1、Rxx2EM7Magnetic fields of Helmholtz coils (HC)THEORYSingle CoilFor a coil of wire having radius R and N turns of wire, the magnetic field along the perpendicular axis through the center of the coil (x is the distance from the center of the coil) is given by23xNIBo(1)The magnetic field at the center
2、of the coil is obtained by setting x=0, to give RI20Figure 1: Single CoilTwo CoilsFigure 2: Two Coils with Arbitrary SeparationFor two coils, the total magnetic field is the sum of the magnetic fields from each of the coils.xRdNIxRdNIBoo 2223231 (2)RRdxB1 B2 xRxRRFor Helmholtz coils, the coil separa
3、tion (d ) equals the radius (R) of the coils. This coil separation gives a uniform magnetic field between the coils. Plugging in x = 0 gives the magnetic field at a point on the x-axis centered between the two coils:xNIBo1258(3)Figure 3: Helmholtz CoilsINTRODUCTIONThe magnetic fields of various coil
4、s are plotted versus position as the Magnetic Field Sensor is passed through the coils, guided by a track. The position is recorded by a string attached to the Magnetic Field Sensor that passes over the Rotary Motion Sensor pulley to a hanging mass.It is particularly interesting to compare the field
5、 from Helmholtz coils at the proper separation of the coil radius to the field from coils separated at less than or more than the coil radius. Preparatory Procedure for the Magnetic field sensor and Rotary motion sensor1. Switch on the computer, without the PASCO ScienceWorkshop 750 USB connected to
6、 it. After Windows has been up, switch on and connect the ScienceWorkshop 750 interface to the PCs USB interface. 2. Launch Data studio, either by clicking the icon in the desktop or Start All Programs Data Studio Data Studio.3. When the Data studio is launched you will be prompted a Welcome to Data
7、Studion message. You should click Create Experiment. A screen with the title Experimental Setup will be launched. If everything goes accordingly, you should also see at the bottom of the screen the statement The interface is ready for use.4. Plug in both the yellow and black jacks of the rotary moti
8、on sensors into the holes labeled 1 and 2 of the 750 interface. Point the mouse to the hole 1 on the picture of the Scientific Interface 750 on the screen. You will be prompted a drop down windows choose sensors or instrument. Choose rotary motion sensor.5. In the visibility, name (under the measure
9、ment tab), check position, Ch 1 it is otherwise if the detector is not moving along the symmetric axis. Optimise your measurement using this argument as a guidance to produce a measurement of B that is as closed as possible stick on the axis of symmetry. Data manipulation and interpretation1. Plot a
10、 graph of B vs. x. Comment on the graph obtained. 2. Plot a graph, using the functionalities provided in the DataStudio, of vs. . Deduce lnB2lxRthe gradient of log-log graph. Plot on the same graph also the theoretical curve of vs. based on Eq. (1).2lnxR3. What is the expected (i.e. theoretical) val
11、ue of this gradient? Compare the measured value of the gradient (from your graph) with the theoretical one. 4. Deduce the value of N of a single HC. Compare it with the given value of N, and comment about the accuracy of your measurement on N. Note that if your measurement is done properly (with B f
12、ield symmetric about the center of HC along the symmetric axis), with the magnetic field sensor being moved on a perfect straight line in parallel to the axis and going through the center of and the HC, you would have a perfect fit between the experimental line and theoretical one in the log-log gra
13、ph. Any deviation from the ideal axis will show up in the mismatch of your experimental data when fitted against the theoretical curve. 5. From the experimental graph obtained, deduce the experimental value of B0, the magnitude of B when x = 0. Using the values of I, N, R as measured, deduce the val
14、ue of . Compare this value with the theoretical one, which is (teslameters)/amps.70146. Comment on your results of your measurements. Experiment 2: Helmholtz coilsFor this experiment, you have to refer to Eq. (2).PROCEDURE1. Attach a second coil to the Helmholtz Base at a distance from the other coi
15、l equal to the radius of the coil (this makes d = R) in equation (2). Make sure the coils are parallel to each other. See Figure 6. 2. Connect the second coils in series with the first coil, as shown in Figure 7. Make sure that the direction of the current in the wiring is taken care of correctly. T
16、his ensures that the magnetic field produced in both coils is in the same direction. 3. Fix the current I. Measure the magnetic field B at various position x as in experiment 1 with the help of rotary motion sensor.4. Now change the separation between the coils to 1.5 times the radius of the coils.
17、Repeat step 3.5. Now change the separation between the coils to half the radius of the coils. Repeat step 3.Figure 6: Helmholtz CoilsFigure 7: Helmholtz WiringData manipulation and interpretation1. For each coil-coil separation distance, d:a. Plot a graph of B vs. x. Comment on the graph obtained. I
18、n particular, comment on the quality of the region where the magnetic field remains constant. b. Plot also the theoretical curve of Eq. (2) on the same graph. From the graphs plotted, Plot B0 (experiment) vs. d, B0 (theory) vs. d on a same graph. B0 is the value of the magnetic field at the midpoint between the Helmholtz coils.2. Comment on your results of your measurements. In particular, discuss the factors that may have caused the difference between these.Experiment/write-up prepared by Yoon Tiem LeongFeb 2009PP Sains Fizik, USM
