The Magnetic Field. Magnetic fields generated by current-carrying wires

Transcription

1 OBJECTIVES The Magnetic Field Use a Magnetic Field Sensor to measure the field of a long current carrying wire and at the center of a coil. Determine the relationship between magnetic field and the number of turns in a current carrying coil. Determine the relationship between magnetic field and the current in a current carrying wire/coil. Determine the relationship between magnetic field and the distance from a long current carrying wire. MATERIALS Computer Vernier Lab Pro computer interface Vernier Magnetic Field Sensor Logger Pro Clay Tape Switch Metric Ruler Adjustable power supply Long straight section of insulated wire Circular frame with 10 loops of insulated wire THEORY Magnetic fields generated by current-carrying wires Circular magnetic fields are generated around current carrying wires. The strength of these fields varies directly with the size of the current flowing through the wire and inversely to the distance from the wire. In the left diagram, the solid circle in the center represents a cross-section of a currentcarrying wire in which the current is coming out of the plane of the paper. In the right diagram, a side view of this arrangement is shown. End View Side View The Magnetic Field - Page 1

2 The concentric circles surrounding the wire's cross-section represent magnetic field lines. The rule to determine the direction of the magnetic field lines is called the right hand curl rule. In this rule, your thumb points in the direction of the current fingers curl in the direction of B. The equation to calculate the strength of the magnetic field around a current-carrying wire is: μ0i B = 2 πr Equation 1 Where, µ o, permeability of free space = 4π x 10-7 Tm/A I, current flowing through the wire, measured in amps B, magnetic field strength, measured in Tesla R, distance from the wire, measured in meters Magnetic fields generated by current-carrying loops A solenoid is a coil of wire designed to create a strong magnetic field inside the coil. By wrapping the same wire many times around a cylinder, the magnetic field due to the wires can become quite strong. More loops will bring about a stronger magnetic field. The formula for the field inside the solenoid is: µ B on I L = [ONLY near the center!] Equation 2 Where, µ o, permeability of free space = 4π x 10-7 Tm/A N, number of turns of wire around the solenoid, measured as a whole # I, current flowing through the wire, measured in amps B, magnetic field strength, measured in Tesla L, length from one end of the coil to the other, measured in meters In a solenoid, a large field is produced parallel to the axis of the solenoid. Components of the magnetic field in other directions are cancelled by opposing fields from neighbouring coils. Outside the solenoid the field is also very weak due to this cancellation effect and for a solenoid which is long in comparison to its diameter, the field is very close to zero. Inside the solenoid the fields from individual coils add together to form a very strong field along the center of the solenoid. The Magnetic Field - Page 2

3 However, Equation 2 only works for solenoid that is long and narrow; length >> diameter. The solenoid used in this experiment is a large (diameter compared to length) coil. This coil will be positioned so that the center of the coil is aligned with the center of the magnetic field probe. So, for a coil of this type, the expression for the magnetic field of a solenoid must be modified to include the diameter, as shown in Equation 3 below: µ o B = N I L 1+ 1 D L 2 Equation 3 Where, μo, permeability of free space = 4π x 10-7 Tm/A N, number of turns of wire around the solenoid, measured as a whole # I, current flowing through the wire, measured in amps B, magnetic field strength, measured in Tesla L, length from one end of the coil to the other, measured in meters D, is the diameter of the coil, measured in meters Note that Equation 3 reduces to the more familiar expression for the magnetic field near the center of a solenoid (Equation 2) when the diameter is very, very small compared to the length. The magnetic field is measured at the center of the coil. As the probe used in the experiment can't be placed in the exact center of the coil, your experimental value should be less than the theoretical value. Based on the experimental setup used, this value could differ by as much as 10% - 20%. The Magnetic Field - Page 3

4 INITIAL SETUP MAGNETIC FIELD OF A CURRENT-CARRYING WIRE 1. Connect the Vernier Magnetic Field Sensor to Channel 1 of the interface. Set the switch on the sensor to high amplification (x200). 2. Start LoggerPro You will need to set up this sensor if it is not automatically recognized: o To do this, select Experiment from the top menu bar o Choose Set Up Sensors, Show All Interfaces o Along the right side menu is a list of analog sensors. Scroll down and find the magnetic field sensor. o Drag and drop this sensor to the illustration of the LabPro where it shows CH1 o Ignore any requests to calibrate the sensor o Close all of these set-up windows o A graph of magnetic field vs. time should now appear on the screen. 3. Stretch a long section of insulated wire vertically from the lab table to a support stand. 4. Connect the wire, switch, and power supply. PROCEDURE Keep other magnetic field producing items (power supplies, extra current carrying wires, cell phones, etc.) away from the magnetic field sensor!! For the first part of the experiment you will determine the relationship between the magnetic field of a current carrying wire as a function of distance and the current through the wire. Leave the current off except when making a measurement. Wire - Part I 1. Set the power supply so that the current will be 0.5 A when the switch is closed. Reopen the switch before continuing. 2. Carefully clamp the Magnetic Field Sensor in the stand and place it in a horizontal position so that the flat end is TOUCHING the wire. The Magnetic Field - Page 4

