L=0.6m L=1.0m L=1.4m L=1.8m L=2.2m L=2.6m Time B Time B Time B Time B Time B Time B (s) (mT) (s) (mT) (s) (mT) (s) (mT) (s) (mT) (s) (mT ) 0.00 0.758 0.00 0.427 0.00 0.337 0.00 0.258 0.00 0.219 0.00 0.187 0.05 0.754 0.05 0.424 0.05 0.333 0.05 0.254 0.05 0.219 0.05 0.183 0.10 0.754 0.10 0.424 0.10 0.337 0.10 0.254 0.10 0.219 0.10 0.183 0.15 0.754 0.15 0.424 0.15 0.341 0.15 0.254 0.15 0.219 0.15 0.187 0.20 0.754 0.20 0.427 0.20 0.341 0.20 0.254 0.20 0.219 0.20 0.187 0.25 0.754 0.25 0.427 0.25 0.341 0.25 0.254 0.25 0.223 0.25 0.183 0.30 0.758 0.30 0.427 0.30 0.337 0.30 0.250 0.30 0.223 0.30 0.183 0.35 0.758 0.35 0.427 0.35 0.333 0.35 0.254 0.35 0.223 0.35 0.179 0.40 0.754 0.40 0.427 0.40 0.337 0.40 0.250 0.40 0.223 0.40 0.183 0.45 0.758 0.45 0.427 0.45 0.337 0.45 0.254 0.45 0.223 0.45 0.183 0.50 0.754 0.50 0.424 0.50 0.341 0.50 0.254 0.50 0.219 0.50 0.187 0.55 0.754 0.55 0.424 0.55 0.337 0.55 0.250 0.55 0.219 0.55 0.183 0.60 0.754 0.60 0.424 0.60 0.341 0.60 0.258 0.60 0.219 0.60 0.187 0.65 0.754 0.65 0.424 0.65 0.337 0.65 0.250 0.65 0.219 0.65 0.183 0.70 0.758 0.70 0.424 0.70 0.333 0.70 0.250 0.70 0.223 0.70 0.183 0.75 0.754 0.75 0.427 0.75 0.341 0.75 0.258 0.75 0.219 0.75 0.183 0.80 0.758 0.80 0.427 0.80 0.337 0.80 0.254 0.80 0.219 0.80 0.183 0.85 0.758 0.85 0.427 0.85 0.337 0.85 0.258 0.85 0.219 0.85 0. 183 0.90 0.754 0.90 0.427 0.90 0.341 0.90 0.258 0.90 0.219 0.90 0.187 0.95 0.754 0.95 0.431 0.95 0.337 0.95 0.254 0.95 0.215 0.95 0.183 1.00 0.754 1.00 0.424 1.00 0.337 1.00 0.254 1.00 0.219 1.00 0.183 1.05 0.754 1.05 0.427 1.05 0.341 1.05 0.250 1.05 0.219 1.05 0. 187 1.10 0.754 1.10 0.431 1.10 0.341 1.10 0.250 1.10 0.219 1.10 0.187 1.15 0.754 1.15 0.431 1.15 0.341 1.15 0.254 1.15 0.219 1.15 0.191 1.20 0.758 1.20 0.431 1.20 0.337 1.20 0.254 1.20 0.219 1.20 0.187 1.25 0.758 1.25 0.427 1.25 0.337 1.25 0.250 1.25 0.215 1.25 0.187 1.30 0.758 1.30 0.427 1.30 0.341 1.30 0.250 1.30 0.215 1.30 0.187 1.35 0.754 1.35 0.427 1.35 0.341 1.35 0.250 1.35 0.219 1.35 0.187 1.40 0.758 1.40 0.427 1.40 0.341 1.40 0.250 1.40 0.219 1.40 0.187 1.45 0.754 1.45 0.427 1.45 0.341 1.45 0.254 1.45 0.219 1.45 0.191 1.50 0.758 1.50 0.427 1.50 0.337 1.50 0.254 1.50 0.227 1.50 0. 187 1.55 0.754 1.55 0.427 1.55 0.337 1.55 0.250 1.55 0.219 1.55 0.187 1.60 0.754 1.60 0.427 1.60 0.337 1.60 0.250 1.60 0.215 1.60 0. 187 1.65 0.754 1.65 0.427 1.65 0.337 1.65 0.254 1.65 0.215 1.65 0. 187 1.70 0.758 1.70 0.427 1.70 0.337 1.70 0.250 1.70 0.211 1.70 0.187 1.75 0.758 1.75 0.427 1.75 0.337 1.75 0.250 1.75 0.215 1.75 0.183Magnetic Field (mT) 0.7 .0 01 Statistics for: L=1.4m | Magnetic Field min: 0.3290 at 3.650 max: 0.3408 at 0.1500 mean: 0.3374 median: 0.3369 std. dev: 0.002492 samples: 101 AB: 0.012 Statistics for: L=1.8m | Magnetic Field min: 0.2463 at 2.150 max: 0.2581 at 0 mean: 0.2526 median: 0.2542 std. dev: 0.002854 samples: 101 AB: 0.012 Statistics for: L=1.0m | Magnetic Field min: 0.4196 at 1.900 max: 0.4314 at 0.9500 mean: 0.4272 median: 0.4274 std. dev: 0.002774 samples: 101 AB: 0.012 Statistics for: L=2.2m | Magnetic Field min: 0.2069 at 3.650 max: 0.2266 at 1.500 mean: 0.2160 median: 0.2148 std. dev: 0.003502 samples: 101 AB: 0.020 Statistics for: L=0.6m | Magnetic Field min: 0.7503 at 2.800 max: 0.7622 at 2.300 mean: 0.7566 median: 0.7582 ' std. dev: 0.002563 samples: 