Lab 8_ Magnetic Field of a Solenoid

Members: Anna Karlsson (6388973), Olivia Mancini (6490410), William Coleman (6404570), Matthew Burton (6280856) Lab 8: Magnetic Field of a Solenoid Preliminary Questions 1. Hold the switch closed. The current should be about 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? The largest magnetic field reading occurred when the white dot on the sensor was pointed toward the end of the slinky (along the x axis). 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? The magnetic field strength decreases when the sensor is facing the other way. The reading was very near to zero when the white dot was pointing perpendicular to the slinky. 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? The magnetic field outside the slinky will be barely noticeable because opposing fields from nearby coils cancel out the components of the magnetic field pointing in other directions. The magnetic field at the ends of the slinky will be half that at its center if we measure the magnetic field there. This is because, in contrast to the middle, where a slinky is present on both sides, the end only has a slinky on one side. 4. Check the magnetic field intensity just outside the solenoid. The magnetic field decreases in intensity as the sensor moves farther away from the center of the slinky. Analysis 1. Plot a graph of magnetic field B vs. the current I through the solenoid. You may launch a fresh copy of LoggerPro, or use the file "magnetic field graph' in the Lab 08 folder.

(See Graphs) 2. How is the magnetic field related to the current through the solenoid? As the current in the solenoid increases, the magnetic field also increases. The graph shows a linear relation. 3. Determine the equation of the best-fit line, including the y-intercept. Note the constants and their units. [ ? = ?? + ?] → ? = 0. 04490 ?𝑇 ? * ? + 0. 001495?𝑇 4. For each of the measurements of Part II, calculate the number of turns per meter. Enter these values in the data table. (See part II Table) 5. Plot a graph of magnetic field B vs. the turns per meter of the solenoid (n). Use either Graphical Analysis or graph paper. (See graphs) 6. How is the magnetic field related to the turns/meter of the solenoid? The number of turns per meter in a solenoid tells us the strength of the magnetic field produced by the solenoid. The more turns per meter, the stronger the magnetic field will be. 7. Determine the equation of the best-fit line to your graph. Note the constants and their units. [? = ?? + ?] → ? = 0. 001032 ?𝑇 ? * ? − 0. 02908?𝑇 8. From Ampere’s law, it can be shown that the magnetic field B inside a long solenoid is ? = µ 0 ?𝐼 where is the permeability constant. Do your results agree with this equation? Explain. µ 0 µ 0 = 4𝜋 * 10 −7 = 1. 25663706212 * 10 −6 𝑇?/? ? = 79 ? −1 𝐼 = 1. 5 ???? ? = µ 0 ?𝐼 = (1. 25663706212 * 10 −6 )(79)(1. 5) = 1. 489114917 * 10 −4 𝑇 ? = ?? + ? = 0. 001032 ?𝑇 ? * (79?) − 0. 02908?𝑇 = 0. 052448?𝑇 = 5. 2448 * 10 −5 𝑇 Our results do not agree with this equation. Two different values for the solenoid’s magnetic field were yielded.

1.0 79 0.05284 1.5 53 0.02455 2.0 40 0.01294 Number of turns in Slinky 79 Graphs Part 1 Part 2