is given by one-half the rate of change of the axial component.Experimental ProcedureA.Measurement of the Helmholtz Coil FieldYou will use a commercial gaussmeter to measure the magnetic fields. There are twotypes of probes available: axial and transverse. The axial probe has a round cross section andJGmeasures the component of the B parallel to the cylinder axis. The end of transverse probe has aJGrectangular cross section and measures the component of B perpendicular to its broad face.

Physics 401 Experiment 67Page 10/31Hall Probe Measurement of Magnetic FieldsThe AlphaLab Hall DC magnetometer and probes have been calibrated by themanufacture. No other calibration should be necessary. There is a calibrated permanent magnetavailable to check the calibration. There is an OFFSET control which is used to cancel out anexisting field by adding or subtracting a certain value from the field strength. Fields of up to 10 G can be cancelled with this control. The AC/DC switch selects measurement of timevarying and steady magnetic fields. The fields in this experiment are constant in time. Insert theprobe into the zero-gauss chamber and adjust the control to obtain zero gauss on the 200 G scale.Note that there is a filter in the electronics for the 200 G scale which requires at least 3 s toobtain a reading. The Magnetometer must be zeroed if the probe is changed from axial totransverse, or vice versa.1. Record the necessary parameters of the Helmholtz coil in your notebook. Connect theHelmholtz coil as shown in Figure 11. This is a split coil having a separation equal to the radiusof one of the windings. Adjust the current until 3.0 A flows in the Helmholtz coil. Use a DMMFigure 11. Basic circuit for field measurement with Helmholtz measure the current. The meter in the power supply only has one digit precision. (Be sure

Physics 401 Experiment 67Page 11/31Hall Probe Measurement of Magnetic Fieldsyour power supply is operating in the current regulating mode, and not in the voltage-regulatingmode. Check the power supply manual for current regulating mode operation.) Before makingmeasurements, zero the probe.2. In this part we demonstrate that the field at the center of the Helmholtz coil is axial.Measure the field at the center of the pair on the median plane for various angles of placement ofthe transverse Hall probe, see Figure 12 below. Measure the field while rotating the transverseprobe at the angular intervals of 30 over a 180 range.Part A2 Direction of field at center of Helmholtz coilsyxztransverseprobeFigure 12. Procedure for finding direction of field at center of Helmholtz coil.3. In this part we map the axial field along the axis of the coils, i.e. Bz(0,0,z) vs. z.Switch to the axial probe and zero it again. Measure the field along the axis of the Helmholtzcoil from z -20 cm to z 20 cm in steps of 2 cm. See Figure 13 below. It may be easier tomove the coil and leave the probe fixed.

Physics 401 Experiment 67Page 12/31Hall Probe Measurement of Magnetic FieldsPart A3 Bz on axis of Helmholtz coilsBz(0,0,z) vs zyxzzaxialprobeFigure 13. Procedure for measuring the field on the axis of Helmholtz coil.4.In this part we map the field on the median plane of the Helmholtz coil using thetransverse probe, i.e. Bz(x,0,0) vs x. (We switch to the transverse probe to avoid running intothe coils.) Measure the field from x -20 cm to x 20 cm in steps of 2 cm, see Figure 14below.Part A4 Bz on median plane of Helmholz coilsBz(x,0,0) vs xyxztransverseprobeFigure 14. Procedure for measuring the field on the median plans of the Helmholtz coil.

Physics 401 Experiment 67B.Page 13/31Hall Probe Measurement of Magnetic FieldsMeasurement of the Solenoid Field1. Record the necessary parameters of the solenoid coil in your notebook. Connect thesolenoid in place of the Helmholtz coil and adjust the current to 3.0 A.2. In this part we map the axial field of the solenoid on the axis of the solenoid. SeeFigure 15 below. Take at least twenty (20) measurements at intervals of 1 cm from the center ofthe solenoid. Near the end of the solenoid make measurements in 0.5 cm steps. Measure only inone direction from the center of the coil.Part B2 Bz on axis of solenoidBz(0,0,z) vs zyxaxialprobezFigure 15. Procedure for measuring the field on the axis of the solenoid.3. In this step we measure the component of field parallel to the axis, i.e. Bz, just insideand just outside of the coil. With these data we will compare to Ampere’s Law. See Figures16a and 16b below. Take at least twenty (20) measurements at intervals of 1 cm from the centerof the solenoid.