101 AB: 0.012 Statistics for: L=2.6m | Magnetic Field min: 0.1794 at 0.3500 max: 0.1951 at 2.100 mean: 0.1865 median: 0.1872 \\ std. dev: 0.002694 samples: 101 AB: 0.016 0.1 Til-\"fl {n\\ Magnetic Field (mT) 1.0 0.8 .0 a: 0.4 0.2 0.0 Statistics for: l=1.6A | Magnetic Field min: 0.2660 at 0.6500 max: 0.2778 at 0.2000 mean: 0.2721 median: 0.2739 std. dev: 0.002919 samples: 101 AB: 0.012 Statistics for: l=0.4A| Magnetic Field min: 0.05337 at 0.05000 max: 0.06124 at 0.1500 mean: 0.05843 median: 0.05730 std. dev: 0.002511 samples: 101 AB: 0.008 Statistics for: l=2.0A| Magnetic Field min: 0.3329 at 0.1000 max: 0.3408 at 0.2500 mean: 0.3373 median: 0.3369 std. dev: 0.002121 samples: 101 AB: 0.008 Statistics for: l=0.8A| Magnetic Field min: 0.1203 at 0.1000 max: 0.1321 at 0.2500 mean: 0.1271 median: 0.1282 std. dev: 0.002735 samples: 101 AB: 0.012 'I'imn In\\ Statistics for: |=2.4A| Magnetic Field min: 0.3999 at 3.400 max: 0.4156 at 1.800 mean: 0.4068 median: 0.4078 std. dev: 0.002516 samples: 101 AB: 0.016 Statistics for: l=1.2A| Magnetic Field min: 0.1912 at 3.800 max: 0.2030 at 0.3000 mean: 0.1986 median: 0.1991 std. dev: 0.002508 samples: 101 AB: 0.012 1=0.4A 1=0.8A 1=1.2A 1=1.6A 1=2.0A 1=2.4 A B ime B Time B Time B ime B Time B Time B nT ) (s) (mT) (s) mT (s) (mT) (s) (mT) (s) mT) (s) (mT) 0.00 0.057 0.00 .128 0.00 0. 199 0.00 0.274 0.00 0.337 0.00 0.408 0.05 0.053 0.05 0.128 0.05 0. 199 0.05 0.274 0.05 0.337 0.05 0.404 0.10 0.057 0.10 0.120 0.10 0. 195 0.10 0.270 0.10 0.333 0.10 0.404 0.15 0.061 0.15 0.128 0.15 0. 199 0.15 0.270 0.15 0.337 0.15 0.404 0.20 0.057 0.20 0.128 0.20 0. 199 0.20 0.278 0.20 0.337 .20 0.404 0.25 0.057 0.25 0.132 0.25 0.199 0.25 0.270 0.25 0.341 0.25 0.412 0.30 0.061 0.30 0.132 .30 0.203 0.30 0.270 0.30 0.337 .30 0.404 0.35 0.057 0.35 0.124 0.35 0.195 0.35 0.274 0.35 0.337 0.35 0.404 0.40 0.053 0.40 0.124 0.40 0.199 0.40 0.274 0.40 0.341 0.40 0.404 0.45 0.061 0.45 0.128 0.45 0. 199 0.45 0.270 0.45 0.337 0.45 0.404 0.50 0.061 0.50 0.124 0.50 0. 199 0.50 0.274 0.50 0.337 0.50 0.404 0.55 0.061 0.55 0.132 0.55 0. 199 0.55 0.270 0.55 0.337 0.55 0.408 0.60 0.061 0.60 0.128 0.60 0. 199 0.60 0.274 0.60 0.341 0.60 0.408 0.65 0.057 ).65 0.124 0.65 0.199 0.65 0.266 0.65 0.333 .65 0.404 0.70 0.057 0.70 0.128 0.70 0.203 0.70 0.270 0.70 0.337 0.70 0.404 0.75 0.061 0.75 0.128 0.75 0.199 0.75 0.274 0.75 0.341 0.75 0.408 0.80 0.061 0.80 0.132 0.80 0. 199 0.80 0.274 0.80 0.341 0.80 0.408 0.85 0.061 0.85 0.132 0.85 0. 199 0.85 0.270 0.85 0.337 0.85 0.408 0.90 0.057 ).90 0.128 .90 0.199 0.90 0.274 0.90 0.333 .90 0.404 0.95 0.057 0.95 0.128 0.95 0.199 0.95 0.270 0.95 0.337 0.95 0.404 1.00 0.057 1.00 0.128 1.00 0.195 1.00 0.266 1.00 0.341 1.00 0.408 1.05 0.061 1.05 0.132 1.05 0. 199 1.05 0.274 1.05 0.333 1.05 0.408 1.10 0.057 1.10 0.128 1.10 0.199 1.10 0.274 1.10 0.341 1.10 0.408 1.15 0.057 1.15 0.128 1.15 0.199 1.15 0.274 1.15 0.341 1.15 0.408 1.20 0.061 1.20 0.128 1.20 0.199 1.20 0.274 1.20 0.337 1.20 0.404 1.25 0.053 1.25 0.128 1.25 0. 199 1.25 0.270 1.25 0.337 1.25 0.404 1.30 0.057 1.30 0. 124 1.30 0.195 1.30 0.274 1.30 0.337 1.30 0.404 1.35 0.061 1.35 0.128 1.35 0.195 1.35 0.274 1.35 0.337 1.35 0.408 1.40 0.061 1.40 0.124 1.40 0.203 1.40 0.270 1.40 0.341 1.40 0.408 1.45 0.057 1.45 0.128 1.45 0.199 1.45 0.266 1.45 0.337 1.45 0.408 1.50 0.061 1.50 .128 1.50 0. 