PHY122 lab 9 magnetic field

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School

Stony Brook University *

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122

Subject

Physics

Date

Apr 3, 2024

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docx

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Uploaded by EarlMantisMaster964

Introduction:

In this lab I will be measuring the magnetic field that is created by a current flowing through a long straight wire. Using the lab devices magnetometer with the wheel to measure the magnetic field as a function of position near to a wire carrying a large current. The analysis of the data will confirm the result from Ampere’s Law and also the shape of the magnetic field as being composed of concentric circles surrounding the wire. Objectives: ● Measuring magnetic field strength and direction ● Understand how to derive the field of a wire using Ampere's law ● Verify the shape of the magnetic field around a wire (circles) ● Verify that the magnitude of the field dallas off as 1/r Materials needed: ● 3 or 4 D batteries with appropriate battery cage ● Breadboard ● Two 0.5 resistors ● 12 ft spool of wire ● Wire leads We will be measuring the magnetic field due to a large amount of current flowing through a wire. The magnetic fields will be rather small . When it comes to Ampere’s law, a collection of currents that exhibits sufficient symmetry, provides the simplest means by which to calculate the magnetic field. This law states that: Simple solutions are available when the magnetic field is uniform along some closed path. The screenshot below contains a diagram which was shown in the lab.

The field lines make circles which are centered on the wire and define that we should walk a circular amperes path. On this path, B is both constant and also parallel to dL.. Meaning:

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In this experiment, I was able to show how this formula is correct. The measurement: The lab device has a magnetometer in its upper left corner. We will be using the same setup as we did in the last lab, using three “ D cells” and two high power 0.5 ohm resistors to make a large enough current in order to sense the magnetic field. Then we will roll the lab device magnetometer through the field.

In the diagram above, the blue circle represents a wire carrying current into the screen, which the field lines then make concentric clockwise circles. The lab device will be placed wheels down and rolling along the direction indicated by the dashed black arrow. The lab device coordinate system will match the axes shown in the figure above, positive Z is downward and positive Y is to the right. The magnetometer is inside the lab device and will pass 1 cm above the wire itself. The y component of the field is always positive and is at its largest when the magnetometer is closest to the wire, or in other words directly above it. The purple marks on the figure represent what one might expect for the z component of the magnetic field. Everywhere to the left of the wire, the lines point up and everywhere to the right of the wire, the lines point down. The z component of the magnetic field should be expected to slip as the lab device crosses y=0. Just before the flipping sign, the z component will peak due to the close proximity of the wire. Both of these behaviors are shown in the figure below In this lab I was certain that: ● I understand why these components behave as they do

● Able to deduce the direction of the current using either the Bz or By measurement. / Curves like the red and purple lines in the figure above represent the data collected in this lab and show the field lines make circles around the wire. I used my data to make a more profound conclusion about the rate at which the field falls with r.

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The plot in the center shows the correct calculations of Bz vs By since it uses the correct formula for the magnetic field ( a 1/r dependence). This plot makes a perfect circle with the width and the height being the same, while the other two are not circles since they have different r dependencies of the fall off of the magnetic field. The shape of the plot in the above diagram indicates the correct “ power of r” that the field formula follows. In this lab I measured this correlation and compared it to my results to these three figures to see if the lab device measurement is able to prove the 1/r result from Ampere’s law. Calibration: The magnetic probe is very sensitive and measures small magnetic fields, so the measurements can be disturbed by stray fields in the environment very easily. This is why I was sure to calibrate the sensor in order to verify the accuracy of the calibration before making my measurements. It is important to make sure that this is done in a good space and not on a magnetic surface, while being far away from high current devices and field sources like the neodymium magnets that are in the lab kit. The video in the lab shows how to calibrate and also verify the lab device. Experimental setup: In this lab I am using the same setup which was used in the last lab, it can be seen in the figure below.

