Magnetic Fields of Bar Magnets

Magnetic Fields of Bar Magnets Studio Physics I Situation Statement: You want to measure the magnetic field near a Magnetic Resonance Imaging (MRI) system in a hospital to make sure that the magnetic field in unrestricted areas outside the MRI room is below the government mandated safe level of 5 gauss. To make this measurement, you have obtained a Hall probe (the sensor on your table). You decide to practice with your Hall probe, making sure that it works, by using it with bar magnets. Since you already know the map of the magnetic field of a bar magnet, you decide to use the Hall probe to determine how the magnitude of the magnetic field varies as you move away from the magnet along each of its axes. While thinking about this measurement you wonder if a bar magnet’s magnetic field might be the result of the sum of the magnetic field of each pole. Although, to date, no isolated magnetic monopoles have ever been discovered, you wonder if you can model the situation as two magnetic monopoles, one at each end of the magnet. Is it possible that the magnetic field from a single magnetic pole, a monopole, if they exist, has the same behavior as the electric field from a point charge? You decide to check it out.

You will have a bar magnet, a meter stick, a Hall probe (Check the attached instructions!!!!!), and LoggerPro software to collect data. You will also have a compass. Using this equipment, you will answer the following questions: A) How does the magnitude of the magnetic field from a bar magnet along each of its axes depend on the distance from the magnet? B) Is that behavior consistent with the dependence of the magnetic field of the distance away from a single pole? That is, does the magnetic field behave the same as the electric field from a point charge?

1. Using the compass and bar magnet, explore and sketch the magnetic field around a bar magnet. The magnetic force and the electric force are NOT the same force. The electric field and magnetic field are NOT the same field. Nevertheless, we will explore in what ways the magnetic field due to a bar magnet (which you mapped out in #1) is similar to the electric field produced by an electric dipole. An electric dipole is a pair of equal magnitude but opposite charges separated by some distance. 2. Draw an electric dipole consisting of two charges of equal strength but opposite sign, separated by some distance. Label each charge with a strength (arbitrarily chosen) and a sign. Identify and label the two axes of symmetry of the dipole. Draw a coordinate system that takes advantage of the axes of symmetry. 3. Select a point along one of the axes, outside the dipole, at which you will calculate the electric field. Assign variable names to the distance between your point and each charge. Assign a variable name to the separation of the two charges. Rewrite one of the distances in terms of the other distance and the separation of the two charges. 4. What are relative directions of the electric field from each charge at the point of interest? What is the expression for the magnitude of each component of the electric field from each charge at the point of interest? Add the electric field (remember it is a vector) from each charge at that point to get the total electric field at that point. Show all your work on your activity sheet. 5. Repeat steps 3 and 4 for the other axis. 6. Does the field have only an x component or only a y component at either of the two points you investigated? If so, state that here.

7. Based on the compass readings you used to map the magnetic field strength in question #1, and your answers from the question (#6) above, would you say that the magnetic field from the bar magnetic appears to be that of a magnetic dipole (assuming a magnetic dipole behaves like an electric dipole)? In what ways would you say yes? In what ways would you say no?

8. In order to explore this idea further, we will now measure the magnetic field along the two axes of the magnet. Set up your Hall probe as explained on the attached sheet. Open the software program LoggerPro. Get the file magnet.mbl from the course web site Activities page or from your Studio Physics CD in the Physics 1 folder. Click the collect button to collect data. Experiment with using the probe. You will notice that even when the probe is held away from obvious sources of magnetic fields, such as your bar magnets, you see a non-zero reading. From the behavior of the probe measurements, determine if this is caused by a real magnetic field or is an electronics artifact or both. Discuss that on your activity sheet.

9. Take one of the bar magnets and use the probe to freely explore the variation of the magnetic field around the magnet. Based on your previous determination of the magnetic field map (question #1), be sure to orient the Hall probe correctly (the field must be perpendicular to the probe face). Where is the field the strongest? The weakest? How far away from the bar magnet can you still measure the field with the wand? Based on your exploration, choose a scale for a graph of magnetic field strength against position that would include all of the points that you might measure.

10. Describe how you plan to measure (in some systematic way) the magnetic field along the two axes of the magnet.

11. Choose an axis of the bar magnet and take measurements of the magnetic field strength in a straight line along the axis of the magnet. Be sure that the field is always perpendicular to the probe. (See the attached instructions.) Make a graph and a table of data as you go. Add a point on your graph of magnetic field strength versus position every time you take a data point. Use this graph to determine where you should take your next data point to map out the function in the most efficient manner.

12. Repeat for each axis of the magnet.

13. Along which axis of the bar magnet does the magnetic field fall off faster? Did your measured graph agree with your theoretical expression for the field due to a dipole? If so, how? State your results in the most general terms supported by your analysis. Is it reasonable to assume that the functional form of the magnetic field of a monopole is the same as that of an electric charge? Explain your reasoning.

14. What are possible sources of systematic uncertainty? Does the equipment contribute? Do you? Be specific in explaining how and why.

15. Can you break a bar magnet and obtain isolated magnetic monopoles? THE MAGNETIC FIELD SENSOR (HALL PROBE)

To measure magnetic field strength, you will need a measurement probe (the magnetic field sensor) and an interface to the computer. Each of these components is described below.

Magnetic Field Sensor

The magnetic field sensor is composed of the wand, the amplifier, and the Universal Lab Interface (ULI). These parts are sketched below.

Amplifier Box

DIN 2 Universal Lab Interface (ULI) The Wand is a hollow plastic tube with a Hall effect transducer chip at one end (shown above as the circle on the right hand end of the wand). The chip produces a voltage that is linear with the magnetic field. The maximum output of the chip occurs when the area vector of the white dot on the sensor points directly toward a magnetic south pole, as shown below:

The ULI allows the computer to communicate with the wand. In order to measure magnetic fields, the wire leading out of the amplifier box must be plugged into the ULI port labeled "DIN 2". The ULI itself should be plugged into the modem port of the computer. The red switch in the back of the ULI turns it on. A green light on the front of the ULI indicates that it is on. The Amplifier is contained in a small box and allows you to measure a greater range of magnetic field strengths. The switch on the box is used to select the desired amplification. The low amplification setting is used to measure strong magnetic fields. The range of the sensor in low mode is about ±64 gauss. The high amplification setting is used to measure weak fields. The range of the sensor in high mode is around ±3.2 gauss. The actual range will vary from one magnetic field sensor to another. Note: 1 tesla = 10 4 gauss, the magnetic field of the earth is approximately half a gauss.

The amplifier setting should be on low to measure fields due to bar magnets.