199 1.50 0.266 1.50 0.337 1.50 0.412 1.55 0.053 1.55 0.124 1.55 0.199 1.55 0.266 1.55 0.337 1.55 0.408 1.60 0.053 1.60 0.124 1.60 0.195 1.60 0.266 1.60 0.337 1.60 0.408 1.65 0.057 1.65 0.124 1.65 0.203 1.65 0.274 1.65 0.333 1.65 0.408 1.70 0.057 1.70 0.128 1.70 0.195 1.70 0.270 1.70 0.337 1.70 0.408 1.75 0.061 1.75 0.132 1.75 0.195 1.75 0.266 1.75 0.337 1.75 0.408Lab 6 "The Magnetic Field in a Slinky." A solenoid is made by taking a tube and wrapping it with many turns of wire. A metal Slinky" is the same shape and will serve as our solenoid. When a current passes through the wire, a magnetic field is present inside the solenoid. Solenoids are used in electronic circuits or as electromagnets. In this lab we will explore factors that affect the magnetic field inside the solenoid and study how the field varies in different parts of the solenoid. By inserting a Magnetic Field Sensor between the coils of the Slinky, you can measure the magnetic field inside the coil. You will also measure Mo, the permeability constant. The permeability constant is a fundamental constant of physics. OBJECTIVES . Determine the relationship between magnetic field and the current in a solenoid. . Determine the relationship between magnetic field and the number of turns per meter in a solenoid. . Study how the field varies inside and outside a solenoid. . Determine the value of Ho, the permeability constant. Power supply Interface Ammeter 12 Switch Figure 1 MATERIALS: computer meter stick Vernier computer interface DC power supply with switch Logger Pro ammeter Vernier Magnetic Field Sensor cardboard spacers Slinky connecting wires tape and cardboard INITIAL SETUP: 1. Connect the Vernier Magnetic Field Sensor to Channel 1 of the interface. Set the switch on the sensor to High. 2. Stretch the Slinky until it is about 1 m long. The distance between the coils should be about 1 cm. Use a non-conducting material (tape, cardboard, etc.) to hold the Slinky at this length. 3. Set up the circuit and equipment as shown in Figure 1. Wires with clips on the end should be used to connect to the Slinky. If your power supply has an accurate internal ammeter you do not need an additional external ammeter.4. Turn on the power supply and adjust it so that the ammeter reads 2.0 A when the switch is held closed. Note: This lab requires fairly large currents to flow through the wires and Slinky. Only close the switch so the current flows when you are taking a measurement. The Slinky, wires, and possibly the power supply may get hot if left on continuously. 5. Open the file "29 Magnetic Field in Slinky" in the Physics with Computers folder. A graph will appear on the screen. The meter displays magnetic field in millitesla, mT. The meter is a live display of the magnetic field intensity. PRELIMINARY QUESTIONS: 1. Hold the switch closed. The current should be 2.0 A. Place the Magnetic Field Sensor between the turns of the Slinky near its center. Rotate the sensor and determine which direction gives the largest magnetic field reading. What direction is the white dot on the sensor pointing? 2. What happens if you rotate the white dot to point the opposite way? What happens if you rotate the white dot so it points perpendicular to the axis of the solenoid? 