Physics 401 Experiment 67Page 14/31Hall Probe Measurement of Magnetic FieldsPart B3b Bz outside solenoid near coilBz(xo,0,z) vs zPart B3a Bz inside solenoid nearcoilyyxxaxialprobeaxialprobezzFigs 16a and 16b. Procedure for measuring the axial field off the axis inside and outside of thesolenoid.4. In this part we measure the component of the field perpendicular to the axis near theend of the solenoid. With these data we will compare to the divergance law. Switch to thetransverse probe. Map field along the transverse direction at the end of the solenoid. See Figure17 below. Make measurements from -5 cm x 5 cm. Use steps of 0.5 cm.Part B4 Bx outside solenoid near coilBx(x,0,b) vs xyxztransverseprobeFigure 17. Procedure for measuring the transverse field outside the solenoid.Calculations and Discussion

Physics 401 Experiment 67Page 15/31Hall Probe Measurement of Magnetic FieldsUse proper units consistently. Note: 1 Tesla 104 gauss.A.Make a plot of the measured B field vs. angle for the Helmholtz coil using the resultsobtained in procedure A2. Comment on the dependence of the measured A on angle.B.Make a plot of Bz vs. z for the Helmholtz coil, using the results obtained in procedureA3. Compare the measurements with the field calculated with Eq 2.C.Make a plot of Bz vs. x for the Helmholtz coil, using the results obtained in procedureA4. Comment on the results.D.Utilizing the plots obtained in (C) and (D) above, estimate the radius of a sphericalvolume centered within the Helmholtz coil within which the field is constant to 5%.E.Make a plot of Bz vs. z for the solenoid, using the results obtained in procedure B2.Compare the measurements with the field calculated with Eq. 2. to your values of Bz for themiddle and the end of the solenoid with the theoretical values.Make a plot of Δ Bz Bz ,inside Bz ,outside vs. z for the solenoid as obtained in procedureB3. Compare your maximum value of Δ Bz with the value calculated with Eq 3.F.G.B4.Make a plot of Bx vs x for the field at the end of the solenoid as obtained in procedure Bx Bzfrom the data of part F and part H. Compare theirand z xratio to the expected value from Eq 4. (Note they must both be evaluated at the same point inspace.)H.Determine the slopesReportIn the report must include:1.The specifications of the solenoid and Helmholtz coil.2.The radius of the sphere in part E above.3.Theoretical and experimental values for the central fields of the Helmholtz coil andsolenoid.4.Answers to all questions and all plots mentioned under Calculations and Discussion. Nodetailed error analysis is required.

Physics 401 Experiment 67Page 16/31Hall Probe Measurement of Magnetic FieldsAppendix ITheory of the Hall effectLet us begin by considering the motion of charge carriers, each of charge q, in aconductor of thickness b and width a as shown in Fig. A1. We note that q could be eitherpositive or negative. This conductor is referred to as the Hall element in this experiment.Figure A1. The Hall element.If there are N charge carriers per unit volume, each small element of length dx contains a chargedQ N q a b dx(A1)associated with the carriers. A current is made to flow in the x direction if a battery isconnected to the ends of the element as shown in the figure below.

