## AP Physics - Froehlich's Physics

readings. As for the solenoid, we will use everyone's favorite toy, a Slinky®. ... Connect the magnetic field sensor to an analog port of a Vernier LabPro. Set the.

AP Physics Magnetic Field within a Solenoid Lab You can make a solenoid by taking a tube and wrapping it with many turns of insulated wire, such that the length of the tube and associated windings is substantially greater than the diameter. When a current runs through the wire, the magnetic fields produced by all those turns add up in the center of the solenoid to produce a large magnetic field. You already have familiarity with Ampere’s law in which the line integral of B around any closed path equals µ0 times the current through the area enclosed by the path. Ampere’s law symbolically stated:

∫ B⋅ ds = µ I

0 encl

In this lab we will investigate the magnetic field produced by a solenoid and determine how various factors affect the size of the magnetic field inside the solenoid. To measure the magnetic field we will€use a hall-effect magnetic field probe, which measures the component of the magnetic field that passes perpendicularly through the end of the sensor. Keep this in mind as the orientation of the sensor may greatly affect your readings. As for the solenoid, we will use everyone’s favorite toy, a Slinky®. The apparatus will look somewhat like the illustration below if this experiment were to be done in a Japanese teahouse. We will be placing our apparatus on a Western-height bench, with some changes in the indicated components. Power supply Interface

V

mV

Ammeter

Switch

Setup 1. Connect the magnetic field sensor to an analog port of a Vernier LabPro. Set the switch on the sensor to low amplification. 2. Stretch the Slinky until the distance between the coils is large enough to accommodate the magnetic field sensor, as shown in the illustration above. Use masking tape to hold the ends of the Slinky in position.

magfield_1a_rev1.doc  -­‐-­‐  froehlich

3. Connect the power supply (Agilent UA8001A) through a digital ammeter to a slinky, as shown in the diagram. We will not be using a switch in our circuit – the power supply’s output on/off button will serve the same function. 4. Turn on the power supply and adjust it so the current through the circuit is 1.0 A. Once this is established, turn off the current. 5. Download the magnetic field template from www.froehlichsphysics.com. Go to Links à AP Simulation Labs à Vernier Magnetic Field Lab. This file will set up the LabPro to read the magnetic fields we will be generating. The horizontal axis is the time base and should allow about 20 seconds of measurement. The meter window is a live display of magnetic field intensity. Preliminary Investigation 1. Turn on the current and verify that you still have 1.0 A going through the Slinky. Place the magnetic field sensor between the turns of the Slinky near the axial and radial center. Rotate the sensor to change the orientation of the white dot. Note which direction the dot is facing to give the largest reading. Maintain that position and turn off the current. Note the sensor reading. This reading is due to the magnetic field of Earth and any other stray magnetic fields in the vicinity. You can zero the sensor through Logger Pro. 2. Have Beans turn on the juice again. What happens if you rotate the white dot to point in the opposite direction? What happens if the white dot points perpendicularly to the axis of the Slinky? 3. Put the magnetic field sensor through different locations along the Slinky to explore how the field varies along the length. Always point the sensor to read a maximum magnetic field. How does the magnetic field inside the solenoid seem to vary along its length? 4. Check the magnetic field intensity just outside the solenoid. Investigation – Part I 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. 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 that for either the turns or

magfield_1a_rev1.doc  -­‐-­‐  froehlich

the length. Calculate the number of turns per meter of the stretched portion. Record the length, turns, and the number of turns per meter. 2. With the probe in a fixed location, turn on the circuit and adjust the probe to read a maximum. Turn off the current and zero the magnetic field sensor in Logger Pro. This step is necessary to eliminate reading stray magnetic fields. 3. Vary the current and record the magnetic field reading. Feel free to run the current up to the maximum available from the power supply. Collect sufficient data pairs to create a plot of |B| vs I. Determine the significance and value of the slope. Investigation – Part II For the second part of the experiment, you will determine the relationship between the magnetic field in the center of a coil and the number of turns of wire per meter of the solenoid. You will keep the current constant. The sensor will be oriented as it was before, so that it measures the field down the middle of the solenoid. You will be changing the length of the Slinky to change the number of turns per meter (n). It is your challenge to devise a procedure to accomplish this. Once you have collected adequate data, create a plot of |B| vs n. Determine the significance and value of the slope. Analysis Some things to consider: • How is magnetic field related to the current through the solenoid? •

Determine the equation of the best-fit line, including the y-intercept. Note the constants and their units. Put this equation on your graph from Part I.

How is magnetic field related to the turns/unit length of the solenoid?

Determine the equation of the best-fit line to your graph from Part II. Note the constants and their units.

Using Ampere’s law, determine the magnetic field equation for a solenoid. Compare the theoretical solenoid performance to your empirical results. Do your results agree with this equation? Explain.

Assuming the equation in the previous question applies for your solenoid, calculate the value of μ0. Compare your results to the published value through percent error.

Error analysis. Do not forget to include an abstract for your report.

Expansion See if you can form the Slinky into a toroid. Be careful that the coils do not touch each other. Use Ampere’s law to find the relationship of |B| to r. Compare the theoretical to the measured.

magfield_1a_rev1.doc  -­‐-­‐  froehlich