3. Stick the Magnetic Field Sensor through different locations along the Slinky to explore how the field varies along the length. Always orient the sensor to read the maximum magnetic field at that point along the Slinky. How does the magnetic field inside the solenoid seem to vary along its length? 4. Check the magnetic field intensity just outside the solenoid. PROCEDURE: Part I Magnetic Field vs. Current in a Solenoid? For the first part of the experiment you will determine the relationship between the magnetic field at the center of a solenoid and the current flowing through the solenoid. As before, leave the current off except when making a measurement. 1. Place the Magnetic Field Sensor between the turns of the Slinky near its center. 2. Close the switch and rotate the sensor so that the white dot points directly down the long axis of the solenoid. This will be the position for all of the magnetic field measurements for the rest of this lab. Figure 210. 11. Click , Collect to begin data collection. Wait a few seconds and close the switch to turn on the current. If the magnetic eld increases when the switch is closed, you are ready to take data. If the eld decreases when you close the switch, rotate the Magnetic Field Sensor so that it points the other direction down the solenoid. With the Magnetic Field Sensor in position and the switch open, click the Zero button, a Zero 1, to zero the sensor and remove readings due to the Earth's magnetic eld, any magnetism in the metal of the Slinky, or the table. Adjust the power supply so that 0.5 A will ow through the coil when the switch is closed. Click v Collect to begin data collection. Close the switch for at least 10 seconds during the data collection. View the eld vs. time graph and determine the region of the curve where the current was owing in the wire. Select this region on the graph by dragging over it. Determine the average field strength while the current was on by clicking the Statistics button, +52. Record the average eld in the data table. Increase the current by 0.5 A and repeat Steps 7" and 8. Repeat Step 9 up to a maximum of 2.0 A. Count the number of turns of the Slinky and measure its length. If you have any unstretched part of the Slinky at the ends, do not count it for either the turns or the length. Calculate the number of turns per meter of the stretched portion. Record the length, turns, and the number of turns per meter in the data table. Part II Magnetic Field vs. Number of Tums per length? 12. 13. 14. 15. 16. For the second part of the experiment, you will determine the relationship between the magnetic eld in the center of a coil and the number of turns of wire per meter of the solenoid. You will keep the current constant. Leave the Slinky set up as shown in Figure 1. The sensor will be oriented as it was before, so that it measures the eld down the middle of the solenoid. You will be changing the length of the Slinky 'om 0.5 to 2.0 m to change the number of turns per meter. Adjust the power supply so that the current will be 1.5 A when the switch is closed. With the Magnetic Field Sensor in position, but no current owing, click a Zero to zero the sensor and remove readings due to the Earth's magnetic eld and any magnetism in the metal of the Slinky. Since the Slinky