Physics 401 Experiment 67Page 17/31Hall Probe Measurement of Magnetic FieldsFigure A2. Electrical connections to the Hall element.The carriers are accelerated but, because of collisions within the conductor, they attain anaverage velocity vx called the drift velocity. In a time dt the carriers move an average distancedx vx dt . Hence a chargedQ N q a b vx dt(A2)passes out of each volume element into the next during a time interval dt . This motion justdescribes a current I c dQ dt , which we will call the control current. We can writeGvx Ic ˆi.N qab(A3)

Physics 401 Experiment 67Page 18/31Hall Probe Measurement of Magnetic FieldsG(Note that the sign of q determines the direction of vx . I c is in the x direction with ourJGchoice of battery orientation.) If we now turn on a magnetic field, B Bz kˆ , in the z directionas shown in Fig. A2 above, the drifting carriers experience a forceJG Ic ˆ I BG GF qv B q i Bz kˆ c z ˆjN ab N qab ( )(A4)in the –y direction. As a result of this force the charge carriers move to the -y edge of theconductor. This motion produces an excess of charge on the -y edge and a deficit of charge onthe y edge. On the -y edge there is then a net charge density σ, which has the same sign as thecharge carriers, and on the y edge , there is a net charge density of -σ, which has the oppositesign as the charge carriers. These charge densities give rise to an electric field, E y , in the ydirection, if the charge carriers are positive, or in the -y direction, if the charge carriers arenegative. This electric field exerts a force on the carriers in the y direction which opposes themagnetic force of Eq. A4. Carriers continue to flow toward the -y edge until the electric forceand the magnetic force balance, that is, untilI Bq E y ˆj c z ˆj 0 .N abSubstituting the value of vx from Eq. A3, we findEy I c Bz.N qab(A5)This equilibrium field is determined by measuring the potential difference across the sampleusing the voltmeter, V, shown in Fig. A2 above. The potential difference, VH , is a 2aaVH V (0, , 0) V (0, , 0) E y dy E y a22 a 2Using Eq. A5 for E y , we obtain for VH , the Hall voltage,

Physics 401 Experiment 67VH Page 19/31Hall Probe Measurement of Magnetic FieldsI c Bz.N qb(A6)Note that the Hall voltage is negative if q 0 and positive if q 0 , given our choices for thedirections of the current and the magnetic field. We define a quantity RH 1, the HallNqcoefficient, which depends only the sign and density of the charge carriers. We can rearrangeEq. A6 into the form b VH.Bz RH I c(A7)JGThe Hall voltage then determines the component of B which is perpendicular to the face of theHall element, namely Bz . We would need to change the orientation of the Hall element todetermine field components in other directions. In general, we would need three orthogonalJGdirections to determine all components of B .Table 1 gives Hall coefficients for various materials. The value of RH for Bi and InAsare given with the proper sign. The magnitude is only approximate. The charge carriers for thematerials in which RH 0 are electrons for which q e . The charge carriers for the materialsin which RH 0 have q e and are known as holes.Table 1MaterialRH (m3/ C)CuNaCrBiInAs (approx.)-5.3 10-11-21.0 10-11 35.0 103-11-10 107-11-10 10-11If the actual Hall probe were perfect, it would be possible to determine the constantb RH in Eq. A7 by simply placing the Hall probe in a known (reference) magnetic field andmeasuring VH and I c . In a perfect probe, the transverse connections are exactly opposite each

Physics 401 Experiment 67Page 20/31Hall Probe Measurement of Magnetic Fieldsother, and the Hall voltage VH is zero in the absence of a magnetic field. In practice there isalways some misalignment, δ, as shown in Fig. A3. Therefore the voltmeter does not measurejust VH .xz-y--Vo-----V VH - I cEquipotentialsAssociated with BEquipotentialsAssociated with IcFigure A3. The Offset voltage.Fig. A3 is a view of the Hall element looking down the z axis toward the origin. We canimagine the actual potential field to be separated into two sets of equipotentials. The setdesignated by horizontal lines is due to the Hall effect considered in the last section. The set ofequipotentials designated by vertical lines is related to the current I c flowing through the Hallelement. From Fig. A3 we see that the voltmeter measures the sum of two voltages,Vmeas VH VO ,where VH voltage.ρδab(A8)I c Bzρδis the Hall voltage previously discussed and VO I cis the offsetN qbabis recognized as the resistance of a length δ of Hall element. It is easy todetermine VO . In the absence of a magnetic field, Eq. A6 shows that there is no Hall voltage.

