PHY 213: General Physics IIIpage1 of 5

PCC-Cascade

Experiment:The Magnetic Fields due to Electric Currents

Objectives

  • Determine the relationship between magnetic field and the current in a current carrying wire
  • Determine the relationship between magnetic field, the current and the number of turns per meter in a solenoid.
  • Observe how the field varies inside and outside a solenoid.
  • Determine the value of o, the permeability constant.

Materials

  • LabPro interface
/
  • meter stick

  • Logger Prosoftware
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  • DC power supply

  • Exposed copper wire
/
  • Ammeter

  • Magnetic Field Sensor
/
  • cardboard spacers

  • Slinky
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  • connecting wires

  • switch
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  • tape and cardboard

  • straight copper wire
/
  • compass

Introduction

When current flows through a wire, a magnetic field is generated due to the moving charge. Clearly the magnitude of the magnetic field depends on the size of the current and the distance away from the wire. According to Ampere’s Law, the magnitude of magnetic field vector is described by:

The direction of B “curls” around the length of the wire according to the right-hand rule.

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. The magnitude of magnetic field vector within the solenoid is described by:

In this lab the direction of the magnetic field outside a current-carrying wire will be observed. In addition, the factors that affect the magnetic field inside a solenoid will be explored using a compass and a magnetic field sensor. Lastly, you will also measure o, the permeability constant using a solenoid. The permeability constant is a fundamental constant of physics.

Figure 1

Part I: A Current-Carrying Wire

Part A: How is the Magnetic Field in a Wire Related to the Current?

  1. Set-up the circuit shown above in Figure 1.

Warning: This lab requires fairly large currents to flow through the wires. Only connect the circuit so the current flows when you are taking measurements. The wires and possibly the power supply may get hot if left on continuously.

  1. Probe the region around the wire using a compass.
  2. Sketch the direction of the magnetic field:

Part 2: The Slinky as a solenoid

Figure 2

1.Connect the Vernier Magnetic Field Sensor to theLabPro interface. Set the switch on the sensor to High.

2.Stretch the Slinky until it is about 1 m in length. 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 2. Wires with clips on the end should be used to connect to the Slinky.

4.Turn on the power supply and adjust it so that the ammeter reads 2.0 A when the switch is held closed.

5.Using a compass, sketch out the direction of the magnetic field associated with the solenoid.

6.Disconnect the circuit.

7.Open the file, “Exp 29” from the Physics with Computers experiment files.

Part A:Relation of Field in a Solenoid to Current (constant length)

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 of the sensor for all of the magnetic field measurements during the rest of this lab.

3.Click to begin data collection. Wait a few seconds and close the switch to turn on the current.

4.If the magnetic field increases when the switch is closed, you are ready to take data. If the field decreases when you close the switch, rotate the Magnetic Field Sensor so that it points the other direction down the solenoid.

5.With the switch open, zero the sensor to remove readings due to the Earth’s magnetic field, any magnetism in the metal of the Slinky, the table, etc.

6.Adjust the power supply so that 0.5 A will flow through the coil when the switch is closed.

7.Collect measurements forat least 10 seconds with the switch closed.

8.Observe the B-Field vs. Time graph. Use LoggerPro to determine the average field strength while the current was on. Record the value and uncertainty in the data table.

9.Increase the current by 0.5 A then repeat Steps 7 and 8.

10.Repeat Step 9 up to a maximum of 2.0 A.

11.Count the # of turns of the Slinky and measure its length. Do not include un-stretched end regions of the Slinky in the measurements. Calculate the # turns per meter (n) of the stretched portion. Record values.

Part B:Relation of the Field in a Solenoid to the Turn Spacing (constant current)

1.Adjust the power supply so that the current will be 1.5 A when the switch is closed.

2.Zero field sensor with no current. Since the Slinky is made of an iron alloy, it can be magnetized itself. Moving the Slinky around can cause a change in the field, even if no current is flowing. This means you will need to zero the reading each time you move or adjust the Slinky.

3.Begin data collection then close the switch. Collect measurements for about 10 seconds of current flow.

4.Calculate the average field value while the current was on using LoggerPro. Record the length of the Slinky and the average field in the data table.

5.Repeat Steps 2 – 4for Slinky lengthsof 0.5 m, 1.5 m, and 2.0 m. Note: Be sure to zero the Magnetic Field Sensor with the current off before each trial and make sure the current remains at 1.5 A.

Data Table

Part A

isolenoid, in A / Bavg / ±B
0.5
1.0
1.5
2.0
Length of solenoid (m)
Number of turns
Turns/meter, n (m–1)

Part B

Length of solenoid / n
(turns/meter) / Bavg / ±B
Number of turns in Slinky

Analysis

1.Using Graphical Analysis, create a graph of B vs. iusing data from Part 2A.

2.How is B related to i?

3.Fit the graph to the most appropriate equation and record the coefficient values (and uncertainty) and units, including the y-intercept.

4.Use your graph of B vs. i, to calculate the value of o, including uncertainty.

5.For each of the measurements for Part 2B, calculate the # of turns per meter. Enter values in the data table.

6.Using Graphical Analysis, plot a graph of B vs. n.

7.How is B related to n?

8.Fit the graph to the most appropriate equation and record the coefficient values (and uncertainty) and units, including the y-intercept.

9.Do your results agree with the prediction for Ampere’s Law? Explain.

10.Use your graph of B vs. n,to calculate the value of o, including uncertainty.

11.Look up the value of o. Calculate the % Error between your average measured value for o and the accepted value.

12.Was your Slinky positioned along an east-west, north-south, or on some other axis? Should this have any effect on your readings?