is made of an iron alloy, it can be magnetized itself. Moving the Slinky aron can cause a change in the eld, even if no current is owing. This means you will need to zero the reading each time you move or adjust the Slinky. Click b Collect to begin data collection. Close and hold the switch for about 10 seconds during the data collection. As before, leave the switch closed only during actual data collection. View the eld vs. time graph and determine where the current was owing in the wire. Select this region on the graph by dragging over it. Find the average eld while the current was on by clicking on the Statistics button, Count the number of turns of the Slinky and measure its length. If you have any unstretched part of the Slinky at the ends, do not count it for either the turns or the length. Record the length of the Slinky and the average eld in the data table. Repeat Steps 13 15 after changing the length of the Slinky. Each time, zero the Magnetic Field Sensor with the current off. Make sure that the current remains at 1.5 A each time you turn it on. DATA TABLES: Part I Electric Current I (A) Magnetic Field B (mT) Length of solenoid 1.25 Number of turns 181 Turns/meter (m-1 Part II Length of solenoid Turns/meter Magnetic field L(m) n ( m ] ) B (mT Current (A) 2.0 Number of turns in Slinky 181 ANALYSIS: 1. Use Logger Pro to create a graph magnetic field B vs. the current / through the solenoid. 2. How is magnetic field related to the current through the solenoid? 3. Determine the equation of the best-fit line, including the y-intercept. Note the constants and their units. 4. For each of the measurements of Part II, calculate the number of turns per meter. Enter these values in the data table.5. Use the slope and determine the permeability of the free space (Ho) B = MON yields -I = slopel - " slope = MON 7 L 6. Determine the percentage error with the true Mo = 4x X 10-7I'm A 7. Use Logger Pro and graph of magnetic field vs. Length (B vs. L). Obtain the equation of best fit for this relationship, describe the relationship. 8. Use Logger pro and graph of Magnetic Field vs the number of turns per unit of length (B vs. n). Get the Linear regression, explain the meaning of the slope and the y-intercept. 9. Use the slope and determine the permeability of the free space (Ho) B = HoIN(-) = slope()- yields slope = HoIN 11. Ampere's law, it can be shown that the magnetic field B inside a long solenoid is B = Hon! where / is the permeability constant. Do your results agree with this equation? Explain. 12. Was your Slinky positioned along an east-west, north-south, or on some other axis? Will this have any effect on your readings? 13. Our slinkies are made from steel, so they contain Iron. Does the material of the slinky influences the value of the magnetic field? Why? CONCLUSIONS: 1. Definitions: Magnetic Field, Sources of Magnetic Field, Gauss's Law for Magnetism, Ampere's Law, magnetic materials classification. 2. Include a brief explanation of how in MRI (magnetic resonance imaging) work, and how the magnetic field in MRI machines is created. 3. Physical Meaning of the Slope and the y-intercepts 4. Derivation of Equations and Mathematical representation of Definitions: Especially that of the magnetic field of a solenoid. 5. Sources of errors