Physics 401 Experiment 67Page 21/31Hall Probe Measurement of Magnetic FieldsThus VO Vmeas . Because of the earth's magnetic field, it is necessary to insert the Hall elementinto a magnet shield to make this measurement.A working equation is obtained by combining Eqs. A7 and A8, b Vmeas VO.Bz Ic RH (A9)Remember that both Vmeas and VO can be positive or negative. The signs of Vmeas and VO affectthe magnitude as well as the sign of Bz when using Eq. A9.Note also that the voltmeter, V, in Figs. A2 and A3 must have a large internal resistanceto prevent the charge buildup on the edges of the Hall element from being conducted away. Theinternal resistance of the DMM used in this laboratory, 1010Ω, satisfies this requirement.

Physics 401 Experiment 67Page 22/31Hall Probe Measurement of Magnetic FieldsExperiment 67 usingArrick Robotics MD-2 dual stepper motor system (XY table),AlphaLab high sensitivity magnetometer (hall probe) andHP34401 DMMThese instructions are a supplement to the Experiment 67 handout and should be used inconjunction with the handout. This supplement describes how to do the Experiment 67 exerciseswith the XY table. It includes one additional exercise, namely, a two-dimensional scan.The apparatus for Experiment 67 is shown in Figure 1. It consists of an Arrick Robotics MD-2dual stepper motor system XY table, an AlphaLab high sensitivity magnetometer (hall probe)with axial (identified by the white cylindrical plastic probe casing) and transverse (identified byrectangular brass probe casing) probes and an HP34401 DMM. The stepper motor system andthe DMM are interfaced to a PC.Figure 1 Experiment 67 apparatusThe bed of the XY table is fitted with a 12” ThorLab horizontal rail and a 3” ThorLab verticaltranslating postholder and post. The post carries an annular clamp that holds a brass rod ontowhich the hall probes are taped. The Thorlab rail and postholder allow for convenient, butaccurate, movement of the hall probe. The thumbscrew on the base of the postholder secures thepost the rail. By loosening one thumbscrew on the postholder, approximately 3” of free vertical

Physics 401 Experiment 67Page 23/31Hall Probe Measurement of Magnetic Fieldsmotion of the post is available. By loosening the other thumbscrew on the postholder,approximately 1/2” of vertical adjustment of the post by the knurled nut on the postholder isavailable. All thumbscrews should be tightened for mapping operations.Setup of HP34401 DMM communication with the PCThe HP34401A DMM has both a RS-232 and a GPIB interface. Since the serial port (RS-232) isstill common PC hardware, it is used to connect the DMM to the PC. The connection is to PCserial port COM1 through a standard cable. This connection is made by the 401 staff inpreparation for the laboratory. The I/O parameters of the HP34401A must be setup beforerunning the mapping program. The I/O parameters are stored in non-volatile memory, and it ispossible that the correct parameters are in the DMM memory. You can test the communicationlink in the mapping program as described in the next section. Note that the magnetometer hasthe convenient calibration of 1 G 1 mV. Full scale is 200 G (200 mV) and readings are stableat least 0.1 G (0.1 mV.)Arrick dual stepper motor system and MagnetMapper programThe Arrick dual stepper motor system, MD-2, consists of an XY translation stage with amaximum travel of 9” in each direction. The stage is moved by two stepper motors with 1/200”per step. The two motors are connected to the MD-2 driver box with two stepper motor cables.The driver box is connected to the PC through the standard parallel port. The stepper motors anddriver box are connected by 401 staff in preparation for the laboratory. It is not expect that theuser will connect or remove cables, and the MD-2 instructions explicitly state: DO NOTREMOVE MOTOR OR COMPUTER CABLES WHILE THE UNIT IS UNDER POWER.Figure 2 Magnet Mapper Instrument Panel