5 The white dot should face side-to-side along the table as illustrated below: Wire Clamp Magnetic Field Sensor Stand 3. We will first zero the sensor when no current is flowing; that is, we will remove the effect of the Earth s magnetic field and any local magnetism. With the switch open, click. 4. Leaving the Magnetic Field Sensor touching the wire, close the switch and click to begin data collection. 5. A field vs. time graph will be created for 10 s while the current is flowing in the wire. Determine the average field while the current was on by clicking on the Statistics button,. The entire 10 s data collection region should be automatically selected. Record the absolute value (a positive number only) of the mean magnetic field for the 0.5 A current. Regardless of whether or not your actual value is negative, you must only record a POSITIVE number in the data table! 6. Repeat the data collection for 1.0 A, 1.5 A, 2.0 A, 2.5 A, and 3.0 A current settings. Wire - Part II 1. Set the power supply so that the current will be approximately 5.0 A when the switch is closed. Reopen the switch before continuing. 2. We will again re-zero the sensor when no current is flowing; that is, we will remove the effect of the Earth s magnetic field and any local magnetism. With the switch open, click. The Magnetic Field - Page 5

6 3. Place the center of the white dot on the Magnetic Field Sensor at a distance of 1cm from the center of the wire, close the switch and click collection. to begin data 4. Again, determine the average field while the current was on by clicking on the Statistics button,. Record the absolute value (a positive number only) of the mean magnetic field for the 1.0 cm distance. Regardless of whether or not your actual value is negative, you must only record a POSITIVE number in the data table! 5. Leave the current set at 5.0 A and repeat the data collection for 2 cm, 3 cm, 4 cm, and 5 cm distances. INITIAL SETUP MAGNETIC FIELD OF A CURRENT-CARRYING LOOP 1. Connect the Vernier Magnetic Field Sensor to Channel 1 of the interface. Set the switch on the sensor to high amplification (x200). 2. You have a round frame coil on which ten loops of magnetic wire have been wound. 3. Connect the coil, switch, and power supply. The connections for the coil need to be made nears the ends of the magnetic wire where the enamel coating has been removed (look carefully). Connecting the enamel sections with result in an open circuit. 4. Carefully clamp the Magnetic Field Sensor in the stand and place it in a horizontal position so that the flat end is in the CENTER of the coil and as close to the coil as possible. In particular, notice that the coil wires are closer to one side vs. the other; place the sensor on the side closest to the wires. The white dot should face AWAY from the plane of the coil as illustrated below: Coil Clamp Magnetic Field Sensor Stand The Magnetic Field - Page 6

7 PROCEDURE Loop Part I - How Is The Magnetic Field In A Coil Related To The Current? For the first part of the experiment you will determine the relationship between the magnetic field in the center of a coil and the current through the coil. Use the loop with all ten turns for all of Part I. As before, leave the current off except when making a measurement. 1. Set the power supply so that the current will be 0.5 A when the switch is closed. Reopen the switch before continuing. 2. We again zero the sensor when no current is flowing; that is, we will remove the effect of the Earth s magnetic field and any local magnetism. With the switch open, click. 3. Close the switch, click to begin data collection. 4. You'll again determine the average field while the current was on by clicking on the Statistics button,. Record the absolute value (a positive number only) of the mean magnetic field and the current through the coil in the data table. Regardless of whether or not your actual value is negative, you must only record a POSITIVE number in the data table! 5. Briefly close the switch and increase the current by 0.5 A and repeat Steps 3 and Repeat Step 5 up to a maximum of 3.0 A. Loop Part II - How Is The Magnetic Field In A Coil Related To The Number Of Turns? For the second part of the experiment you will determine the relationship between the magnetic field at the center of a coil and the number of turns in the coil. The Magnetic Field Sensor should be oriented as before. Leave the current off except when making a measurement. 1. Set the power supply so that the current will be 3.0 A when the switch is closed. Reopen the switch before continuing. 2. We will again zero the sensor when no current is flowing. That is, we will remove the effect of the Earth s magnetic field and local magnetism. With the switch open, click on. 3. Be sure the Magnetic Field Sensor is in the position indicated, close the switch and click. The Magnetic Field - Page 7