The 4.5 Volt is the pack of 3-D cell batteries here and the current will be measured using the two 0.5 volt high power resistors. I was sure to use the correct resistors since lower power resistors will become very hot and may result in smoke due to that much power going through them. Fresh batteries will most likely result in over 2 Amps of current in the circuit. The video in the lab shows how to wire and operate the circuit. Being that the batteries will not last for a long time because we are drawing a large current from the batteries, it is important that the long wire is not plugged in when the circuit is not being used. Taking Data: After data is taken, press the button found along the top of the lab software screen in order to enter parametric plot mode, which will then result in2 plots. Using the top plot for y vs. By, and must change the magnetometer ti By instead of norm, and for y v. Bz, you must change the magnetometer to Bz.When the bottom plot for By v. Bz is used, they must be changed from the norm. The video in the lab shows the data taking process for this lab. Two sets of data are taken in the first step, and the “A7” input of the lab device is used to measure the current flowing through the circuit. Record the voltage across the 0.5 resistor and use this with Ohm’s Law to determine the current that is flowing through the circuit. This is a 0.5 resistor and now a 1 resistor. In the second measurement, roll the lab device across the wire using a few pieces of paper to make it smooth while recording both the magnetometer and the wheel. A few passes with the lab device over wire should allow you to get all of the

data needed in order to complete the full analysis of the lab. The video in the lab shows both the steps required in order to take the data as well as help with how to analyze the data received during the lab. After completing the steps in the video, you are done. It is important that the analysis in the lab write up includes all of the following: ● A measurement of the current through the circuit using Ohm’s Law ● An analysis of the shapes of By vs. y and Bz vs. y. This will be done with two different parametric plots. Make sure the component of the magnetic field on the parametric plot is charged making it so that you are looking at By or Bz, not the total B-field. Explain how these curves are able to tell that the field lines actually do circle the wire as we expected. ● Analysis of the peak value of By and a quantitative comparison of that field value with the one expected from an Ampere’s Law analysis. Use a radius of 1 cm in the Ampere’s Law analysis with the measured current to predict and confirm the measured peak magnetic field. If the field seems low, make sure to check the current in the circuit one final time in order to make sure that the batteries are not dying. ● An analysis of the shape of Bz vs. By which we use “height-to-width” ratio in order to tell whether the field goes as 1/r or some other power of r. The plots shown earlier in this lab can be used as a reference here. Results: Figure 1: As seen in figure 1 above, the voltage was constant after recording for about 5 seconds, as the line does not move at all. The y axis shows the A(V) voltage and the X axis shows the time in which it is in seconds. During this lab, I recorded the voltage to be 1.3075 V. Figure 2:

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The plot in figure 2 above, shows the peak of the magnetic field and position of the By. I recorded the peak being -40.8479 micro teslas, and .0566 m. Figure 3: Figure 3 above shows the parametric plot of the point of inflection, 45.733 micro teslas and 0.0455 m Calculations:

Discussion & Conclusion: While recording the data after setting up, I noticed how the voltage was constant as a few seconds of data was recorded, where the voltage was found to be 1.3075. The graph in the lab was able to show the magnetometer vs. wheel graph of the data in the experiment. When it comes to Ampere’s Law in which we covered throughout this lab, a collection of currents that exhibit sufficient symmetry, the law provides the simplest means by how the magnetic field can be calculated. As shown in the report above and in the lab as well, in the diagram we can see how the field lines make circles that are centered on the wire that also define that we should walk a circular Ampere’s path. I was able to prove the formula for this law to be correct and demonstrated it during the lab. My hypothesis was correct and proven by my results. The shape of the magnetic field was seen to be circular meaning that my results were able to confirm Ampere’s law. As seen in the calculations above, I calculated the expected value of the magnetic field to be 52.024 micro tesla, which was then compared to the experimental value of 45.733 microtesla resulting in 12.09% error. Possible error could have been due to human error or other devices nearby the room, although I tried my absolute best to keep electron devices away from the magnetometer. In order to minimize this percent error, one could repeat the experiment multiple times or be sure to have no other devices around.

PHY122 lab 9 magnetic field

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