# Chapter 5. Magnetic Fields and Forces. 5.1 Introduction

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1 Chapter 5 Magnetic Fields and Forces Helmholtz coils and a gaussmeter, two of the pieces of equipment that you will use in this experiment. 5.1 Introduction Just as stationary electric charges produce electric fields, moving charges (currents) give rise to magnetic fields. In this lab you will investigate the magnetic field produced by different arrangements of currents, starting with the field of the Earth itself. You will then study the field of a straight wire, and use a sensitive force-measuring apparatus (for which our depertment recently received a national award!) to study the right-hand rule and the force on a current-carrying wire. Next, you ll study the field of a circular coil, and a special arrangement of two coils known as Helmholtz coils. Finally, you will also use a Slinky to understand the field of a solenoid. This laboratory normally takes two lab periods to 1

2 2 Chapter 5 Magnetic Fields and Forces complete. Reading and Key Concepts Before starting this lab, you should be familiar with the following physical concepts. If you need to review them, or if you haven t yet discussed them in your lecture course, consult the indicated section in Cutnell & Johnson, Physics. Magnetic fields, Force on a current due to a magnetic field, 21.5 Solenoids, 21.7 Ampère s Law, 21.8 Apparatus Power supply, digital current meter; moving coil current meters Digital multimeter (GoldStar DM332 or similar) Compasses; dip-angle compass DC Gaussmeter Oersted Table 6V Lantern Battery Pair of matched solenoid electromagnet coils (Helmholtz coil pair: TEL502 or equivalent) Stand for Helmholtz coil pair Slinky solenoid and mounting board with hooks Probe stands for solenoid and Helmholtz coils measurements Magnetic Force Balance Table Digital Pocket Scale (Jennings JS-50x or similar) Rotating magnet stand

3 Chapter 5 Magnetic Fields and Forces 3 B B Ruler Sensitive Spot Maximum Field Reading Ruler Zero Field Reading Figure 5.1: Measuring the magnetic field using the gaussmeter. 5.2 Preliminaries Units The SI unit for magnetic field is the Tesla (T). The Tesla is named after the eccentric but brilliant scientist Nikola Tesla, who developed many of the magnetic devices used to generate and use AC (alternating current) electrical power on a large scale. One Tesla is equivalent to 10,000 gauss, where the gauss is an earlier unit that is still in common usage. Since the Tesla is a very large unit, corresponding to an unusually strong field, it is more common to use units of millitesla (mt) or gauss (G), 1G = 10 4 T (5.1) For example, the Earth s field is about 0.5 G. The gaussmeter that you will use in this experiment also measures in gauss Equipment Magnetic Field Sensor (Gaussmeter) The device used to measure magnetic fields is traditionally called a gaussmeter (for reasons explained in Section 5.2.1). The magnetic field is a vector quantity, and while the compass is only sensitive to its direction, the gaussmeter is sensitive to both its magnitude and direction. The sensitive area of the probe is a small spot located a few mm from the end of the probe tip, marked with a white dot. The probe measures the component of the magnetic field that is perpendicular to the probe face. This is illustrated in Figure 5.1. In this experiment, you will use the G setting on the gaussmeter. 5.3 The Experiments The Earth s Field Procedure The Earth s magnetic field is both familiar and a potential source of systematic error in many of our experiments, so it is important to know both its magnitude and its direction. In order to measure the magnitude of the Earth s field, we must first align the gaussmeter with the field. On the table in the middle of the room, there is a piece of tape indicating the direction of the field in the plane of the table. Use one of your compasses to confirm that it is correctly oriented. Note that this does not tell us anything about the vertical component of

4 4 Chapter 5 Magnetic Fields and Forces Geographic north pole?? Geographic south pole Figure 5.2: Gaussmeter. Figure 5.3: dipole. The earth is a magnetic the Earth s field. Now, line up the dip compass with the piece of tape when the needle stops moving, it should be pointing in the direction of the Earth s field. Line up your gaussmeter and take a measurement. We will call this measurement B +. Then, point your meter in the exact opposite direction and take another measurement. This measurement is B. To find a value for earth s field, take B E = 1 2 (B + B ). (Note that this is not an average, since the average would involve taking the sum. Why do we take the difference of the two measured values here?) Analysis Record your data on your worksheet. Include a sketch indicating the direction of the field relative to the floor or vertical. You should observe that the magnitude of the earth s field at Ann Arbor is about 0.5 gauss, and it points nearly vertically (and a little northward) into the earth. The angle which the earth s field makes with the vertical is called the dip angle. The dip angle will depend on the position on the earth s surface (i.e., the latitude) relative to the earth s northsouth axis. At the latitude of Ann Arbor (43 ; i.e., about half way between the equator (0 ) and the north pole (90 )), the dip angle will be about 20 with respect to the vertical. Your compass lines up with magnetic fields because it is a magnetic dipole the north pole points in the direction of the magnetic field. You know that the magnetic north pole of the compass usually points (roughly) toward the geographic north pole of the Earth. You can think of the Earth s magnetic field as being generated by a bar magnet, as illustrated in figure 5.3. How is this bar magnet oriented? That is, what kind of magnetic pole is found near the north geographic pole? Magnetic Field Near a Current-Carrying Wire Procedure Connect the 6V lantern battery to the oersted apparatus shown in Figure 5.4. Arrange four small compasses at equidistant points around the wire on the stand. Press the red button on top of the apparatus to complete the circuit and note the change in the compass needles. WARNING: Do not leave the switch closed for more than a few seconds. This

