| Table of Contents |
Crummett and Western, Physics: Models and Applications,
Sections
Halliday, Resnick, and Walker Fundamentals of Physics (5th
ed.), Section 30-5
Tipler, Physics for Scientists and Engineers (3rd ed.), Section
Whenever an
electric current flows in a conductor, a magnetic field is created in the
space around it. One of the fundamentally important arrangements is a circular
coil. If a current I flows in a coil of N turns of wire,
each of radius R, the magnetic field produced on the axis of the coil,
at a distance x from its center, is given by
(1)
The constant 
,
so the magnetic field strength is in tesla (T). A somewhat more convenient
unit is the gauss (G): 1 T = 10,000 G.
In this experiment, you will use an automated data-collection method to measure the magnetic field of the coil at various positions, which you can compare to Eq. (1).
In this experiment,
a tightly-wound circular coil will have a known current passed through
it. A magnetic field probe will pass along the axis of this coil, and magnetic
field data will be taken. The magnetic field probe is attached to an air
cart which is pulled by a weight hung over a pulley (Figure 2). The idea
is to use the shaft encoder (a device which allows one to measure rotations
of the pulley in the form of angle) along with the magnetic field probe
to take magnetic field and angle data as a function of the position of
the probe.
A small weight hung over the pulley will pull the air cart and move the magnetic field probe into the region of the coil. A sweep will be made and saved with the plane of the coil vertical, and another sweep will be made with the plane of the coil horizontal, and the probe passing about one inch above the coil. In the second case the sweep will permit one to check the distance scale derived from the angular measurements, and to review the direction of magnetic field near the loop.
(1) Carefully determine the radius of the pulley on your shaft encoder. You should be able to do this to within about 1%. Explain the method which you use to get this precision. Make a careful estimate of the average diameter of the copper coils. The coil is supposed to be 190 turns of number 22 wire. This AWG 22 enameled wire is listed as 37.0 turns per linear inch, from which you can get the wire diameter including enamel. Measure the thickness of the plastic wall surrounding the wires.
(2) The field mapping program is LOGANGLE.EXE in the C:\LAB directory. Begin by going to Set ANALOG PARAMETERS [item 8] and select channel B, -10v to +10v scale, and SYNC mode. Then go to SET ANGLE DATA PARAMETERS [item 7] and select 400 data points, one channel mode, and set the program to record every 20th point. Later on, during the experiment, you may want a different number of data points, or a different number for measuring every Nth point. Now select MORE ANGLE DATA PARAMETERS [Item 6], and use item 4 in this menu to set the pulley radius in cm. This sets the apparatus for recording distance in cm, rather than angle in radians. Skip the calibration; we will convert it later to appropriate units.
(3) The magnetic field probe is a 'linear Hall effect transducer.' This is a small, black, approximately rectangular solid with three wires connected to it. The probe detects a magnetic field component which is perpendicular to the plane of the small, flat, black detector package. In our experiments, the plane of the probe is vertical, and the direction of the magnetic field component which is detected is along the direction of travel of the air track.
Begin by having the plane of the coil vertical. Adjust the supports under the coil so that the magnetic field probe passes through the center of the coil. Connect the coil to the 6 Volt DC supply through an ammeter. Carefully check the wiring. Turn the supply on. The current should be in the neighborhood of 1/2 ampere (500 mA). Leave the supply on throughout the experiment; it is a bad idea to unplug any wires with current flowing, because the coil has inductance, and sudden disruptions of current create voltage spikes. In analyzing the data later, you will use the current in Equation (1) to calculate the magnetic field in the center, so you can re-graph the data as magnetic field vs. distance.
(4) To make a sweep, set the probe about 30 cm from the center of the coil, with the air supply turned on, and the thread attached to a nut hanging over the pulley. First release the air cart, and then just after the cart has begun to move, press a key to take data. Stop the cart just as it reaches the end of the track. If the program has not finished taking data, you will need to move the cart backward until it says that data taking is complete. When data is complete, plot Z (which is the voltage from the magnetic field sensor) vs. q. [Item 5; the actual plot is V vs. distance]. When you have a run with about equal amounts of data on each side of the maximum, save the data to a file. Note that you may look at the data on the CRT screen if you wish, by using item 3 on the File I/O menu. This will show what variables are saved, and how many data points are saved.
(5) Since you will have to determine the inflection point of the experimental data, do another run starting about 50 cm from the ring, and finishing just after recording a maximum in the magnetic field. This will provide more precision in the position of the inflection point. Save this data to another file.
(6) Now rest the coil on a horizontal surface, and adjust the height of its supports until the probe is about an inch above the top of the coil. Start the probe about 10 cm outside the coil and do a run in which the probe passes over a diameter of the coil, one inch or so above the top of the coil. If things are aligned properly, the positive and negative peaks in the data should be the same size. If this is not the case, try to readjust and do another run. Save this data to a file when you have a record of magnetic field from 10 cm outside the coil going over the center of the coil, and for about 10 cm outside the coil on the other side. Save this data to another file.
(1) Use your three data sets to generate three graphs of magnetic field vs. distance. To do this, you will have to re-scale the magnetic field. You can determine the gauss/volts value from the maximum value of the axial magnetic field (you can calculate what it should be in theory knowing the coil parameters and the current). Then re-scale the data so that it is in gauss. (Remember that it will initially SAY it's gauss in the file, but it's really volts, because we did not calibrate.)
What about the zero of magnetic field? Will you have to make some correction for this? Look over the graphs, decide what to do, and explain carefully what you did in your lab notebook.
(3) Determine from the graphs the distance from the center of the coils to the inflection point in the axial magnetic field. Compare this to the calculated inflection point from the formula for axial magnetic field.
(4) From the data where the plane of the coil is horizontal, locate the positions of maximum positive and negative magnetic field. What do these represent? Draw a sketch of the magnetic field lines around the coil to illustrate your discussion of the coil.
Do the maxima and minima have the same absolute values? (That is, is one the negative of the other?) Based on what you know of the theory of the magnetic field, should one be the negative of the other? Discuss reasons why the experimental measurements may not match the theory. Ask yourself about where the magnetic field is zero, and whether the measured value is really zero.
From this same graph, determine the diameter of the coils, assigning some uncertainty to the value. Compare this to the value you obtained directly with a meter stick or other measuring instrument.
Magnetic Force Between Parallel Currents
From IFYCSEM 6/96