Laboratory #4 Magnetic Field of a Solenoid. The Magnetic Field of a Solenoid

Physics 1051 Laboratory #4 Magnetic Field of a Solenoid The Magnetic Field of a Solenoid Physics 1051 Laboratory #4 Magnetic Field of a Solenoi...
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Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

The Magnetic Field of a Solenoid

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Contents Part I:

Set-Up

Part II: Predictions Part III: Current Dependence Part IV: Turns Per Unit Length Dependence

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Introduction In this lab we will explore the factors that affect the magnetic field inside a solenoid, and how the field varies in different regions of the solenoid. A solenoid is composed of a number of turns of a conducting material, arranged in a cylindrical fashion. A Slinky is a good example of a solenoid. Current passing through the Slinky creates a magnetic field inside the solenoid. Solenoids are commonly used in electronic circuits, and electromagnets.

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Part I: Set-up Connect the Vernier Magnetic Field Sensor to Channel 1 on the LabPro interface. Set the switch on the sensor to LOW.

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Set-up continued… Use the meter stick and silver clamps provided stretch the Slinky so that it is about one metre in length.

Set up the circuit as shown in the figure above. Use alligator clips to connect the Slinky to the power supply, and to help hold it to the meter stick clamps.

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Set-up continued… Turn on the power supply and adjust the settings so that the current in the Slinky is 2.0 A when the switch is closed (power on). This lab requires a fairly large current to flow through the Slinky. Only close the switch when taking measurements. If the switch is left closed for a period of time the apparatus may become extremely HOT! Launch the LoggerPro program by clicking on the icon below.

It should open with an empty graph of Magnetic Field versus Time. The time axis should have a maximum of 60 seconds. If not, double click on the time axis and manually set the limit to 60 seconds. If the data collection stops in less than 60 seconds, the length of the collection may be changed to 60 seconds in the EXPERIMENT | DATA COLLECTION menu.

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Part II: Using the Magnetic Field Sensor Place the Magnetic Field Sensor between the turns of the Slinky near its center. Click the Zero button. Close the switch and click Collect in LoggerPro to begin taking some sample data. Rotate the sensor to determine which direction gives the largest field measurement.

It is important to get used to using the Magnetic Field Sensor before using it in the experiment.

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Using the Magnetic Field Sensor Answer the following questions in your Activity Log.

QUESTION 1: What direction is the white dot on the sensor pointing, relative to the axis of the solenoid, when the largest positive field measurement is registered? QUESTION 2: What happens when you rotate the sensor so that the white dot points the opposite way? QUESTION 3: What happens when you orient the sensor so that the white dot is pointing perpendicular to the axis of the solenoid? QUESTION 4: What is the magnetic field intensity just outside the solenoid?

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

The Field Inside a Solenoid Open the switch and insert the field sensor between the turns of the Slinky near its center. Click the Zero button. This step removes the contributions due to Earth’s magnetic field and magnetism from other sources from your measurements. Insert the magnetic field sensor at different positions along length of the slinky; at the middle, and near the ends. QUESTION 5: Comment on the variation of magnetic field along the length of the solenoid in your Activity Log.

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Part III: Current Dependence In this part of the experiment you will investigate how the magnetic field intensity at the center of the solenoid varies with respect to the current flowing through the solenoid. Remember to leave the switch OPEN, (i.e. power off) when you are not taking measurements. Place the 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, and the field reading is positive. This will be the position for ALL the measurements you will make in this section.

Continued...

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Current Dependence In your LoggerPro window, select the EXPERIMENT | DATA COLLECTION menu to set the limits so that 20 seconds of data collection time is allowed. If necessary, double click the time axis and reset the limit to 20 seconds. Adjust the power supply so that a current of 0.5 A is running through the circuit, then open the switch. Insert the field sensor in its proper position, then click the Zero button. Click Collect to start collecting data. Wait for five seconds, then close the switch to turn on the current. The field should increase to some relatively steady value when you close the switch. If the field decreases when you close the switch, you must reorient your field sensor so that the white dot points in the opposite direction.

Continued...

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Current Dependence: Data Collection Click Collect to take a set of data. After approximately 5 seconds close the switch for about 10 seconds. Your data should look similar to the example. Inspect the Field vs. Time graph, and determine the region for which the current was flowing through the wire. Select this region of the graph by clicking and dragging the mouse over it. (See the next slide for an example). Determine the average field strength and the associated standard deviation by clicking on the Analyze menu, and selecting Statistics. Enter these results in the first row of Table 1 in your Activity Log.

Continued...

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Example of Data Analysis Se le ct D a t a

An a lyze / St a t ist ics

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Current Dependence: Data Collection In LoggerPro select the Experiment menu and click Store Latest Run before collecting the next set of data. This should help you determine if the new field you are measuring is reasonable. Increase the current by 0.5 A, so that around 1.0 A is running through the circuit. Repeat the steps outlined previously, including zeroing the probe, and enter the average field strength and the associated standard deviation for that particular current in Table 1 of your Activity Log. Repeat this part of the procedure for currents of around 1.5 A and 2.0 A, and enter the results in your Activity Log. Measure the length of your Slinky. Enter this value and associated uncertainty in Table 2 of your Activity Log. Print this graph and include it with your Activity Log.

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Current Dependence Sa m p le d a t a f or t w o d if f e r e n t cu r r e n t s

If you r d a t a d oe s n ot r e se m b le t h a t show n h e r e , p le a se consu lt a n in st r u ct or n ow

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Using Ampere’s Law

QUESTION 6: Derive an expression for the slope of a graph of Magnetic Field versus Current in terms of the number of turns in the Slinky, using Ampere’s law for a solenoid as given by Equation 1 in the introduction.