Physics 401 Experiment 67Page 24/31Hall Probe Measurement of Magnetic FieldsThe stepper motor system is controlled by a LabWindows/CVI program, MagnetMapper RS232,written by UIUC physics graduate student Kevin Mantey. Click on the program desktop icon tostart the program. All program commands are entered through the program instrument panel.The program instrument panel is shown in Figure 2. From the instrument panel the user can (1)move the XY table, (2) test the connection to the DMM, (3) set the step size and number ofsteps, (4) see the data as it is acquired, (5) choose the file to which data is written, and (6) startand stop mapping. These options are accessed from buttons and boxes on the instrument panel.See Figure 2 for the instrument panel upon program start-up.To test the communication link between the PC and the DMM, on the Magnet Mapper programinstrument panel, press the button “Test Multimeter.” If the current DMM reading appears, thenthe DMM I/O interface is properly setup. If an error message appears, either on the computerscreen or on the DMM display, setup the DMM and possibly the PC following the instructions inthe Appendix.XY Table and Coil PositioningSince the stepping motor step size is specified in inches, it is also convenient to give manydimensions also in inches. Conversion of inches to metric units should be done in data analysis.Each part of Experiment 67 will require the user to position the probe with respect to the coilbefore the start of mapping. The coils must be set on blocks, since the minimum height of theprobe off the table is approximately 10”. The images in the file, setupwithXYtable.ppt, showone possible arrangement of the probe and coils for both solenoid and Helmholtz coil scans.Regardless of the exact height and position of the probe and coils, the user must insurethat, while the probe is moving, the hall probe cable does not catch in the table movementmechanism, and that the hall probe does not run into the coil. The probe can be damagedif either occurs. Watch the probe as it is moving. If the probe would run into the coil, stopthe scan with the “Stop Mapping” button.Figure 3 Table motion with standard table orientation

Physics 401 Experiment 67Page 25/31Hall Probe Measurement of Magnetic FieldsIt is convenient to orient the XY table so that the motion indicated on the Magnet Mapper panelcorresponds to the motion of the table. Then the “right” (“left”) button will move the probetoward (away) from the coil. Also then the “up” (“down”) button will move the probe towardand away from the user. The usual connection of the controller box will have motor #1 cable tothe motor on the moving platform, and motor #2 cable to the motor on the fixed platform. Motor#1 moves the probe “up” and “down”. Motor #2 moves the probe “right” and “left”. See Figure3.Preparation to Take DataThe Magnet Mapper program writes the DMM readings out to a text file in Excel csv (commaseparated value) format. The user must select the file to which the program writes. Dummy filesmust be prepared and then selected with the “Select File” button on the instrument panel. Thedummy files are conveniently prepared using Excel to save a csv file with a convenient name, forexample, E67 B2.csv. Several dummy files can be prepared in advance and kept in a folder.The user must enter the step size and the number of steps in the appropriate windows on theMagnet Mapper instrument panel. Most of the maps are along one axis, and, assuming that theprobe and coil are oriented so that motion in the y-direction moves the probe in the desireddirection, the user would enter 0 (X-num steps), 0 (X-size steps), 19 (Y-num steps), 100 (Y-sizesteps) to move the probe (19 – 1) 100/200” 9” in 1/2” steps. The instrument panel after theDMM test and step number and size entries is shown in Figure 4. The fields of the solenoid andHelmholtz coils do not vary so rapidly that smaller steps are needed.Figure 4 Magnet Mapper instrument panel after DMM test and step size and number entry

Physics 401 Experiment 67Page 26/31Hall Probe Measurement of Magnetic FieldsTypical sequence for mapping scanBoth the fields a

between the coils, as shown in Fig. 3. By superposition, the total field from the Helmholtz coil is the sum of the fields from each coil may be obtained from our expression for the single loop by applying the coordinate transformation 2 a zz for the right hand coil, and 2 a zz for the left hand coil. Thus the axial field is given by 2 .