5 Chapter 5 Magnetic Fields and Forces 5 Figure 5.4: Oersted apparatus to study the magnetic field of a straight wire. Measure along radial line Gaussmeter N Wire W E Field Lines S Figure 5.5: Determining the radial dependence of the magnetic field of a straight wire. will drain the battery. Be sure to note which way the compass needles move, and what happens when the current is turned on and off. Reverse the leads on the battery and again note the change in the compasses. You have just seen that the field lines generated by the current are circles centered on the wire. You will now determine the radial dependence of the field how quickly the field weakens as you move away from the wire. Position the gaussmeter so that the sensitive portion of the probe is perpendicular to the field lines generated by the current. Place the probe handle along the east-west direction so that as little of the earth s field as possible is entering the probe, as in figure 5.5. Depress the switch and measure the magnetic field at distances of 1-5 cm from the wire in 0.5 cm increments, being careful not to leave the switch closed for more than a few seconds. Remember to take into account the position of the sensitive spot of the probe. It is not located at the very tip of the probe see section

7 Chapter 5 Magnetic Fields and Forces 7 Figure 5.7: The magnetic field between the magnets points from one magnet to another, toward the N on the compass. Here the current and the magnetic field are parallel, so the net force is zero. Instead, gently slide the magnet stand until the wires are no longer touching the magnet. If you aren t sure what to do, ask your GSI for assistance. Turn on the scale and zero it using the button on the lower right corner. Set the dial on the magnet stand to be at 90, re-zeroing the scale if neccessary. Adjust the current on the power supply to 2.0 A and record the force (in grams) on the scale. Notice the way that the wire moves when the power supply is turned on and off. Turn off the power supply and reverse the leads going to it. Re-zero the scale, turn on the power supply, and record the force. Again note the direction the wire moves when the power supply is turned on and off. This process is a nice illustration of Newton s Third Law. We actually measure the force that the magnets exert on the wire by measuring the equal and opposite force that the wire exerts on the magnets (which then exert a force on the scale). With the dial on the scale set to 90 and the scale properly zeroed, measure the force as a function of the current for values of A at 0.5 A increments. Be sure to re-zero the scale if neccessary between measurements. With the power supply off, set the dial on the scale to 0. Make sure that the wire does not touch the magnets and that it is in the center of the gap. Re-zero the scale and adjust the power supply to 2.0 A. Record the force on the scale. Turn off the power supply and rotate the dial to 30. Again check the orientation of the wire and re-zero the scale. Turn on the power supply and record the force. Repeat this measurement at angles of 45, 60, 90, and 270, being careful to re-zero the scale and check the orientation of the wire between measurements.

9 Chapter 5 Magnetic Fields and Forces 9 Figure 5.8: Setup for measuring the magnetic field of one and two coils Magnetic Field of Helmholtz Coils Procedure Now that you know what the magnetic field of a single coil looks like, you will test what the field of two coils connected in series looks like. Helmholtz coils are two identical coils that are separated by a distance equal to the radius of the coils, in this case 7 cm. Using the same equipment as in the previous experiment you will map the magnetic field of these coils. Place the second coil in the stand. (The stand ensures that the coils are aligned and separated by the correct distance.) With the power supply turned off, connect the added coil in series with the other coil. Position the probe in the probe stand 10 cm outside one of the coils. Measure the magnetic field strength along the axis of the coils at 1.0 cm increments from 10 cm outside one coil to 10 cm outside the other (Take 0 cm to be at the center of the two coils. This should make your measurements go from cm to 13.5 cm). Analysis Using what you know about the superposition of magnetic fields and your graph from the previous section, predict what the graph of the magnetic field (in gauss) vs. axial distance will look like for pair of coils. Plot your data and see if it agrees with your prediction. Do you notice anything special about the field between the two coils? Why might this arrangement be useful in real world applications? You will use these Helmholtz coils when you measure the charge-to-mass ratio of the electron later in this course.

12 12 Chapter 5 Magnetic Fields and Forces (b) west; (c) south; (d) down; (e) east.

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