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Graphical Analysis Launch Graphical Analysis by clicking on the icon below.

Use Graphical Analysis to plot Magnetic Field versus Current for your Slinky solenoid. B should be entered in units of T. Calculate and display the regression line for this data set. To do so, pull down the Analyze menu and select Linear Fit. Then double click on the box that appears and in the Standard Deviations section check both the Slope and Intercept. Enter the results in Table 3 of your Activity Log. Print this graph and include it with your Activity Log.

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Analysis The accepted value for the permeability constant is

μo = 4π x 10-7 T m / A

QUESTION 7: Calculate the number of turns in the Slinky using the slope of your Magnetic Field versus Current graph. Be sure to also calculate the associated uncertainty. QUESTION 8: Count the number of turns in your Slinky and reecord the value. Is the result you calculated above consistent with this value? If not, explain why.

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Part IV: Turns Per Unit Length Dependence In this part of the experiment you will investigate how the magnetic field intensity at the center of the solenoid varies with respect to the number of turns per unit length of the solenoid. Use the clamp provided to attach two meter sticks together end-to-end as shown in the picture. Then attach the Slinky clips to each end of your ‘2-metre stick’, and set up your solenoid and circuit again as you did in the first part. Your Slinky should be stretched to almost 2 m in length.

Continued...

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

REMINDER… Sensor Positioning In the middle of the coil, and the midpoint of the length.

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Turns Per Unit Length Dependence In this part of the lab you will be keeping the current in the coil at a constant value. Once you have constructed your circuit, set the power supply to deliver a current of about 1.5 A. Record the actual value of your current in Table 4 of your Activity Log. Count the turns in your Slinky once again. Bunched up turns at the ends do not count. Enter this value in Table 4. Measure the length of your solenoid and calculate the number of turns per unit length. Enter these values in the first row of Table 5 of your Activity Log. With the sensor in position, but the switch OPEN, click Zero to zero the sensor. Since you will be adjusting the metal Slinky for each new set of data in this part of the experiment, the sensor must be zeroed each time before a new set of data is collected.

Continued...

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Turns Per Unit Length Dependence: Data Collection Click Collect to start collecting data. Wait for a 5 seconds, then close the switch to turn on the current. Take data for 10 seconds with the switch closed then open the switch. The field should increase to some relatively steady value when you close the switch. If the field decreases when you close the switch, reorient your field sensor. Inspect the Field vs. Time graph, and determine the region for which the current was flowing through the wire. Select this region of the graph by dragging the mouse over it. Determine the average field strength and the associated standard deviation by clicking on the Analyze menu, and selecting Statistics. Enter these results in Table 5 your Activity Log. In LoggerPro select the Experiment menu and click Store Latest Run before collecting the next set of data.

Continued...

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Turns Per Unit Length Dependence: Data Collection Reduce the length of the Slinky so that it is about 1.50 m long. Measure the length and calculate the number of turns per unit length. Enter these in Table 5 of your Activity Log. Re-zero your sensor and collect a set of data as per the prescribed technique. Enter the results in Table 5 of your Activity Log Repeat the procedure outlined for reducing the length, zeroing the sensor, and taking data, for lengths of approximately 1m and 0.5 m. Do not forget to accurately measure and record the length each time. QUESTION 9: Predict the slope of a plot of Magnetic Field vs Turns per Unit Length. [Use the value recorded in Table 4 for the current and the accepted value for the permeability constant.]

Continued...

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Graphical Analysis Launch Graphical Analysis again (re-open your current file or click the icon below)

Use it to plot Magnetic Field versus Turns per unit Length for your Slinky solenoid. Calculate and display the regression line for this data set. To do so, pull down the Analyze menu and select Linear Fit. Then double click on the box that appears and in the Standard Deviations section check both the Slope and Intercept. Record the slope and intercept (and uncertainties) in Table 6 of your Activity Log. Print this graph and include it with your Activity Log. QUESTION 10: Compare your predicted and actual slopes. If they are not equal within the uncertainties, explain why.

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Summary Questions 1.

Based on your experimental results, which of the following best describes the relationship between magnetic field at the center of the solenoid and current in the solenoid? Justify your answer. A.

B∝i

B. B ∝ i2

C. B ∝ 1/ i

D. B = constant

2.

Based on your experimental results, which of the following best describes the relationship between magnetic field at the center of the solenoid and length of the solenoid (for a fixed number of turns)? Justify your answer. A. B ∝ L B. B ∝ L2 C. B ∝ 1 / L D. B = constant

3.

Combining your answers to the last two questions, which choice best describes the relationship between the magnetic field at the center of the solenoid, the current in the solenoid, and the length of the solenoid? Justify your answer. A. B ∝ i + L B. B ∝ i L2 C. B ∝ i / L D. B = constant

4.

List the sources of error in this experiment as classify each as reandom or systematic.

Physics 1051

Laboratory #4

Magnetic Field of a Solenoid

Wrap it up! Check that you have completed all the Tables of your Activity Log.

Make sure that you have answered all the Questions completely, including the Summary Questions.

Attached to your Activity Log should be the following graphs: – Magnetic Field versus Current (Graphical Analysis) – Magnetic Field versus Turns per unit Length (Graphical Analysis) – Magnetic Field versus Current (LoggerPro)