8 4. Again, determine the mean field while the current was on by clicking on the Statistics button,. Record the absolute value (a positive number only) of the mean magnetic field for the 10-turn coil. Regardless of whether or not your actual value is negative, you must only record a POSITIVE number in the data table! 5. Remove one loop of wire from the coil to reduce the number of turns to 9 and repeat the magnetic field measurement. Upon unwrapping the first loop (and any successive loops) secure the free end with the tape as opposed to trying to secure it through the bindings holes in the coil. If you move the frame or the sensor, make sure that you get it back to the same orientation as the previous measurement. 6. Repeat these steps through one turn of wire on the frame. Keep the current at 3.0 A. ANALYSIS - Unplug the LabPro from the computer - Open a new, blank sheet in Logger Pro Wire - Part I: Change in Current 1. Using Logger Pro, plot a graph of magnetic field (y-axis) vs. current through the wire (x-axis). What is the relationship between the current in a wire and the resulting magnetic field of the wire? Explain the expectation based on theory. 2. Using the Linear Regression tool, determine the slope of this line. Qualitatively explain the significance of the value of the slope? Using Equation 1, calculate the value that the slope should be for comparison. Print a copy of this graph for inclusion in your laboratory report. Answer the ANALYSIS questions on the back of the graph page. Wire - Part II: Change in Distance 1. Using Logger Pro, plot a graph of magnetic field (y-axis) vs. distance from the wire (xaxis). What is the relationship between the distance from the wire and the resulting magnetic field of the wire? Explain the expectation based on theory. 2. Using the Linear Regression tool, determine the slope of this line. Qualitatively explain the significance of the value of the slope? No actual calculations are required here! Print a copy of this graph for inclusion in your laboratory report. Answer the ANALYSIS questions on the back of the graph page. The Magnetic Field - Page 8

9 Loop - Part I: Change in Current 1. Using Logger Pro, plot a graph of magnetic field (y-axis) vs. current through the coil (x-axis). Page 2 of the experiment file is set up for this graph. What is the relationship between the current in a coil and the resulting magnetic field at the center of the coil? Explain the expectation based on theory. 2. Using the Linear Regression tool, determine the slope of this line. Qualitatively explain the significance of the value of the slope? Using Equation 3, calculate the value that the slope should be for comparison. Print a copy of this graph for inclusion in your laboratory report. Answer the ANALYSIS questions on the back of the graph page. Loop - Part II: Change in Number of Loops 1. Using Logger Pro, plot a graph of magnetic field (y-axis) vs. the number of turns on the coil (x-axis). What is the relationship between the magnetic field and the number of turns on the coil? Explain the expectation based on theory. 2. Using the Linear Regression tool, determine the slope of this line. Qualitatively explain the significance of the value of the slope? No actual calculations are required here! Print a copy of this graph for inclusion in your laboratory report. Answer the ANALYSIS questions on the back of the graph page. COVER PAGE REPORT ITEMS (To be submitted and stapled in the order indicated below) (-5 points if this is not done properly) Lab Title Each lab group member's first and last name printed clearly Group Color Date DATA (worth up to 20 points) Data tables are available as a downloadable Excel file DATA ANALYSIS (worth up to 0 points) None The Magnetic Field - Page 9

10 GRAPHS (worth up to 20 points) I vs. B for wire x vs. B for a wire I vs. B for a loop # Turns vs. B for a loop GRAPH ANALYSIS (worth up to 20 points) I vs. B for wire questions/conclusions x vs. B for a wire questions/conclusions I vs. B for a loop questions/conclusions # Turns vs. B for a loop questions/conclusions CONCLUSION (worth up to 30 points) See the Physics Laboratory Report Expectations document for detailed information related to each of the four questions indicated below. 1. What was the lab designed to show? 2. What were your results? 3. How do the results support (or not support) what the lab was supposed to show? 4. What are some reasons that the results were not perfect? QUESTIONS (worth up to 0 points) DO NOT forget to include the answers to questions that were asked within the experimental procedure None The Magnetic Field - Page 10