The Magnetic Field in a Slinky

No Prelab ☺

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 µ0, the permeability constant. The permeability constant is a fundamental constant of physics (µ0 = 4 π x 10 –7 Tm/A). The magnetic field in a solenoid is a uniform field that depends only on N, the number of turns; I, the current; and L the length of the solenoid. The relationship is given by B = µ0 I N/L

(1)

To explore the above equation, the experiment takes data in three parts. In part 1, measurements are taken at different locations, holding N, I, and L constant, to show that the field produced inside the coil is uniform. In part 2, N and L and held constant and I is varied. Finally, in part 3, I is held constant and the ratio, N/L, is varied.

Fig. 1

MATERIALS Logger Pro software ammeter Vernier Magnetic Field Sensor Slinky_ push to connect switch

meter stick, clamps DC power supply alligator clips connecting wires

PROCEDURE 1. Connect the Vernier Magnetic Field Sensor to the Logger Pro. Set the switch on the sensor to High. On the computer, find the Logger Pro folder and then open “Physics with Computers” and “ 29 Magnetic Field of a Slinky”. The computer should open a graph that shows Magnetic field in mT on the vertical axis and time on the horizontal axis. (Note: mT = 10-3 T) 2. Stretch the Slinky until it is about 1 m in length. The distance between the coils should be about 1 cm. Use the meter stick clamps and tape to hold the Slinky at this length. 3. Set up the circuit and equipment as shown in Figure 1 above. Wires with clips on one end should be used to connect to the Slinky. 4. Turn on the power supply and adjust it so that the ammeter reads 1.0 A when the switch is held closed. Warning: This lab requires fairly large currents to flow through the wires and Slinky. Only close the switch when you are taking a measurement. The Slinky, wires, and possibly the power supply could get hot if left on continuously. 5. Place the Magnetic Field Sensor between the turns of the Slinky near its center with the white dot on the sensor pointing to the left. Push the zero icon on the computer screen. After the probe has been zeroed, click the collect icon and observe the data collection. The data should be zero, if not, repeat the zeroing procedure. Now close the switch and hold the sensor with white dot to left. Rotate the sensor and hold the sensor so that the white dot is up and then to the right and then down. The graph should have horizontal sections that correspond to the different positions of the white dot. With the mouse select each section, and click the “Statistics” icon. The mean is the average magnetic field. Record the data in the data section. Part 1: How Is The Magnetic Field In A Solenoid varies inside and outside a solenoid?

6. Place the Magnetic Field Sensor at three 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. At each point, record the magnetic field at the center, along the edge closer to you, and along the edge away from you. At each location, check the magnetic field intensity just outside the solenoid.

Part 2: How Is The Magnetic Field In A Solenoid Related To The Current?

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. 7. Place the Magnetic Field Sensor between the turns of the Slinky near its center. Close the switch and rotate the sensor so that the white dot points directly along the long axis of the solenoid. This will be the position for all of the magnetic field measurements for the rest of this lab. (Note: You may have to repeat the zeroing process if the magnetic field is not zero with the switch open.) Click the collect icon to begin data collection. Wait a few seconds and close the switch to turn on the current, hold for a few seconds, and then release the switch. Use the Statistics icon to find the average magnetic field. Record the value in the data table. Repeat the process for 0.8 A, 0.6 A, and so on. 8.

Count the number of turns of the Slinky and measure its length between the clips where the current is connected. If you have any un-stretched 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 and turns in the data table.

9.

Plot the magnetic field B versus the current I. Record the slope in the data table. From the slope, calculate the magnetic permeability, µ 0.

Part 3: How Is The Magnetic Field In A Solenoid Related To The Spacing Of The Turns?

For the third 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. Leave the Slinky set up as shown in Figure 1. The sensor will be oriented as it was before, so that it measures the field along the axis in the middle of the solenoid. You will be changing the length of the Slinky from 0.5 to 2.0 m by stretching it to change the number of turns per meter. 10.

Adjust the power supply so that the current will be 1.0 A when the switch is closed. Click collect icon to begin data collection. Close and hold the switch for a few seconds and then release the button during the data collection. As before, leave the switch closed only during actual data collection. Record N, L, I and B in the data table

11.

Now vary N and L so that the ratio of N/L is different. The number of turns could be kept constant and then the length of the Slinky could be changed to 0.5 m, 1.5 m, and 2.0 m. Each time, zero the Magnetic Field Sensor with the current off. Make sure that the current remains at 1.0A each time you turn it on.

12.

Plot the magnetic field B versus the ratio of N/L. Record the slope in the data table. From the slope, calculate the magnetic permeability, µ 0.

DATA TABLE Magnetic Field versus the orientation of the detector

Orientation of Detector

Magnetic field B (mT)

To the left up To the right down

Part 1: Magnetic field versus the location of detector

Position of Detector

Magnetic field B (mT) center

Inside close

Inside away

outside

Position 1 Position 2 Position 3

Part 2: Magnetic Field Versus the Current in the Solenoid Length of solenoid (m) = ________________ Number of turns = _______________ Current in Solenoid

Magnetic Field (mT)

0.2 A 0.4 A 0.6 A 0.8 A

Slope of B Versus I graph = _____________ µ = ______________________ 0

Percent error = ______________

Part 3: Magnetic Field Versus the ratio of N/L Current in the solenoid = _______________

Number of Turns

Length of Solenoid

Ratio of N/L

Slope of B versus N/L graph = _________________________ µ = ______________________ 0

Percent error = ______________

Magnetic Field